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

Author:

Ugwunnadi Godwin C.1,Izuchukwu Chinedu2,Mewomo Oluwatosin T.3

Affiliation:

1. Department of Mathematics , University of Swaziland , Kwaluseni , Swaziland

2. School of Mathematics, Statistics and Computer Science , University of KwaZulu-Natal , Durban ; and DST-NRF Center of Excellence in Mathematical and Statistical Sciences (CoE-MaSS), Johannesburg , South Africa

3. School of Mathematics, Statistics and Computer Science , University of KwaZulu-Natal , Durban , South Africa

Abstract

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.

Funder

National Research Foundation

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Computational Theory and Mathematics,Statistics, Probability and Uncertainty,Mathematical Physics

Reference37 articles.

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2. D. Ariza-Ruiz, G. López-Acedo and A. Nicolae, The asymptotic behavior of the composition of firmly nonexpansive mappings, J. Optim. Theory Appl. 167 (2015), no. 2, 409–429.

3. K. Ball, E. A. Carlen and E. H. Lieb, Sharp uniform convexity and smoothness inequalities for trace norms, Invent. Math. 115 (1994), no. 3, 463–482.

4. M. Bethke, Approximation von Fixpunkten streng pseudokontraktiver Operatoren, Wiss. Z. Pädagog. Hochsch. “Liselotte Herrmann” Güstrow Math.-Natur. Fak. 27 (1989), no. 2, 263–270.

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