Nowadays, the usage of the existence and convergence results of a common fixed point for nonlinear semigroups of various kinds of self-mappings is applied to several problems in mathematics and another branches. Surprisingly, nobody considered the study on the nonlinear semigroups of weak contraction self-mappings in the sense of Berinde. The purpose of this paper is to attempt to complete this direction and so we investigate the existence of the common fixed point for nonlinear semigroups of weak contraction self-mappings in the sense of Berinde on a bounded closed convex subset of a real Banach space with uniformly normal structure. More precisely, we prove the convergence theorem for the common fixed point of a weak contraction semigroups. An illustrative example is presented.

中文翻译：

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弱收缩非线性半群的公共不动点的存在性和收敛性定理

如今，将各种自映射的非线性半群的公共不动点的存在性和收敛性结果用于数学和其他分支的若干问题。出乎意料的是，没有人考虑在贝林德的意义上研究弱收缩自映射的非线性半群。本文的目的是尝试完成该方向，因此我们研究了在Berande意义上，均匀一致的实际Banach空间的有界封闭凸子集上的弱收缩自映射的非线性半群的公共不动点的存在正常结构。更确切地说，我们证明了弱收缩半群的公共不动点的收敛定理。给出了说明性示例。