. The main aim of this paper is to investigate the existence of nontrivial solutions for a class of variable exponent p ( x ) -Kirchhoff type equations. We prove the existence of three solutions by using the mountain pass theorem and Ekeland’s variational principle. Moreover, when λ = 0, we obtain the existence of infinite many solutions by using the symmetric mountain pass theorem.
{"title":"Multiple solutions for a class of non-homogeneous p(x)-Kirchhoff type equations","authors":"","doi":"10.23952/jnfa.2023.17","DOIUrl":"https://doi.org/10.23952/jnfa.2023.17","url":null,"abstract":". The main aim of this paper is to investigate the existence of nontrivial solutions for a class of variable exponent p ( x ) -Kirchhoff type equations. We prove the existence of three solutions by using the mountain pass theorem and Ekeland’s variational principle. Moreover, when λ = 0, we obtain the existence of infinite many solutions by using the symmetric mountain pass theorem.","PeriodicalId":44514,"journal":{"name":"Journal of Nonlinear Functional Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136004418","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 propose a new modified inertial simultaneous algorithm of common fixed point problems for a finite family of demicontractive mappings and obtain some strong convergence results in real Hilbert spaces. Meanwhile, we also give a numerical example to demonstrate the efficiency of our proposed algorithm. Our results improve and extend some corresponding known results.
{"title":"Viscosity approximation of a modified inertial simultaneous algorithm for a finite family of demicontractive mappings","authors":"","doi":"10.23952/jnfa.2023.7","DOIUrl":"https://doi.org/10.23952/jnfa.2023.7","url":null,"abstract":". In this paper, we propose a new modified inertial simultaneous algorithm of common fixed point problems for a finite family of demicontractive mappings and obtain some strong convergence results in real Hilbert spaces. Meanwhile, we also give a numerical example to demonstrate the efficiency of our proposed algorithm. Our results improve and extend some corresponding known results.","PeriodicalId":44514,"journal":{"name":"Journal of Nonlinear Functional Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136004422","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 the paper, by using Darbo-Sadovskii fixed point theorem for condensing operators on Fr ´ echet spaces with respect to vector-valued measure of noncompactness, we prove the existence results for the second-order Cauchy problem u (cid:48)(cid:48) ( t ) = f ( t , u ( t )) , t ∈ ( 0 , T ) , u ( 0 ) = u 0 , u (cid:48) ( 0 ) = u 1 , in a scale of Banach spaces. The result is applied to the Kirchhoff equations in Gevrey class.
{"title":"The second-order Cauchy problem in a scale of Banach spaces with vector-valued measures of noncompactness and an application to Kirchhoff equations","authors":"","doi":"10.23952/jnfa.2023.10","DOIUrl":"https://doi.org/10.23952/jnfa.2023.10","url":null,"abstract":". In the paper, by using Darbo-Sadovskii fixed point theorem for condensing operators on Fr ´ echet spaces with respect to vector-valued measure of noncompactness, we prove the existence results for the second-order Cauchy problem u (cid:48)(cid:48) ( t ) = f ( t , u ( t )) , t ∈ ( 0 , T ) , u ( 0 ) = u 0 , u (cid:48) ( 0 ) = u 1 , in a scale of Banach spaces. The result is applied to the Kirchhoff equations in Gevrey class.","PeriodicalId":44514,"journal":{"name":"Journal of Nonlinear Functional Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136004435","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":"A relaxed extended CQ algorithm for the split feasibility problem in Hilbert spaces","authors":"","doi":"10.23952/jnfa.2023.18","DOIUrl":"https://doi.org/10.23952/jnfa.2023.18","url":null,"abstract":"","PeriodicalId":44514,"journal":{"name":"Journal of Nonlinear Functional Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136004427","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":"Existence of mild solutions of fractional measure evolution inclusions","authors":"","doi":"10.23952/jnfa.2023.5","DOIUrl":"https://doi.org/10.23952/jnfa.2023.5","url":null,"abstract":"","PeriodicalId":44514,"journal":{"name":"Journal of Nonlinear Functional Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136004446","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 constructs a new iterative method for identifying a common solution of a general system of variational inequalities and a fixed point problem of a nonexpansive mapping. Furthermore, this paper establishes some necessary and sufficient conditions of strong convergence of iterative sequences without any assumption that the solution set of the problem is nonempty in Hilbert spaces. Finally, some applications and examples are provided to support the main results
