Abstract
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.
Original language | English |
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Pages (from-to) | 849-858 |
Number of pages | 10 |
Journal | Applicable Analysis and Discrete Mathematics |
Volume | 13 |
Issue number | 3 |
DOIs | |
Publication status | Published - 1 Dec 2019 |
Externally published | Yes |
Keywords
- Caristi type maps
- Contractive mappings
- Fixed point
- K-continuity
ASJC Scopus subject areas
- Analysis
- Discrete Mathematics and Combinatorics
- Applied Mathematics