Pub Date : 2022-01-24DOI: 10.1186/s13663-022-00714-x
Paoli, Laetitia
We consider an unsteady non-isothermal flow problem for a general class of non-Newtonian fluids. More precisely the stress tensor follows a power law of parameter p, namely $sigma = 2 mu ( theta , upsilon , | D(upsilon ) |) |D( upsilon ) |^{p-2} D(upsilon ) - pi mathrm{Id}$ where θ is the temperature, π is the pressure, υ is the velocity, and $D(upsilon )$ is the strain rate tensor of the fluid. The problem is then described by a non-stationary p-Laplacian Stokes system coupled to an $L^{1}$ -parabolic equation describing thermal effects in the fluid. We also assume that the velocity field satisfies non-standard threshold slip-adhesion boundary conditions reminiscent of Tresca’s friction law for solids. First, we consider an approximate problem $(P_{delta })$ , where the $L^{1}$ coupling term in the heat equation is replaced by a bounded one depending on a small parameter $0 < delta ll 1$ , and we establish the existence of a solution to $(P_{delta })$ by using a fixed point technique. Then we prove the convergence of the approximate solutions to a solution to our original fluid flow/heat transfer problem as δ tends to zero.
{"title":"Unsteady non-Newtonian fluid flow with heat transfer and Tresca’s friction boundary conditions","authors":"Paoli, Laetitia","doi":"10.1186/s13663-022-00714-x","DOIUrl":"https://doi.org/10.1186/s13663-022-00714-x","url":null,"abstract":"We consider an unsteady non-isothermal flow problem for a general class of non-Newtonian fluids. More precisely the stress tensor follows a power law of parameter p, namely $sigma = 2 mu ( theta , upsilon , | D(upsilon ) |) |D( upsilon ) |^{p-2} D(upsilon ) - pi mathrm{Id}$ where θ is the temperature, π is the pressure, υ is the velocity, and $D(upsilon )$ is the strain rate tensor of the fluid. The problem is then described by a non-stationary p-Laplacian Stokes system coupled to an $L^{1}$ -parabolic equation describing thermal effects in the fluid. We also assume that the velocity field satisfies non-standard threshold slip-adhesion boundary conditions reminiscent of Tresca’s friction law for solids. First, we consider an approximate problem $(P_{delta })$ , where the $L^{1}$ coupling term in the heat equation is replaced by a bounded one depending on a small parameter $0 < delta ll 1$ , and we establish the existence of a solution to $(P_{delta })$ by using a fixed point technique. Then we prove the convergence of the approximate solutions to a solution to our original fluid flow/heat transfer problem as δ tends to zero.","PeriodicalId":12293,"journal":{"name":"Fixed Point Theory and Applications","volume":"13 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138532708","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper is devoted to numerical analysis of doubly-history dependent variational inequalities in contact mechanics. A fully discrete method is introduced for the variational inequalities, in which the doubly-history dependent operator is approximated by repeated left endpoint rule and the spatial variable is approximated by the linear element method. An optimal order error estimate is derived under appropriate solution regularities, and numerical examples illustrate the convergence orders of the method.
{"title":"Numerical analysis of doubly-history dependent variational inequalities in contact mechanics","authors":"Xu, Wei, Wang, Cheng, He, Mingyan, Chen, Wenbin, Han, Weimin, Huang, Ziping","doi":"10.1186/s13663-021-00710-7","DOIUrl":"https://doi.org/10.1186/s13663-021-00710-7","url":null,"abstract":"This paper is devoted to numerical analysis of doubly-history dependent variational inequalities in contact mechanics. A fully discrete method is introduced for the variational inequalities, in which the doubly-history dependent operator is approximated by repeated left endpoint rule and the spatial variable is approximated by the linear element method. An optimal order error estimate is derived under appropriate solution regularities, and numerical examples illustrate the convergence orders of the method.","PeriodicalId":12293,"journal":{"name":"Fixed Point Theory and Applications","volume":"53 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138532714","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-15DOI: 10.1186/s13663-021-00705-4
Flåm, Sjur Didrik
By the first welfare theorem, competitive market equilibria belong to the core and hence are Pareto optimal. Letting money be a commodity, this paper turns these two inclusions around. More precisely, by generalizing the second welfare theorem we show that the said solutions may coincide as a common fixed point for one and the same system. Mathematical arguments invoke conjugation, convolution, and generalized gradients. Convexity is merely needed via subdifferentiablity of aggregate “cost”, and at one point only. Economic arguments hinge on idealized market mechanisms. Construed as algorithms, each stops, and a steady state prevails if and only if price-taking markets clear and value added is nil.
