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Hybrid pseudo-viscosity approximation schemes for systems of equilibrium problems and fixed point problems of infinite family and semigroup of non-expansive mappings

机译:非膨胀映象的无限族和半群的平衡问题和不动点问题的系统的混合伪粘度逼近方案

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摘要

In this paper, we introduce hybrid pseudo-viscosity approximation schemes with strongly positive bounded linear operators for finding a common element of the set of solutions to a system of equilibrium problems, the set of fixed points of an infinite family and left amenable semigroup of non-expansive mappings in the frame work of Hilbert spaces. Our goal is to prove a result of strong convergence for hybrid pseudo-viscosity approximation schemes to approach a solution of systems of equilibrium problems which is also a common fixed point of an infinite family and left amenable semigroup of non-expansive mappings. The results presented in this paper can be treated as an extension and improvement of the corresponding results announced by Ceng et al. [L.C. Ceng, Q.H. Ansari, and J.C. Yao, Hybrid pseudo-viscosity approximation schemes for equilibrium problems and fixed point problems of infinitely many non-expansive mappings, Nonlinear Analysis 4 (2010) 743754] and many others.
机译:在本文中,我们引入具有强正有界线性算子的混合伪粘度逼近方案,以找到平衡问题系统解集的一个公共元素,一个无限族的不动点集和一个非左定左半群希尔伯特空间框架中的扩展映射。我们的目标是证明混合伪粘度逼近方案的强收敛结果,以解决系统平衡问题的解决方案,该问题也是无限族和非扩张映射的左半适应组的共同固定点。本文介绍的结果可以视为Ceng等人发表的相应结果的扩展和改进。 [L.C.曾庆辉Ansari和J.C. Yao,针对无限多个非膨胀映射的平衡问题和不动点问题的混合伪粘度逼近方案,非线性分析4(2010)743754]等。

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