. In this paper, we consider a fully discrete approximation scheme for nonlinear fractional parabolic equations. The main aim of this paper is to investigate the convergence and superconvergence of interpolated coefficient finite element solutions. Some numerical examples are presented to demonstrate our theoretical results.
{"title":"Error analysis of interpolated coefficient finite elements for nonlinear fractional parabolic equations","authors":"Yuelong Tang, Y. Hua, Y. Tang, Y. Hua","doi":"10.23952/jnfa.2021.20","DOIUrl":"https://doi.org/10.23952/jnfa.2021.20","url":null,"abstract":". In this paper, we consider a fully discrete approximation scheme for nonlinear fractional parabolic equations. The main aim of this paper is to investigate the convergence and superconvergence of interpolated coefficient finite element solutions. Some numerical examples are presented to demonstrate our theoretical results.","PeriodicalId":44514,"journal":{"name":"Journal of Nonlinear Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68778002","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}
. In this paper, we study a fractional viscoelastic equation of Kirchhoff type with logarithmic nonlinearity. Under suitable conditions, we prove the existence of global solutions and the exponential decay of the energy.
{"title":"Fractional viscoelastic equation of Kirchhoff type with logarithmic nonlinearity","authors":"Eugenio Cabanillas","doi":"10.23952/jnfa.2021.6","DOIUrl":"https://doi.org/10.23952/jnfa.2021.6","url":null,"abstract":". In this paper, we study a fractional viscoelastic equation of Kirchhoff type with logarithmic nonlinearity. Under suitable conditions, we prove the existence of global solutions and the exponential decay of the energy.","PeriodicalId":44514,"journal":{"name":"Journal of Nonlinear Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68778072","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}
. The aim of this paper is to present new fixed point theorems for Chandrabhan type multimaps on abstract convex uniform spaces. We obtain fixed point theorems for various Chandrabhan type multimaps such as upper semicontinuous or closed maps in Hausdorff KKM uniform spaces, and the maps whose ranges are Φ -sets. We also obtain fixed point theorems in hyperconvex metric spaces.
{"title":"Fixed point theorems for Chandrabhan type maps in abstract convex uniform spaces","authors":"Hoonjoo Kim, H. Kim","doi":"10.23952/jnfa.2021.17","DOIUrl":"https://doi.org/10.23952/jnfa.2021.17","url":null,"abstract":". The aim of this paper is to present new fixed point theorems for Chandrabhan type multimaps on abstract convex uniform spaces. We obtain fixed point theorems for various Chandrabhan type multimaps such as upper semicontinuous or closed maps in Hausdorff KKM uniform spaces, and the maps whose ranges are Φ -sets. We also obtain fixed point theorems in hyperconvex metric spaces.","PeriodicalId":44514,"journal":{"name":"Journal of Nonlinear Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68777945","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}
In this paper, we introduce a new relaxed projection onto the level sets of the convex functions. We propose new relaxed projection methods by applying the proposed relaxed projection to solve split feasibility problems and split equality problems. The weak convergence of the relaxed projection methods is established. A preliminary numerical experiment is presented to support the new relaxed projection.
{"title":"A new relaxed projection and its applications","authors":"Q. Dong, KE S.H., HE S., X. Qin","doi":"10.23952/jnfa.2021.19","DOIUrl":"https://doi.org/10.23952/jnfa.2021.19","url":null,"abstract":"In this paper, we introduce a new relaxed projection onto the level sets of the convex functions. We propose new relaxed projection methods by applying the proposed relaxed projection to solve split feasibility problems and split equality problems. The weak convergence of the relaxed projection methods is established. A preliminary numerical experiment is presented to support the new relaxed projection.","PeriodicalId":44514,"journal":{"name":"Journal of Nonlinear Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68777979","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}
. In this paper, we investigate the existence of a weak solution of a fractional Kirchhoff type problem driven by a nonlocal operator of elliptic type in a fractional Orlicz-Sobolev space with homogeneous Dirichlet boundary conditions. The approach is based on the mountain pass theorem and some variational methods.
{"title":"Mountain pass type solutions for a nonlacal fractional a(.)-Kirchhoff type problems","authors":"A. Benkirane, M. Srati","doi":"10.23952/jnfa.2021.3","DOIUrl":"https://doi.org/10.23952/jnfa.2021.3","url":null,"abstract":". In this paper, we investigate the existence of a weak solution of a fractional Kirchhoff type problem driven by a nonlocal operator of elliptic type in a fractional Orlicz-Sobolev space with homogeneous Dirichlet boundary conditions. The approach is based on the mountain pass theorem and some variational methods.","PeriodicalId":44514,"journal":{"name":"Journal of Nonlinear Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68778012","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}
We construct a class of metric spaces Xω+k whose transfinite asymptotic dimension and complementary-finite asymptotic dimension are both ω+k for any k ∈N, where ω is the smallest infinite ordinal number and a metric space Y2ω whose transfinite asymptotic dimension and complementary-finite asymptotic dimension are both 2ω . Finally, we introduce a geometric property called decomposition dimension (decodim). Using decomposition dimension, we prove that the metric spaces Xω+k and Y2ω have finite decomposition complexity.
