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An Inertial Iterative Algorithm to Find Common Solution of a Split Generalized Equilibrium and a Variational Inequality Problem in Hilbert Spaces

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  • Mohammad Farid
  • Rehan Ali
  • Watcharaporn Cholamjiak
  • Jen-Chih Yao

Abstract

In this paper, we introduce and study an iterative algorithm via inertial and viscosity techniques to find a common solution of a split generalized equilibrium and a variational inequality problem in Hilbert spaces. Further, we prove that the sequence generated by the proposed theorem converges strongly to the common solution of our problem. Furthermore, we list some consequences of our established algorithm. Finally, we construct a numerical example to demonstrate the applicability of the theorem. We emphasize that the result accounted in the manuscript unifies and extends various results in this field of study.

Suggested Citation

  • Mohammad Farid & Rehan Ali & Watcharaporn Cholamjiak & Jen-Chih Yao, 2021. "An Inertial Iterative Algorithm to Find Common Solution of a Split Generalized Equilibrium and a Variational Inequality Problem in Hilbert Spaces," Journal of Mathematics, Hindawi, vol. 2021, pages 1-17, November.
    • Handle: RePEc:hin:jjmath:3653807
    DOI: 10.1155/2021/3653807
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