2一致凸Banach空间中均衡问题、变分不等式问题和不动点问题的一个弱收敛定理

A Weak Convergence Theorem for Equilibrium Problems, Variational Inequalities and Fixed Point Problems in 2-Uniformly Convex Banach Spaces

中文关键词:  相对非扩展映射  $\alpha-$ 逆强单调算子  均衡问题  变分不等式  弱收敛  不动点.

英文关键词:relatively nonexpansive mapping  $\alpha$-inversely strongly monotone operator  equilibrium problem  variational inequality  weak convergence  fixed point.

中文摘要:

      在实一致光滑且2一致凸的Banach空间中,引进了一种新的迭代算法,用以逼近均衡问题的解集、含有 $\alpha-$逆-强单调算子的变分不等式的解集及相对非扩展映射的不动点集的公共元.证明了一些弱收敛定理,并推广了以往的研究工作.

英文摘要:

      In this paper, we introduce a new iterative scheme for finding the common element of the set of solutions of an equilibrium problem, the set of solutions of variational inequalities for an $\alpha$-inversely strongly monotone operator and the set of fixed points of relatively nonexpansive mappings in a real uniformly smooth and 2-uniformly convex Banach space. Some weak convergence theorems are obtained, to extend the previous work.