Open AccessCaristi type and meir-keeler type fixed point theorems
Author(s) -
Abhijit Pant,
Neeraj Pant,
Mahesh C. Joshi
Publication year - 2019
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/fil1912711p
Subject(s) - mathematics , fixed point theorem , metric space , type (biology) , intersection (aeronautics) , fixed point , schauder fixed point theorem , discrete mathematics , complete metric space , discontinuity (linguistics) , coincidence point , pure mathematics , brouwer fixed point theorem , mathematical analysis , ecology , engineering , biology , aerospace engineering
We generalize the Caristi fixed point theorem by employing a weaker form of continuity and show that contractive type mappings that satisfy the conditions of our theorem provide new solutions to the Rhoades? problem on continuity at fixed point. We also obtain a Meir-Keeler type fixed point theorem which gives a new solution to the Rhoades? problem on the existence of contractive mappings that admit discontinuity at the fixed point. We prove that our theorems characterize completeness of the metric space as well as Cantor?s intersection property.