{"title":"Market equilibria and money","authors":"Flåm, Sjur Didrik","doi":"10.1186/s13663-021-00705-4","DOIUrl":"https://doi.org/10.1186/s13663-021-00705-4","url":null,"abstract":"By the first welfare theorem, competitive market equilibria belong to the core and hence are Pareto optimal. Letting money be a commodity, this paper turns these two inclusions around. More precisely, by generalizing the second welfare theorem we show that the said solutions may coincide as a common fixed point for one and the same system. Mathematical arguments invoke conjugation, convolution, and generalized gradients. Convexity is merely needed via subdifferentiablity of aggregate “cost”, and at one point only. Economic arguments hinge on idealized market mechanisms. Construed as algorithms, each stops, and a steady state prevails if and only if price-taking markets clear and value added is nil.","PeriodicalId":12293,"journal":{"name":"Fixed Point Theory and Applications","volume":"16 6 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138532707","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-18DOI: 10.1186/s13663-021-00702-7
Adly, Samir, Attouch, Hedy, Vo, Van Nam
In a Hilbert space $mathcal{H}$ , we study a dynamic inertial Newton method which aims to solve additively structured monotone equations involving the sum of potential and nonpotential terms. Precisely, we are looking for the zeros of an operator $A= nabla f +B $ , where ∇f is the gradient of a continuously differentiable convex function f and B is a nonpotential monotone and cocoercive operator. Besides a viscous friction term, the dynamic involves geometric damping terms which are controlled respectively by the Hessian of the potential f and by a Newton-type correction term attached to B. Based on a fixed point argument, we show the well-posedness of the Cauchy problem. Then we show the weak convergence as $tto +infty $ of the generated trajectories towards the zeros of $nabla f +B$ . The convergence analysis is based on the appropriate setting of the viscous and geometric damping parameters. The introduction of these geometric dampings makes it possible to control and attenuate the known oscillations for the viscous damping of inertial methods. Rewriting the second-order evolution equation as a first-order dynamical system enables us to extend the convergence analysis to nonsmooth convex potentials. These results open the door to the design of new first-order accelerated algorithms in optimization taking into account the specific properties of potential and nonpotential terms. The proofs and techniques are original and differ from the classical ones due to the presence of the nonpotential term.
