Fixed Point Methods and Optimization

Electronic ISSN: 3008-1548

DOI: 10.69829/fpmo

Dynamical technique for split monotone variational inclusion and fixed point problems in Banach spaces

Fixed Point Methods and Optimization, Volume 2, Issue 1, April 2025, Pages 77–93

MAGGIE APHANE

Department of Mathematics and Applied Mathematics, Sefako Makgato Health Science University, P.O. Box 94, Pretoria 0204, South Africa

ABUBAKAR ADAMU

Operational Research Center in Healthcare, Near East University, TRNC Mersin 10, Nicosia 99138, Turkey

School of Mathematics, Chongqing Normal University, Chongqing 400047, China

OLAWALE KAZEEM OYEWOLE

Department of Mathematics, Tshwane University of Technology, Arcadia, PMB 0007, Pretoria, South Africa

HAMMED ANUOLUWAPO ABASS

Department of Mathematics and Applied Mathematics, Sefako Makgato Health Science University, P.O. Box 94, Pretoria 0204, South Africa


Abstract

In this manuscript, we propose a modified Halpern iterative method for approximating solutions of split monotone variational inclusion and fixed point problems of Bregman demigeneralized mappings in the framework of \(p-\)uniformly convex and uniformly smooth real Banach spaces. We establish a strong convergence result for the sequence generated by our iterative scheme under some mild conditions without the computation of the operator norm. We state some consequences and present some examples to show the efficiency and implementation of our proposed method. The result discussed in this paper extends and generalizes many recent results in this direction.


Cite this Article as

Maggie Aphane, Abubakar Adamu, Olawale Kazeem Oyewole, and Hammed Anuoluwapo Abass, Dynamical technique for split monotone variational inclusion and fixed point problems in Banach spaces, Fixed Point Methods and Optimization, 2(1), 77–93, 2025