@article{Aldosary2025, 
author = {Saud Fahad Aldosary and Mohammad Farid},
title = {A viscosity-based iterative method for solving split generalized equilibrium and fixed point problems of strict pseudo-contractions},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {4},
pages = {8753-8776},
keywords = {fixed point problem, split generalized equilibrium problem, ϵ- strict pseudo-contractive mapping, variational inequality problem, nonexpansive mapping, iterative methods, extragradient iterative methods},
url = {https://www.sciopen.com/article/10.3934/math.2025401},
doi = {10.3934/math.2025401},
abstract = {In this paper, we developed a viscosity-based extragradient iterative algorithm to approximate the solution of the split generalized equilibrium problem, the variational inequality problem, and the fixed point problem for a finite family of    ϵ-strict pseudo-contractive and a nonexpansive mapping in Hilbert space. The main purpose was to establish strong convergence of the proposed algorithm under suitable conditions. We presented a comprehensive computational analysis to illustrate the effectiveness of our method and compared its performance with existing approaches. Our results extend and unify several well-known results in the literature, contributing significantly to the field.}
}