在Hilbert空间$mathcal{H}$中，我们研究了一种动态惯性牛顿法，其目的是求解包含势项和非势项和的加性结构单调方程。确切地说，我们正在寻找一个算子$A= nabla f +B $的零点，其中∇f是一个连续可微凸函数f的梯度，而B是一个非势单调和coercive算子。除了粘性摩擦项外，动力学还涉及几何阻尼项，它们分别由势f的Hessian和附加在b上的牛顿型修正项控制。基于不动点论证，我们证明了柯西问题的适定性。然后我们将生成的轨迹向$nabla f +B$零点的弱收敛性表示为$tto +infty $。收敛分析是建立在适当设置粘性和几何阻尼参数的基础上的。这些几何阻尼的引入使得控制和衰减已知的惯性方法的粘性阻尼振荡成为可能。将二阶演化方程改写为一阶动力系统，使我们能够将收敛分析扩展到非光滑凸势。这些结果为考虑势项和非势项的特定性质的一阶优化加速算法的设计打开了大门。由于非势项的存在，证明和技术是原创的，与经典的证明和技术不同。
{"title":"Asymptotic behavior of Newton-like inertial dynamics involving the sum of potential and nonpotential terms","authors":"Adly, Samir, Attouch, Hedy, Vo, Van Nam","doi":"10.1186/s13663-021-00702-7","DOIUrl":"https://doi.org/10.1186/s13663-021-00702-7","url":null,"abstract":"In a Hilbert space $mathcal{H}$ , we study a dynamic inertial Newton method which aims to solve additively structured monotone equations involving the sum of potential and nonpotential terms. Precisely, we are looking for the zeros of an operator $A= nabla f +B $ , where ∇f is the gradient of a continuously differentiable convex function f and B is a nonpotential monotone and cocoercive operator. Besides a viscous friction term, the dynamic involves geometric damping terms which are controlled respectively by the Hessian of the potential f and by a Newton-type correction term attached to B. Based on a fixed point argument, we show the well-posedness of the Cauchy problem. Then we show the weak convergence as $tto +infty $ of the generated trajectories towards the zeros of $nabla f +B$ . The convergence analysis is based on the appropriate setting of the viscous and geometric damping parameters. The introduction of these geometric dampings makes it possible to control and attenuate the known oscillations for the viscous damping of inertial methods. Rewriting the second-order evolution equation as a first-order dynamical system enables us to extend the convergence analysis to nonsmooth convex potentials. These results open the door to the design of new first-order accelerated algorithms in optimization taking into account the specific properties of potential and nonpotential terms. The proofs and techniques are original and differ from the classical ones due to the presence of the nonpotential term.","PeriodicalId":12293,"journal":{"name":"Fixed Point Theory and Applications","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138532701","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-04DOI: 10.1186/s13663-021-00701-8
Dao, Minh N., Phan, Hung M.
Splitting algorithms for finding a zero of sum of operators often involve multiple steps which are referred to as forward or backward steps. Forward steps are the explicit use of the operators and backward steps involve the operators implicitly via their resolvents. In this paper, we study an adaptive splitting algorithm for finding a zero of the sum of three operators. We assume that two of the operators are generalized monotone and their resolvents are computable, while the other operator is cocoercive but its resolvent is missing or costly to compute. Our splitting algorithm adapts new parameters to the generalized monotonicity of the operators and, at the same time, combines appropriate forward and backward steps to guarantee convergence to a solution of the problem.
{"title":"An adaptive splitting algorithm for the sum of two generalized monotone operators and one cocoercive operator","authors":"Dao, Minh N., Phan, Hung M.","doi":"10.1186/s13663-021-00701-8","DOIUrl":"https://doi.org/10.1186/s13663-021-00701-8","url":null,"abstract":"Splitting algorithms for finding a zero of sum of operators often involve multiple steps which are referred to as forward or backward steps. Forward steps are the explicit use of the operators and backward steps involve the operators implicitly via their resolvents. In this paper, we study an adaptive splitting algorithm for finding a zero of the sum of three operators. We assume that two of the operators are generalized monotone and their resolvents are computable, while the other operator is cocoercive but its resolvent is missing or costly to compute. Our splitting algorithm adapts new parameters to the generalized monotonicity of the operators and, at the same time, combines appropriate forward and backward steps to guarantee convergence to a solution of the problem.","PeriodicalId":12293,"journal":{"name":"Fixed Point Theory and Applications","volume":"40 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138532713","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-09-20DOI: 10.1186/s13663-021-00700-9
Burachik, Regina S., Caldwell, Bethany I., Kaya, C. Yalçın
It is well known that the Newton method may not converge when the initial guess does not belong to a specific quadratic convergence region. We propose a family of new variants of the Newton method with the potential advantage of having a larger convergence region as well as more desirable properties near a solution. We prove quadratic convergence of the new family, and provide specific bounds for the asymptotic error constant. We illustrate the advantages of the new methods by means of test problems, including two and six variable polynomial systems, as well as a challenging signal processing example. We present a numerical experimental methodology which uses a large number of randomized initial guesses for a number of methods from the new family, in turn providing advice as to which of the methods employed is preferable to use in a particular search domain.
