Existence and Convergence Theorem for Fixed Point Problem of Various Nonlinear Mappings and Variational Inequality Problems without Some Assumptions

Wongvisarut Khuangsatung, Atid Kangtunyakarn

Abstract


The purpose of this article, we give a necessary and sufficient condition for the modified Mann iterative process in order to obtain strong convergence theorem for finding a common element of the set of fixed point of a finite family of nonexpansive mappings and variational inequality problem in Hilbert space without the conditions $\bigcap_{i=1}^{N}Fix(T_i)\cap VI(C,A)\neq\emptyset$. Moreover, we utilize our main result to fixed point problems of strictly pseudocontractive mappings and the set of solutions of variational inequality problem.

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