# Proximal quasi-normal structure and existence of best proximity points

## TL;DR

This paper introduces the concept of proximal quasi-normal structure to establish the existence of best proximity points across various classes of mappings, thereby generalizing recent results in the field.

## Contribution

It extends the theory of best proximity points by applying proximal quasi-normal structure to a broad range of mappings, unifying and generalizing previous findings.

## Key findings

- Existence of best proximity points established for cyclic mappings
- Generalization of recent results in proximity point theory
- Application to various nonexpansive and orbitally nonexpansive mappings

## Abstract

In this paper, we use the concept of proximal quasi-normal structure (P. Q-N. S) to study the existence of best proximity points for cyclic mappings, cyclic contractions, relatively Kannan nonexpansive mappings, as well as for orbitally nonexpansive mappings. In this way, we generalize several recent results obtained by others.