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Strong Convergence Theorems for Fixed Point Problems for Nonexpansive Mappings and Zero Point Problems for Accretive Operators Using Viscosity Implicit Midpoint Rules in Banach Spaces

1
Qinggong College, North China University of Science and Technology, Tangshan 063000, China
2
Qian’an College, North China University of Science and Technology, Tangshan 064400, China
3
Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, China
*
Author to whom correspondence should be addressed.
Mathematics 2018, 6(11), 257; https://doi.org/10.3390/math6110257
Received: 13 October 2018 / Revised: 11 November 2018 / Accepted: 14 November 2018 / Published: 16 November 2018
(This article belongs to the Special Issue Fixed Point Theory and Related Nonlinear Problems with Applications)
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Abstract

This paper uses the viscosity implicit midpoint rule to find common points of the fixed point set of a nonexpansive mapping and the zero point set of an accretive operator in Banach space. Under certain conditions, this paper obtains the strong convergence results of the proposed algorithm and improves the relevant results of researchers in this field. In the end, this paper gives numerical examples to support the main results. View Full-Text
Keywords: viscosity implicit midpoint rule; nonexpansive mapping; accretive operator; zero point problem viscosity implicit midpoint rule; nonexpansive mapping; accretive operator; zero point problem
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Zhang, H.; Qu, Y.; Su, Y. Strong Convergence Theorems for Fixed Point Problems for Nonexpansive Mappings and Zero Point Problems for Accretive Operators Using Viscosity Implicit Midpoint Rules in Banach Spaces. Mathematics 2018, 6, 257.

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