Convergence Theorem of Inertial P-iteration Method for a Family of Nonexpansive Mappings with Applications

Attapol Kaewkhao, Limpapat Bussaban, Suthep Suantai

Abstract

In this paper, an algorithm called inertial P-iteration method is proposed for finding a common fixed point of a family of nonexpansive mappings and proved under some suitable conditions that the sequence generated by the proposed method weakly converges to a common fixed point of a family of nonexpansive mappings. In application, our method can be applied for finding zero point of sum of two monotone operators and minizer of sum of two convex functions.