Multi-step iterative algorithm for minimization and fixed point problems in p-uniformly convex metric spaces

Kazeem Olalekan Aremu; Chinedu Izuchukwu; Grace Nnenanya Ogwo; Oluwatosin Temitope Mewomo

doi:10.3934/jimo.2020063

Article Contents

2021, Volume 17, Issue 4: 2161-2180. Doi: 10.3934/jimo.2020063

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Multi-step iterative algorithm for minimization and fixed point problems in p-uniformly convex metric spaces

1.
School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa
2.
DSI-NRF Center of Excellence in, Mathematical and Statistical Sciences (CoE-MaSS), Johannesburg, South Africa

^* Corresponding author: O. T. Mewomo
^* Corresponding author: O. T. Mewomo

Received: April 30, 2019

Revised: September 30, 2019

Early access: March 2020

Published: July 2021

The second author is supported by the Department of Science and Innovation and National Research Foundation, 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 African Institute for Mathematical Sciences (AIMS), South Africa. The fourth author is supported by the National Research Foundation (NRF) of South Africa Incentive Funding for Rated Researchers (Grant Number 119903)

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Abstract

In this paper, we propose and study a multi-step iterative algorithm that comprises of a finite family of asymptotically $ k_i $-strictly pseudocontractive mappings with respect to $ p, $ and a $ p $-resolvent operator associated with a proper convex and lower semicontinuous function in a $ p $-uniformly convex metric space. Also, we establish the $ \Delta $-convergence of the proposed algorithm to a common fixed point of finite family of asymptotically $ k_i $-strictly pseudocontractive mappings which is also a minimizer of a proper convex and lower semicontinuous function. Furthermore, nontrivial numerical examples of our algorithm are given to show its applicability. Our results complement a host of recent results in literature.

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Mathematics Subject Classification: Primary: 47H09; 47H10; 49J20; 49J40.

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Figure 1. Errors vs Iteration numbers(n) for Example 4.1: Case 1 (top left); Case 2 (top right); Case 3 (bottom left); Case 4 (bottom right)

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Figure 2. Errors vs Iteration numbers(n) for Example 4.2: Case 1 (top left); Case 2 (top right); Case 3 (bottom left); Case 4 (bottom right)

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