Fixed point theorem for mixed monotone nearly asymptotically nonexpansive mappings and applications to integral equations. (English) Zbl 1506.54018
Summary: This work concerns the existence of a fixed point for mixed monotone nearly asymptotically nonexpansive mappings. We extend and generalize some well-known results concerning nearly asymptotically nonexpansive mappings in a uniformly convex hyperbolic metric space. As application of our results, we study the existence of solutions for an integral equation.
MSC:
| 54H25 | Fixed-point and coincidence theorems (topological aspects) |
| 54E40 | Special maps on metric spaces |
| 54F05 | Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces |
| 45G10 | Other nonlinear integral equations |
Keywords:
fixed point theorem; hyperbolic metric space; integral equation mixed monotone operator; monotone nearly asymptotically nonexpansive operatorReferences:
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