Coincidence and common fixed points of weakly reciprocally continuous and compatible hybrid mappings via an implicit relation and an application

Sunny Chauhan; Mohammad Imdad; Zoran Kadelburg; Calogero Vetro

doi:10.5644/SJM.11.1.06

Authors

Sunny Chauhan Near Nehru Training Center, Uttar Pradesh, India
Mohammad Imdad Department of Mathematics, Aligarh Muslim Univeristy, Aligarh, India
Zoran Kadelburg Faculty of Mathematics, University of Belgrade, Beograd, Serbia
Calogero Vetro Dipartimento di Matematica e Informatica, Universita degli Studi di Palermo, Palermo, Italy

DOI:

https://doi.org/10.5644/SJM.11.1.06

Keywords:

Hybrid pair of mappings, compatible mappings, non-compatible mappings, weak reciprocal continuity, coincidence point, common fixed point, implicit relation

Abstract

Using the hybrid version of the notion of weakly reciprocally continuous pairs of mappings due to Gairola et al. [Coincidence and fixed point for weakly reciprocally continuous single-valued and multi-valued maps, Demonstratio Math. (2013/2014), accepted], we prove a coincidence and common fixed point theorem for a hybrid pair of compatible mappings via an implicit relation. Our main result improves and generalizes a host of previously known theorems. As an application, we give a homotopy theorem which supports our main result.

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