ABSTRACT

The purpose of this paper is to find a common element in the intersection of the set of zeros of the inclusion problem of sum of two monotone mappings and the set of fixed points of a Bregman quasi nonexpansive mapping in a reflexive Banach space by using Bregman distance and shrinking projection method. Under suitable conditions, some strong convergence theorems are proved. As applications, we utilize our results to study the convex minimization problem, variational inequality problem.

中文翻译：

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求解自反Banach空间中包含问题和不动点问题的收缩投影方法

摘要

本文的目的是利用Bregman距离在自反Banach空间中寻找两个单调映射和的包含问题的零集与Bregman拟非扩张映射的不动点集的交集的公共元素和收缩投影法。在合适的条件下，证明了一些强收敛定理。作为应用，我们利用我们的结果来研究凸最小化问题、变分不等式问题。