A Strongly Convergent Hybrid Method to Unify Split Generalized Mixed Equilibrium and Fixed Point Problems

Rizvi, Shuja Haider; Sikander, Fahad

doi:10.28924/2291-8639-22-2024-168

Research Article

A Strongly Convergent Hybrid Method to Unify Split Generalized Mixed Equilibrium and Fixed Point Problems

Shuja Haider Rizvi*
Fahad Sikander

* Corresponding author

Abstract

The aim of this paper is twofold, we propose an extension to the split generalized mixed equilibrium problem firstly and introduce an iterative method based on a hybrid extragradient method. The goal is to efficiently find a common solution for both the split generalized mixed equilibrium problem and the fixed point problem concerning a nonexpansive mapping within the context of real Hilbert spaces. We conduct a thorough analysis of the proposed iterative method and establish a strong convergence theorem under certain mild conditions. Moreover, we present various implications derived from our main result and conduct numerical experiments to validate our findings. Our outcomes represent a substantial expansion and generalization of existing iterative methods and results within this field.

How to Cite

S. H. Rizvi, F. Sikander, A Strongly Convergent Hybrid Method to Unify Split Generalized Mixed Equilibrium and Fixed Point Problems, Int. J. Anal. Appl. 22 (2024), 168. https://doi.org/10.28924/2291-8639-22-2024-168

BibTeX

@article{Rizvi2024,
  author  = {Rizvi, Shuja Haider and Sikander, Fahad},
  title   = {A Strongly Convergent Hybrid Method to Unify Split Generalized Mixed Equilibrium and Fixed Point Problems},
  journal = {Int. J. Anal. Appl.},
  volume  = {22},
  year    = {2024},
  pages   = {168},
  doi     = {10.28924/2291-8639-22-2024-168}
}

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