Optimal pair of fixed points for a new class of noncyclic mappings under a $ (\varphi, \mathcal{R}^t) $-enriched contraction condition

Abstract

In the present study, we commenced by presenting a new class of maps, termed noncyclic $ (\varphi, \mathcal{R}^t) $-enriched quasi-contractions within metric spaces equipped with a transitive relation $ \mathcal{R}^t $. Subsequently, we identified the conditions for the existence of an optimal pair of fixed points pertaining to these mappings, thereby extending and refining a selection of contemporary findings documented in some articles. Specifically, our analysis will encompass the outcomes pertinent to reflexive and strictly convex Banach spaces.

Keywords

• optimal pair of fixed points
• noncyclic $ (\varphi
• \mathcal{r}^t) $-enriched quasi-contraction
• metric space
• transitive relation
• reflexive banach space