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Caristi type and meir-keeler type fixed point theorems
- Source :
- Filomat. 33:3711-3721
- Publication Year :
- 2019
- Publisher :
- National Library of Serbia, 2019.
-
Abstract
- 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.
- Subjects :
- Pure mathematics
General Mathematics
010102 general mathematics
Fixed-point theorem
Fixed point
Type (model theory)
01 natural sciences
010101 applied mathematics
Discontinuity (linguistics)
Metric space
Caristi fixed-point theorem
Intersection
0101 mathematics
Completeness (statistics)
Mathematics
Subjects
Details
- ISSN :
- 24060933 and 03545180
- Volume :
- 33
- Database :
- OpenAIRE
- Journal :
- Filomat
- Accession number :
- edsair.doi...........5bae1e81910247179dd09c523665f352