Abstract
In this paper, we obtain the results of coincidence and common fixed points in b-metric spaces. We work with a new type of multivalued quasi-contractive mapping with nonlinear comparison functions. Our results generalize and improve several recent results. Additionally, we give an application of the obtained results to dynamical systems.
Highlights
In this paper, we obtain the results of coincidence and common fixed points in b-metric spaces
We give the results on the existence of a point of coincidence and a common strict fixed point for a hybrid pair of single-valued and multivalued mappings defined in b-metric spaces, which satisfy quasi-contractive inequality with nonlinear comparison function
We consider a new type of multivalued quasi-contractive mapping with nonlinear comparison functions
Summary
The first result of a fixed point for quasi-contractive mappings was presented by Lj. Ćirić [1] in 1974. The result of Ćirić is the most general result with linear comparison function in metric fixed-point theory (see [2,3]). Existence and uniqueness of fixed point for quasi-contractive mapping with nonlinear comparison function on metric spaces, considered by J. The results of common fixed points as a generalization result of Ćirıć was obtained in [9] and in [10] with linear and nonlinear comparison functions, respectively. A common fixed-point result for single-valued nonlinear quasi-contractions was presented by Z. We give the results on the existence of a point of coincidence and a common strict fixed point for a hybrid pair of single-valued and multivalued mappings defined in b-metric spaces, which satisfy quasi-contractive inequality with nonlinear comparison function.
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