{"title":"A generalized multivariable Newton method","authors":"Burachik, Regina S., Caldwell, Bethany I., Kaya, C. Yalçın","doi":"10.1186/s13663-021-00700-9","DOIUrl":"https://doi.org/10.1186/s13663-021-00700-9","url":null,"abstract":"It is well known that the Newton method may not converge when the initial guess does not belong to a specific quadratic convergence region. We propose a family of new variants of the Newton method with the potential advantage of having a larger convergence region as well as more desirable properties near a solution. We prove quadratic convergence of the new family, and provide specific bounds for the asymptotic error constant. We illustrate the advantages of the new methods by means of test problems, including two and six variable polynomial systems, as well as a challenging signal processing example. We present a numerical experimental methodology which uses a large number of randomized initial guesses for a number of methods from the new family, in turn providing advice as to which of the methods employed is preferable to use in a particular search domain.","PeriodicalId":12293,"journal":{"name":"Fixed Point Theory and Applications","volume":"10 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138532710","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-09-06DOI: 10.1186/s13663-021-00699-z
Abbasi, Malek, Théra, Michel
In this paper, we use a robust lower directional derivative and provide some sufficient conditions to ensure the strong regularity of a given mapping at a certain point. Then, we discuss the Hoffman estimation and achieve some results for the estimate of the distance to the set of solutions to a system of linear equalities. The advantage of our estimate is that it allows one to calculate the coefficient of the error bound.
{"title":"Strongly regular points of mappings","authors":"Abbasi, Malek, Théra, Michel","doi":"10.1186/s13663-021-00699-z","DOIUrl":"https://doi.org/10.1186/s13663-021-00699-z","url":null,"abstract":"In this paper, we use a robust lower directional derivative and provide some sufficient conditions to ensure the strong regularity of a given mapping at a certain point. Then, we discuss the Hoffman estimation and achieve some results for the estimate of the distance to the set of solutions to a system of linear equalities. The advantage of our estimate is that it allows one to calculate the coefficient of the error bound.","PeriodicalId":12293,"journal":{"name":"Fixed Point Theory and Applications","volume":"76 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138532712","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-08-24DOI: 10.1186/s13663-021-00698-0
Lauster, Florian, Luke, D. Russell
In the setting of $operatorname{CAT}(kappa)$ spaces, common fixed point iterations built from prox mappings (e.g. prox-prox, Krasnoselsky–Mann relaxations, nonlinear projected-gradients) converge locally linearly under the assumption of linear metric subregularity. Linear metric subregularity is in any case necessary for linearly convergent fixed point sequences, so the result is tight. To show this, we develop a theory of fixed point mappings that violate the usual assumptions of nonexpansiveness and firm nonexpansiveness in p-uniformly convex spaces.
{"title":"Convergence of proximal splitting algorithms in (operatorname{CAT}(kappa)) spaces and beyond","authors":"Lauster, Florian, Luke, D. Russell","doi":"10.1186/s13663-021-00698-0","DOIUrl":"https://doi.org/10.1186/s13663-021-00698-0","url":null,"abstract":"In the setting of $operatorname{CAT}(kappa)$ spaces, common fixed point iterations built from prox mappings (e.g. prox-prox, Krasnoselsky–Mann relaxations, nonlinear projected-gradients) converge locally linearly under the assumption of linear metric subregularity. Linear metric subregularity is in any case necessary for linearly convergent fixed point sequences, so the result is tight. To show this, we develop a theory of fixed point mappings that violate the usual assumptions of nonexpansiveness and firm nonexpansiveness in p-uniformly convex spaces.","PeriodicalId":12293,"journal":{"name":"Fixed Point Theory and Applications","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138532711","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-07-26DOI: 10.1186/s13663-021-00697-1
Veit Elser
We explore a new approach for training neural networks where all loss functions are replaced by hard constraints. The same approach is very successful in phase retrieval, where signals are reconstructed from magnitude constraints and general characteristics (sparsity, support, etc.). Instead of taking gradient steps, the optimizer in the constraint based approach, called relaxed–reflect–reflect (RRR), derives its steps from projections to local constraints. In neural networks one such projection makes the minimal modification to the inputs x, the associated weights w, and the pre-activation value y at each neuron, to satisfy the equation $xcdot w=y$ . These projections, along with a host of other local projections (constraining pre- and post-activations, etc.) can be partitioned into two sets such that all the projections in each set can be applied concurrently—across the network and across all data in the training batch. This partitioning into two sets is analogous to the situation in phase retrieval and the setting for which the general purpose RRR optimizer was designed. Owing to the novelty of the method, this paper also serves as a self-contained tutorial. Starting with a single-layer network that performs nonnegative matrix factorization, and concluding with a generative model comprising an autoencoder and classifier, all applications and their implementations by projections are described in complete detail. Although the new approach has the potential to extend the scope of neural networks (e.g. by defining activation not through functions but constraint sets), most of the featured models are standard to allow comparison with stochastic gradient descent.
