Document Type : Research Paper

Authors

• Hammed Anuoluwapo Abass ^{1, 2}
• Kazeem Oewole ¹
• Kazeem Olalekan Aremu ^{3, 4}
• Akindele Adebayo Mebawondu ^{1, 2}
• Ojen Kumar Narain ¹

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), South Africa

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, Usmanu Danfodiyo University Sokoto, PMB 2346, Sokoto State, Nigeria

Abstract

In this paper, we first introduce the Halpern iteration process for approximating the solution of the fixed point problem of a finite family of $k$-strictly pseudo-contractive mappings in Hadamard spaces. We also propose an extra gradient Halpern iterative algorithm for approximating a common solution of a finite family of $k_j$-strictly pseudocontractive mappings and a pseudomonotone equilibrium problem in Hadamard space. We prove a strong convergence result without imposing any strict (compactness) conditions for approximating the solutions to the aforementioned problems. We state some consequences of our results and display some numerical examples to show the performance of our results. Our results improve and generalize many recent results in the literature.

Keywords

• Strictly pseudo-contractive mapping
• Hadamard spaces
• pseudomonotone equilibrium
• extragradient algorithm
• fixed point problem