Open AccessMeir-Keeler type and Caristi type fixed point theorems
Author(s) -
Abhijit Pant,
Neeraj Pant,
Vladimir Rakočević
Publication year - 2019
Publication title -
applicable analysis and discrete mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.69
H-Index - 26
eISSN - 2406-100X
pISSN - 1452-8630
DOI - 10.2298/aadm181224037p
Subject(s) - mathematics , type (biology) , fixed point theorem , fixed point , discontinuity (linguistics) , discrete mathematics , pure mathematics , mathematical analysis , biology , ecology
Agarwal et al [1] have proved some interesting local and global fixed point theorems for Meir-Keeler [7] type and Caristi [2] type maps. We obtain analogues of the main results of Agarwal et al [1] under weaker conditions so as to include continuous as well as discontinuous maps. Our results provide new answers to Rhoades' problem ([15], p. 242) on existence of contractive definitions which admit discontinuity at the fixed point. Several examples are given to illustrate our results.