Open AccessA unified common fixed point theorem for a family of mappings
Author(s) -
Vijay Dalakoti,
Ravindra K. Bisht,
Neeraj Pant,
C Mahesh Joshi
Publication year - 2021
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2103759d
Subject(s) - mathematics , fixed point theorem , fixed point , coincidence point , metric space , type (biology) , discrete mathematics , set (abstract data type) , least fixed point , point (geometry) , pure mathematics , schauder fixed point theorem , brouwer fixed point theorem , mathematical analysis , computer science , geometry , ecology , biology , programming language
The main objective of the paper is to prove some unified common fixed point theorems for a family of mappings under a minimal set of sufficient conditions. Our results subsume and improve a host of common fixed point theorems for contractive type mappings available in the literature of the metric fixed point theory. Simultaneously, we provide some new answers in a general framework to the problem posed by Rhoades (Contemp Math 72, 233-245, 1988) regarding the existence of a contractive definition which is strong enough to generate a fixed point, but which does not force the mapping to be continuous at the fixed point. Concrete examples are also given to illustrate the applicability of our proved results.