{"title":"An approximate approach for solving fixed point and systems of variational inequality problems without certain constraints","authors":"","doi":"10.23952/jnfa.2023.24","DOIUrl":"https://doi.org/10.23952/jnfa.2023.24","url":null,"abstract":". This paper constructs a new iterative method for identifying a common solution of a general system of variational inequalities and a fixed point problem of a nonexpansive mapping. Furthermore, this paper establishes some necessary and sufficient conditions of strong convergence of iterative sequences without any assumption that the solution set of the problem is nonempty in Hilbert spaces. Finally, some applications and examples are provided to support the main results","PeriodicalId":44514,"journal":{"name":"Journal of Nonlinear Functional Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136002677","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 our investigation into the split feasibility problem with multiple output sets (SF-PMOS), under the assumption that the corresponding convex subsets are level subsets of convex functionals. To approximate the solutions of this problem, we propose a method that combines relaxed projection with a recently proposed technique. Our approach involves establishing a weak convergence theorem for the fixed stepsize, followed by constructing a variable stepsize that is independent of the norm of the linear operator involved. We also modify these methods to ensure strong convergence. As an application, we develop a new relaxed projection algorithm for solving the split feasibility problem.
{"title":"On the relaxed projection method for the SFPMOS","authors":"","doi":"10.23952/jnfa.2023.26","DOIUrl":"https://doi.org/10.23952/jnfa.2023.26","url":null,"abstract":". This paper presents our investigation into the split feasibility problem with multiple output sets (SF-PMOS), under the assumption that the corresponding convex subsets are level subsets of convex functionals. To approximate the solutions of this problem, we propose a method that combines relaxed projection with a recently proposed technique. Our approach involves establishing a weak convergence theorem for the fixed stepsize, followed by constructing a variable stepsize that is independent of the norm of the linear operator involved. We also modify these methods to ensure strong convergence. As an application, we develop a new relaxed projection algorithm for solving the split feasibility problem.","PeriodicalId":44514,"journal":{"name":"Journal of Nonlinear Functional Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136002682","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 purpose of this paper is to investigate a new model, called the generalized weakly-mixed vector equilibrium problem and denoted by GWMVEP, which is an extension of vector equilibrium problems, vector variational inequalities and vector optimization problems. We first verify the existence of the GWMVEP on a noncompact domain by using the KKMF lemma. In addition, we identify a class of the GWMVEP with weaker assumptions such that most of the GWMVEPs are structurally stable and robust in the sense of the Baire classifi-cation.
{"title":"Existence and stability of generalized weakly-mixed vector equilibrium problems","authors":"","doi":"10.23952/jnfa.2023.2","DOIUrl":"https://doi.org/10.23952/jnfa.2023.2","url":null,"abstract":". The purpose of this paper is to investigate a new model, called the generalized weakly-mixed vector equilibrium problem and denoted by GWMVEP, which is an extension of vector equilibrium problems, vector variational inequalities and vector optimization problems. We first verify the existence of the GWMVEP on a noncompact domain by using the KKMF lemma. In addition, we identify a class of the GWMVEP with weaker assumptions such that most of the GWMVEPs are structurally stable and robust in the sense of the Baire classifi-cation.","PeriodicalId":44514,"journal":{"name":"Journal of Nonlinear Functional Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136004431","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, by coupling the modified extra-gradient method with the Mann iteration method, we solve variational inequalities and the fixed point problems of pseudo-contractive mappings without Lipschitz assumptions. Weak and strong convergence theorems are established.
{"title":"Iterative algorithms for variational inequalities and fixed point problems of pseudocontraction without Lipschitz assumptions","authors":"","doi":"10.23952/jnfa.2023.4","DOIUrl":"https://doi.org/10.23952/jnfa.2023.4","url":null,"abstract":". In this paper, by coupling the modified extra-gradient method with the Mann iteration method, we solve variational inequalities and the fixed point problems of pseudo-contractive mappings without Lipschitz assumptions. Weak and strong convergence theorems are established.","PeriodicalId":44514,"journal":{"name":"Journal of Nonlinear Functional Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136004438","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：