Development of Viscosity Iterative Techniques for Split Variational-like Inequalities and Fixed Points Related to Pseudo-Contractions

Ghada AlNemer, Mohammad Farid () and Rehan Ali ()
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Ghada AlNemer: Department of Mathematical Sciences, College of Sciences, Princess Nourah bint Abdulrahman University, Riyadh 11671, Saudi Arabia
Mohammad Farid: Department of Mathematics, College of Science, Qassim University, Saudi Arabia
Rehan Ali: Department of Mathematics, Central University of Kashmir, Ganderbal 191131, Jammu and Kashmir, India

Mathematics, 2025, vol. 13, issue 17, 1-24

Abstract: This work presents an extragradient-type iterative process combined with the viscosity method to find a common solution to a split generalized variational-like inequality, a variational inequality, and a fixed point problem associated with a family of ε -strict pseudo-contractive mappings and a nonexpansive operator in Hilbert spaces. Strong convergence of the proposed algorithm is established, with some remarks derived from the main theorem. Numerical experiments are carried out to verify the applicability of the method and provide comparative observations. The results broaden and unify a range of existing contributions in this field.

Keywords: split generalized general variational-like inequality problem; ε -pseudo-contraction mapping; nonexpansive mapping; fixed point problem; iterative methods; variational inequality problem; extragradient methods (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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