Coincidence and Fixed Point for Weakly Reciprocally Continuous Single-Valued and Multi-Valued Maps

Abstract

Abstract. In the present paper, we extend the concept of Weak Reciprocal Continuity for a hybrid pair of single-valued and multi-valued maps and introduce pT, f q-completeness of the space. Further, we establish some results on the existence of coincidence and fixed points for the hybrid pair of maps. Our results generalize several well known results available in the literature.

Coincidence and Common Fixed Points of Weakly Reciprocally Continuous and Compatible Hybrid Mappings via an Implicit Relation and an Application

“…In 2002, Singh and Mishra [20] extended the notion of reciprocal continuity (due to Pant [12]) to a hybrid pair of mappings and established some common fixed point theorems in metric spaces. Most recently, Gairola et al [5] defined a more general notion, namely weak reciprocal continuity (due to Pant et al [13]) for a hybrid pair of mappings and proved common fixed point theorems for non-expansive mappings. The technical definitions of the earlier mentioned notions are described in the following lines.…”