Startseite Convergence theorems for generalized hemicontractive mapping in p-uniformly convex metric space
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Convergence theorems for generalized hemicontractive mapping in p-uniformly convex metric space

  • Godwin C. Ugwunnadi , Chinedu Izuchukwu und Oluwatosin T. Mewomo EMAIL logo
Veröffentlicht/Copyright: 15. August 2020

Abstract

In this paper, we introduce and study an Ishikawa-type iteration process for the class of generalized hemicontractive mappings in 𝑝-uniformly convex metric spaces, and prove both Δ-convergence and strong convergence theorems for approximating a fixed point of generalized hemicontractive mapping in complete 𝑝-uniformly convex metric spaces. We give a surprising example of this class of mapping that is not a hemicontractive mapping. Our results complement, extend and generalize numerous other recent results in CAT(0) spaces.

MSC 2010: 47H09; 47H10; 49J20; 49J40

Award Identifier / Grant number: 119903

Funding statement: The second author is supported by the Department of Science and Innovation (DSI) and National Research Foundation (NRF), Republic of South Africa Center of Excellence in Mathematical and Statistical Sciences (DSI-NRF COE-MaSS) Doctoral Bursary. The third author is supported by the National Research Foundation (NRF) of South Africa Incentive Funding for Rated Researchers (Grant Number 119903).

Acknowledgements

The authors sincerely thank the anonymous reviewer for his careful reading, constructive comments and fruitful suggestions that substantially improved the manuscript. Opinions expressed and conclusions arrived are those of the authors and are not necessarily to be attributed to the CoE-MaSS or NRF.

  1. Competing Interests: The authors declare that they have no competing interests.

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Received: 2017-11-28
Accepted: 2019-11-25
Published Online: 2020-08-15
Published in Print: 2020-12-01

© 2020 Walter de Gruyter GmbH, Berlin/Boston

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