Abstract
In this paper, in view of the importance of existence and uniqueness theorems, for mappings which admit multiple fixed points we find conditions which imply a unique fixed point. Our results extend and unify several well-known fixed point theorems. We also obtain common fixed point theorems for mappings which need not satisfy any contractive condition. Since general methods for finding common fixed points of non-contractive mappings are not available, our results present a new approach in this direction. We adopt the method used in general fixed point theorems to obtain a novel solution to Rhoade's question on the existence of contractive mappings which admit discontinuity at the fixed point.
| Original language | English |
|---|---|
| Pages (from-to) | 2629-2642 |
| Number of pages | 14 |
| Journal | Journal of Nonlinear and Convex Analysis |
| Volume | 24 |
| Issue number | 12 |
| Publication status | Published - 2023 |
| Externally published | Yes |
Keywords
- Caristi-Kirk mapping
- fixed point
- k-Continuity
- weak orbital continuity
ASJC Scopus subject areas
- Analysis
- Geometry and Topology
- Control and Optimization
- Applied Mathematics