An Adapted Proximal Point Algorithm Utilizing the Golden Ratio Technique for Solving Equilibrium Problems in Banach Spaces

Hammed Anuoluwapo Abass, Olawale Kazeem Oyewole*, Seithuti Philemon Moshokoa, Abubakar Adamu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

This paper explores the iterative approximation of solutions to equilibrium problems and proposes a simple proximal point method for addressing them. We incorporate the golden ratio technique as an extrapolation method, resulting in a two-step iterative process. This method is self-adaptive and does not require any Lipschitz-type conditions for implementation. We present and prove a weak convergence theorem along with a sublinear convergence rate for our method. The results extend some previously published findings from Hilbert spaces to 2-uniformly convex Banach spaces. To demonstrate the effectiveness of the method, we provide several numerical illustrations and compare the results with those from other methods available in the literature.

Original languageEnglish
Article number3773
JournalMathematics
Volume12
Issue number23
DOIs
Publication statusPublished - Dec 2024
Externally publishedYes

Keywords

  • Lyapunov function
  • banach space
  • golden ration technique
  • self-adaptive stepsize
  • variational inequalities

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