Viscosity iterative method for split common null point problems and fixed point problems

Volume 12, Issue 2, pp 86--101 http://dx.doi.org/10.22436/jnsa.012.02.03

Publication Date: October 13, 2018 Submission Date: July 25, 2017 Revision Date: July 25, 2018 Accteptance Date: September 21, 2018

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Authors

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

Abstract

In this paper, we introduce and study an Ishikawa-like iterative algorithm to approximate a common solution of a split common null point problem and a fixed point problem of asymptotically pseudo-contractive mappings in the intermediate sense on unbounded domains. We prove that the sequence generated by the iterative scheme strongly converges to a common solution of the above-said problems. The method in this paper is novel and different from those given in many other papers. The results are the extension and improvement of the recent results in the literature.

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Keywords

• Banach space
• split common null point problem
• fixed point
• metric resolvent
• asymptotically pseudocontractive mapping in the intermediate sense

MSC

•  47H09
•  47H10
•  49H17

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