Observations on relation-theoretic coincidence theorems under Boyd–Wong type nonlinear contractions

Abstract

Abstract In this article, we carry out some observations on existing metrical coincidence theorems of Karapinar et al. (Fixed Point Theory Appl. 2014:92, 2014) and Erhan et al. (J. Inequal. Appl. 2015:52, 2015) proved for Lakshmikantham–Ćirić-type nonlinear contractions involving (f,g) $(f,g)$-closed transitive sets after proving some coincidence theorems satisfying Boyd–Wong-type nonlinear contractivity conditions employing the idea of (f,g) $(f,g)$-closed locally f-transitive binary relation.

Keywords

• 47H10
• 54H25