Common and Coupled common best proximity point theorems for proximal G\'ornicki-type pair of mappings for solving split feasibility and Variational Inequality problem

Durai, Diwakaran

doi:10.30495/maca.2026.2077351.1153

Common and Coupled common best proximity point theorems for proximal G\'ornicki-type pair of mappings for solving split feasibility and Variational Inequality problem

10.30495/maca.2026.2077351.1153

Articles in Press, Accepted Manuscript
Available Online from 07 June 2026

Mathematical Analysis and its Contemporary Applications

Document Type : Original Article

Author

Diwakaran Durai

Peri College of Arts and Science

Abstract

In this paper, we introduce a new mapping called a proximal Gornicki type pair of mappings and prove the existence of common best proximity point theorems for such mappings without assuming continuity. We further prove the common best proximity point theorem for proximal enriched type pair of mappings and demonstrate the existence of the coupled common best proximity points theorem for such mappings in the literature. As applications of our main fixed point theorems, we present two Krasnoselskij projection-type algorithms
for solving split feasibility problems and variational inequality problems.

Keywords

common best proximity points

proximal G\'ornicki mappings

proximal enriched contraction

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