Pakkapon Preechasilp

Viscosity approximation methods for nonexpansive mappings in CAT(0) spaces

AbstractThe purpose of this paper is to study the strong convergence theorems of Moudafi’s viscosity approximation methods for a nonexpansive mapping T in CAT(0) spaces without the property . For a contraction f on C and t∈(0,1), let xt∈C be the unique fixed point of the contraction x↦tf(x)⊕(1−t)Tx; i.e., xt=tf(xt)⊕(1−t)Txt and xn+1=αnf(xn)⊕(1−αn)Txn,n≥0, where x0∈C is arbitrarily chosen and {αn}⊂(0,1) satisfies certain conditions. We prove that the iterative schemes {xt} and {xn} converge strongly to the same point x˜ such that x˜=PF(T)f(x˜), which is the unique solution of the variational inequality (VIP) 〈x˜fx˜→,xx˜→〉≥0,x∈F(T). By using the concept of quasilinearization, we remark that the proof is different from that of Shi and Chen in J. Appl. Math. 2012:421050, 2012. In fact, strong convergence theorems for two given iterative schemes are established in CAT(0) spaces without the property .

Viscosity approximation methods for nonexpansive semigroups in CAT(0) spaces

In this paper, we study the strong convergence of Moudafi’s viscosity approximation methods for approximating a common fixed point of a one-parameter continuous semigroup of nonexpansive mappings in CAT(0) spaces. We prove that the proposed iterative scheme converges strongly to a common fixed point of a one-parameter continuous semigroup of nonexpansive mappings which is also a unique solution of the variational inequality. The results presented in this paper extend and enrich the existing literature.

Continuity of the solution mappings to parametric generalized vector equilibrium problems

Abstract The aim of this paper is to establish the continuity of the efficient solution mappings to a parametric generalized strong vector equilibrium problem, by using the Holder relation. Our result extends and improves some recent results in the references therein.

A New Iterative Scheme for Solving the Equilibrium Problems, Variational Inequality Problems, and Fixed Point Problems in Hilbert Spaces

We introduce the new iterative methods for finding a common solution set of monotone, Lipschitz-type continuous equilibrium problems and the set of fixed point of nonexpansive mappings which is a unique solution of some variational inequality. We prove the strong convergence theorems of such iterative scheme in a real Hilbert space. The main result extends various results existing in the current literature.

Existence theorems of the hemivariational inequality governed by a multi-valued map perturbed with a nonlinear term in Banach spaces

In this paper, we establish some existence results for the hemivariational inequality governed by a multi-valued map perturbed with a nonlinear term in reflexive Banach spaces. Using the concept of the stable

The General Iterative Methods for Asymptotically Nonexpansive Semigroups in Banach Spaces

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The modified general iterative methods for nonexpansive semigroups in banach spaces

-quasimonotonicity, the properties of Clarke’s generalized directional derivative, Clarke’s generalized gradient and KKM technique, some existence theorems of solutions are proved when the constrained set is nonempty, bounded (or unbounded), closed and convex. Our main results extend various results existing in the current literatures.

A note on strict feasibility and solvability for pseudomonotone equilibrium problems

In this article, the modified Noor iterations are considered for the generalized contraction and a nonexpansive semigroup in the framework of a reflexive Banach space which admits a weakly sequentially continuous duality mapping. The strong convergence theorems are obtained under very mild conditions imposed the parameters. The results presented in this article improve and extend the corresponding results announced by Chen and He and Chen et al. and many others.AMS subject classification: 47H09; 47H10; 47H17.