DOI: 10.24193/fpt-ro.2025.2.04

Authors: Y. Arfat, M. A. A. Khan and P. Kumam

Abstract: In this paper, we propose a framework for the investigation of the convex minimization problem over the split equilibrium problems (SEP) and fixed point set of a finite family of multivalued demicontractive mappings in Hilbert spaces. We employ a hybrid steepest-descent approximants scheme which converges strongly to a common solution associated with the fixed point problem (FPP) and the SEP. Theoretical results comprise strong convergence results under suitable sets of constraints, as well as numerical results which are established for the underlying algorithm.

Key Words and Phrases: Hybrid steepest descent method, split equilibrium problems, variational inequality problem, fixed point problems, demicontractive multivalued mapping, convex minimization problem, strong convergence, Hilbert space.

2010 Mathematics Subject Classification: 65C25, 90C25, 47H09, 49M45, 47H10.

Published on-line: May 1st, 2025.

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