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EXISTENCE RESULTS FOR NEW GENERALIZED MIXED EQUILIBRIUM AND FIXED POINT PROBLEMS IN BANACH SPACES
Olawale Kazeem Oyewole,Oluwatosin Temitope Mewomo 경남대학교 수학교육과 2020 Nonlinear Functional Analysis and Applications Vol.25 No.2
In this paper, existence and uniqueness results for the solution of a new classof equilibrium problem is established. Using the KKM technique, we establish the existenceand uniqueness of solutions of a new generalized mixed equilibrium problem (NGMEP) withtrifunctions. Further, we propose an iterative algorithm for finding a common element inthe solution set of the NGMEP and a fixed point set of a nonlinear mapping. We provedthe strong convergence of the algorithm to a common element in the solution set of a systemof NGMEP and a fixed point set of a countable family of totally quasi-φ-asymptoticallynonexpansive mapping in the framework of a real uniformly convex and uniformly smoothBanach space. Our result generalize many other results obtained recently in this direction.
Note for the tripled and quadruple fixed points of the mixed monotone mappings
Jun Wu,Yicheng Liu 대한수학회 2013 대한수학회보 Vol.50 No.3
In this paper, to include more generalized cases, the authors present a modified concept for the tripled and quadruple fixed point of the mixed monotone mappings. Also, they investigate the existence and uniqueness of fixed point of the ordered monotone operator with the Matkowski contractive conditions in the partial ordered metric spaces. As the direct consequences, the existence of coupled fixed point, tripled fixed point and quadruple fixed point are explored at the common framework and some previous results in [T. G. Bhaskar and V. Lakshmikantham, {\it Fixed point theory in partially ordered metric spaces and applications}, Nonlinear Anal. {\bf 65} (2006), 1379--1393; V. Berinde and M. Borcut, {\it Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces}, Nonlinear Anal. {\bf 74} (2011), no. 15, 4889--4897; E. Karapinar and N. V. Luong, {\it Quadruple fixed point theorems for nonlinear contractions}, Computers and Mathematics with Applications (2012), doi:10.1016/j.camwa.2012.02061] are improved. Finally, some fixed point theorems are proved.
NOTE FOR THE TRIPLED AND QUADRUPLE FIXED POINTS OF THE MIXED MONOTONE MAPPINGS
Wu, Jun,Liu, Yicheng Korean Mathematical Society 2013 대한수학회보 Vol.50 No.3
In this paper, to include more generalized cases, the authors present a modified concept for the tripled and quadruple fixed point of the mixed monotone mappings. Also, they investigate the existence and uniqueness of fixed point of the ordered monotone operator with the Matkowski contractive conditions in the partial ordered metric spaces. As the direct consequences, the existence of coupled fixed point, tripled fixed point and quadruple fixed point are explored at the common framework and some previous results in [T. G. Bhaskar and V. Lakshmikan-tham, Fixed point theory in partially ordered metric spaces and applications, Nonlinear Anal. 65 (2006), 1379-1393; V. Berinde and M. Borcut, Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces, Nonlinear Anal. 74 (2011), no. 15, 4889-4897; E. Karapinar and N. V. Luong, Quadruple fixed point theorems for nonlinear contractions, Computers and Mathematics with Applications (2012), doi:10.1016/j.camwa.2012.02061] are improved. Finally, some fixed point theorems are proved.
ERROR BOUNDS FOR NONLINEAR MIXED VARIATIONAL-HEMIVARIATIONAL INEQUALITY PROBLEMS
A. A. H. Ahmadini,Salahuddin,J. K. Kim 경남대학교 수학교육과 2024 Nonlinear Functional Analysis and Applications Vol.29 No.1
In this article, we considered a class of nonlinear variational hemivariational inequality problems and investigated a gap function and regularized gap function for the problems. We discussed the global error bounds for such inequalities in terms of gap function and regularized gap functions by utilizing the Clarke generalized gradient, relaxed monotonicity, and relaxed Lipschitz continuous mappings. Finally, as applications, we addressed an application to non-stationary non-smooth semi-permeability problems.
Bhavana Deshpande,Amrish Handa 한국수학교육학회 2018 純粹 및 應用數學 Vol.25 No.4
We study the existence and uniqueness of xed point for isotone map- pings of any number of arguments under Geraghty-type contraction on a complete metric space endowed with a partial order. As an application of our result we study the existence and uniqueness of the solution to a nonlinear Fredholm integral equation. Our results generalize, extend and unify several classical and very recent related results in the literature in metric spaces.
JUNG, JONG SOO Korean Mathematical Society 2015 대한수학회지 Vol.52 No.6
In this paper, we introduce a new iterative algorithm for finding a common element of the set of solutions of a generalized mixed equilibrium problem related to a continuous monotone mapping, the set of solutions of a variational inequality problem for a continuous monotone mapping, and the set of fixed points of a continuous pseudocontractive mapping in Hilbert spaces. Weak convergence for the proposed iterative algorithm is proved. Our results improve and extend some recent results in the literature.
정종수 대한수학회 2015 대한수학회지 Vol.52 No.6
In this paper, we introduce a new iterative algorithm for finding a common element of the set of solutions of a generalized mixed equilibrium problem related to a continuous monotone mapping, the set of solutions of a variational inequality problem for a continuous monotone mapping, and the set of fixed points of a continuous pseudocontractive mapping in Hilbert spaces. Weak convergence for the proposed iterative algorithm is proved. Our results improve and extend some recent results in the literature.
A HYBRID ITERATIVE METHOD OF SOLUTION FOR MIXED EQUILIBRIUM AND OPTIMIZATION PROBLEMS
Lijuan Zhang,Junmin Chen 영남수학회 2010 East Asian mathematical journal Vol.26 No.1
In this paper, we introduce a hybrid iterative method for finding a common element of the set of solutions of a mixed equilibrium problem, the set of common fixed points of finitely many nonexpansive mappings and the set of solutions of the variational inequality for an inverse strongly monotone mapping in a Hilbert space. We show that the iterative sequences converge strongly to a common element of the three sets. The results extended and improved the corresponding results of L.-C.Ceng and J.-C.Yao.
A HYBRID ITERATIVE METHOD OF SOLUTION FOR MIXED EQUILIBRIUM AND OPTIMIZATION PROBLEMS
Zhang, Lijuan,Chen, Jun-Min The Youngnam Mathematical Society 2010 East Asian mathematical journal Vol.26 No.1
In this paper, we introduce a hybrid iterative method for finding a common element of the set of solutions of a mixed equilibrium problem, the set of common mixed points of finitely many nonexpansive mappings and the set of solutions of the variational inequality for an inverse strongly monotone mapping in a Hilbert space. We show that the iterative sequences converge strongly to a common element of the three sets. The results extended and improved the corresponding results of L.-C.Ceng and J.-C.Yao.
GENERALIZED NONLINEAR MULTIVALUED MIXED QUASI-VARIATIONAL-LIKE INEQUALITIES
Lee, Byung-Soo,Khan M. Firdosh,Salahuddin Salahuddin Korean Mathematical Society 2006 대한수학회논문집 Vol.21 No.4
In this paper, we introduce a new class of generalized nonlinear multivalued mixed quasi-variational-like inequalities and prove the existence and uniqueness of solutions for the class of generalized nonlinear multivalued mixed quasi-variational-like inequalities in reflexive Banach spaces using Fan-KKM Theorem.