Modified inertial algorithm for solving mixed equilibrium problems in Hadamard spaces

Abdul Rahim Khan; Chinedu Izuchukwu; Maggie Aphane; Godwin Chidi Ugwunnadi

doi:10.3934/naco.2021039

Article Contents

2022, Volume 12, Issue 4: 859-877. Doi: 10.3934/naco.2021039

This issue Previous Article Triple-hierarchical problems with variational inequality Next Article

Modified inertial algorithm for solving mixed equilibrium problems in Hadamard spaces

1.
Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia
2.
Department of Mathematics, The Technion-Israel Institute of Technology, 32000 Haifa, Israel
3.
Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Ga-Rankuwa, Pretoria, P.O. Box 60, 0204, South Africa
4.
Department of Mathematics, University of Eswatini, Private Bag 4 Kwaluseni, Eswatini

^* Corresponding author: Godwin Chidi Ugwunnadi
^* Corresponding author: Godwin Chidi Ugwunnadi

Received: March 31, 2021

Revised: July 31, 2021

Early access: September 2021

Published: December 2022

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Abstract

The main purpose of this paper is to introduce the concept of modified inertial algorithm in Hadamard spaces. We emphasize that, as far as we know, this is the first time that this concept is being considered in this setting. Under some weak assumptions, we prove that the modified inertial algorithm converges strongly to a common solution of a finite family of mixed equilibrium problems and fixed point problem of a nonexpansive mapping. We also give a primary numerical illustration in the framework of Hadamard spaces, to show the efficiency of the modified inertial term in our proposed algorithm.

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

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

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