Iterative methods for fixed point problems and generalized split feasibility problems in Banach spaces

Volume 11, Issue 2, pp 198--217 http://dx.doi.org/10.22436/jnsa.011.02.03

Publication Date: January 23, 2018 Submission Date: August 25, 2017 Revision Date: November 23, 2017 Accteptance Date: December 06, 2017

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Authors

Yanlai Song - College of Science, Zhongyuan University of Technology, 450007 Zhengzhou, China.

Abstract

In this paper, we study the Halpern type iterative algorithm to approximate a common solution of fixed point problems of an infinite family of demimetric mappings and generalized split feasibility problems with firmly nonexpansive-like mappings in Banach spaces. We also prove strong convergence theorems for a common solution of the above-said problems by the proposed iterative algorithm and discuss some applications of our results. The methods in this paper are novel and different from those given in many other paper. And the results are the extension and improvement of the recent results in the literature.

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Keywords

• Banach space
• generalized split feasibility problem
• fixed point
• metric resolvent
• demimetric mapping

MSC

•  47H09
•  47H10
•  49H17

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