{"title":"Learning without loss","authors":"Veit Elser","doi":"10.1186/s13663-021-00697-1","DOIUrl":"https://doi.org/10.1186/s13663-021-00697-1","url":null,"abstract":"We explore a new approach for training neural networks where all loss functions are replaced by hard constraints. The same approach is very successful in phase retrieval, where signals are reconstructed from magnitude constraints and general characteristics (sparsity, support, etc.). Instead of taking gradient steps, the optimizer in the constraint based approach, called relaxed–reflect–reflect (RRR), derives its steps from projections to local constraints. In neural networks one such projection makes the minimal modification to the inputs x, the associated weights w, and the pre-activation value y at each neuron, to satisfy the equation $xcdot w=y$ . These projections, along with a host of other local projections (constraining pre- and post-activations, etc.) can be partitioned into two sets such that all the projections in each set can be applied concurrently—across the network and across all data in the training batch. This partitioning into two sets is analogous to the situation in phase retrieval and the setting for which the general purpose RRR optimizer was designed. Owing to the novelty of the method, this paper also serves as a self-contained tutorial. Starting with a single-layer network that performs nonnegative matrix factorization, and concluding with a generative model comprising an autoencoder and classifier, all applications and their implementations by projections are described in complete detail. Although the new approach has the potential to extend the scope of neural networks (e.g. by defining activation not through functions but constraint sets), most of the featured models are standard to allow comparison with stochastic gradient descent.","PeriodicalId":12293,"journal":{"name":"Fixed Point Theory and Applications","volume":"58 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138532702","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-03-29DOI: 10.1186/s13663-021-00691-7
A. U. Bello, M. T. Omojola, J. Yahaya
Let H be a real Hilbert space. Let $F:Hrightarrow 2^{H}$ and $K:Hrightarrow 2^{H}$ be two maximal monotone and bounded operators. Suppose the Hammerstein inclusion $0in u+KFu$ has a solution. We construct an inertial-type algorithm and show its strong convergence to a solution of the inclusion. As far as we know, this is the first inertial-type algorithm for Hammerstein inclusions in Hilbert spaces. We also give numerical examples to compare the new algorithm with some existing ones in the literature.
{"title":"An inertial-type algorithm for approximation of solutions of Hammerstein integral inclusions in Hilbert spaces","authors":"A. U. Bello, M. T. Omojola, J. Yahaya","doi":"10.1186/s13663-021-00691-7","DOIUrl":"https://doi.org/10.1186/s13663-021-00691-7","url":null,"abstract":"Let H be a real Hilbert space. Let $F:Hrightarrow 2^{H}$ and $K:Hrightarrow 2^{H}$ be two maximal monotone and bounded operators. Suppose the Hammerstein inclusion $0in u+KFu$ has a solution. We construct an inertial-type algorithm and show its strong convergence to a solution of the inclusion. As far as we know, this is the first inertial-type algorithm for Hammerstein inclusions in Hilbert spaces. We also give numerical examples to compare the new algorithm with some existing ones in the literature.","PeriodicalId":12293,"journal":{"name":"Fixed Point Theory and Applications","volume":"27 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140885891","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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