{"title":"Metric spaces with asymptotic property C and finite decomposition complexity","authors":"Jingming Zhu, WU Yan, J. Zhu, WU Y.","doi":"10.23952/jnfa.2021.15","DOIUrl":"https://doi.org/10.23952/jnfa.2021.15","url":null,"abstract":"We construct a class of metric spaces Xω+k whose transfinite asymptotic dimension and complementary-finite asymptotic dimension are both ω+k for any k ∈N, where ω is the smallest infinite ordinal number and a metric space Y2ω whose transfinite asymptotic dimension and complementary-finite asymptotic dimension are both 2ω . Finally, we introduce a geometric property called decomposition dimension (decodim). Using decomposition dimension, we prove that the metric spaces Xω+k and Y2ω have finite decomposition complexity.","PeriodicalId":44514,"journal":{"name":"Journal of Nonlinear Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68777880","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}
{"title":"Robust optimality and duality for minimax fractional programming problems with support functions","authors":"","doi":"10.23952/jnfa.2021.5","DOIUrl":"https://doi.org/10.23952/jnfa.2021.5","url":null,"abstract":"","PeriodicalId":44514,"journal":{"name":"Journal of Nonlinear Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68778059","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 presents Fritz John necessary conditions for the weak efficiency of multiobjective fractional optimization problems involving equality, inequality and set constraints. With a constraint qualification of Mangasarian–Fromovitz type, Kuhn–Tucker necessary efficiency conditions are established. Under assumptions on generalized convexity, sufficient conditions for weak efficiency are also given together with the theorems of the weak duality, the strong duality, and the inverse duality of Wolfe and Mond–Weir types.
{"title":"Optimality and duality for nonsmooth multiobjective fractional problems using convexificators","authors":"D. Luu, P. T. Linh","doi":"10.23952/jnfa.2021.1","DOIUrl":"https://doi.org/10.23952/jnfa.2021.1","url":null,"abstract":". This paper presents Fritz John necessary conditions for the weak efficiency of multiobjective fractional optimization problems involving equality, inequality and set constraints. With a constraint qualification of Mangasarian–Fromovitz type, Kuhn–Tucker necessary efficiency conditions are established. Under assumptions on generalized convexity, sufficient conditions for weak efficiency are also given together with the theorems of the weak duality, the strong duality, and the inverse duality of Wolfe and Mond–Weir types.","PeriodicalId":44514,"journal":{"name":"Journal of Nonlinear Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68778241","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}
M. A. Olona, T. O. Alakoya, .-E. Owolabi, O. Mewomo
. In this paper, we study the problem of finding common solutions of equilibrium problems, variational inclusion problems and fixed point problems for an infinite family of strict pseudocontractive mappings. We propose an iterative algorithm, which combines inertial methods with viscosity methods, for approximating common solutions of the above problems. Under mild conditions, we prove a strong theorem in Hilbert spaces and apply our result to optimization problems. Finally, we present a numerical example to demonstrate the efficiency of our algorithm in comparison with other existing methods in the literature
{"title":"Inertial algorithm for solving equilibrium, variational inclusion and fixed point problems for an infinite family of strict pseudocontractive mappings","authors":"M. A. Olona, T. O. Alakoya, .-E. Owolabi, O. Mewomo","doi":"10.23952/jnfa.2021.10","DOIUrl":"https://doi.org/10.23952/jnfa.2021.10","url":null,"abstract":". In this paper, we study the problem of finding common solutions of equilibrium problems, variational inclusion problems and fixed point problems for an infinite family of strict pseudocontractive mappings. We propose an iterative algorithm, which combines inertial methods with viscosity methods, for approximating common solutions of the above problems. Under mild conditions, we prove a strong theorem in Hilbert spaces and apply our result to optimization problems. Finally, we present a numerical example to demonstrate the efficiency of our algorithm in comparison with other existing methods in the literature","PeriodicalId":44514,"journal":{"name":"Journal of Nonlinear Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68778253","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 : 2020-02-28DOI: 10.22541/au.158291222.23595484
B. Sang, Rizgar H. Salih, Ning Wang
The purpose of this paper is to propose some coefficient conditions, characterizing the stability of periodic solutions bifurcated from zero-Hopf bifurcations of the general quadratic jerk system, and apply these theoretical results to a special jerk system in order to predict chaos. First, we characterize the zero-Hopf bifurcations of the general quadratic jerk system in $mathbb{R}^3$. The coefficient conditions on stability of periodic solutions are obtained via the averaging theory of first order. Next, we apply the theoretical results to a two-parameter jerk system. Finally special attention is paid to a jerk system with one non-negative parameter $epsilon$ and one non-linearity. By studying the continuation of periodic solution initiating at the zero-Hopf bifurcation, we numerically find a sequence of period doubling bifurcations which leads to the creation of chaotic attractor.
{"title":"Zero-Hopf bifurcations and chaos of quadratic jerk systems","authors":"B. Sang, Rizgar H. Salih, Ning Wang","doi":"10.22541/au.158291222.23595484","DOIUrl":"https://doi.org/10.22541/au.158291222.23595484","url":null,"abstract":"The purpose of this paper is to propose some coefficient conditions, characterizing the stability of periodic solutions bifurcated from zero-Hopf bifurcations of the general quadratic jerk system, and apply these theoretical results to a special jerk system in order to predict chaos. First, we characterize the zero-Hopf bifurcations of the general quadratic jerk system in $mathbb{R}^3$. The coefficient conditions on stability of periodic solutions are obtained via the averaging theory of first order. Next, we apply the theoretical results to a two-parameter jerk system. Finally special attention is paid to a jerk system with one non-negative parameter $epsilon$ and one non-linearity. By studying the continuation of periodic solution initiating at the zero-Hopf bifurcation, we numerically find a sequence of period doubling bifurcations which leads to the creation of chaotic attractor.","PeriodicalId":44514,"journal":{"name":"Journal of Nonlinear Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2020-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47073912","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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