Islamic University Journal of Applied Sciences

Approximation of a Common Solution to Split Equilibrium and Fixed Point Problems via a Modified Viscosity Method for a Nonexpansive Semigroup

Shuja Haider Rizvi 

Keywords: Split equilibrium problem; Fixed-point problem; Nonexpansive semigroup; Iterative algorithms.

Major: Science

Sub Major: Mathematics

https://doi.org/10.63070/jesc.2026.029; Received 15 February 2026; Revised 21 April 2026; Accepted 26 April 2026.
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Abstract
This paper proposes a new iterative algorithm, grounded in modified viscosity techniques, for approximating a common solution to a split equilibrium problem and a fixed point problem associated with a nonexpansive semigroup in Hilbert spaces. We prove that the sequence generated by the proposed scheme converges strongly to a point that simultaneously solves the split equilibrium problem and the corresponding fixed point problem for the nonexpansive semigroup. Furthermore, the findings presented here offer improvements, generalizations, and refinements of several existing results in the related literature.
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