Abstract
We 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. Meir–Keeler type solutions of the Rhoades’ problem have not been reported in literature before this. Presenting a new approach, we give another solution to this problem using the set of simulation functions. To emphasize the importance of our theoretical results, we obtain two applications of the main results with some illustrative examples.
Original language | English |
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Article number | 39 |
Journal | Journal of Fixed Point Theory and Applications |
Volume | 22 |
Issue number | 2 |
DOIs | |
Publication status | Published - 1 Jun 2020 |
Externally published | Yes |
Keywords
- Fixed point
- discontinuity
- fixed circle
- fixed disc
- simulation function
ASJC Scopus subject areas
- Modeling and Simulation
- Geometry and Topology
- Applied Mathematics