Abstract
In this paper, motivated by the recent work [Journal of Nonlinear Sciences and Applications, 10(4):1544–1537] some generalized nonlinear contractive conditions via implicit functions and α-admissible pairs of multi-valued mappings in the setting of b-metric like spaces have been introduced. Some common fixed point results for such mappings in this framework have been provided. Then, some corollaries and consequences for our obtained results are given. Our results are the multi-valued versions of [Journal of Nonlinear Sciences and Applications, 10(4):1544–1537]. An example also is provided to support our obtained results. The presented results generalize and extend some earlier results in the literature.
Highlights
Fixed point theory is one of applicable mathematical research fields
Fixed point theory is one of mathematical research fields which deals with existence and uniqueness of fixed points, coincidence points and common fixed points of 1 or more than 1 mappings defined on metric spaces and generalized metric spaces such as b-metric spaces, partial metric spaces, metric like spaces etc
We introduce α-implicit contractive pair of multi-valued mappings on b-metric like spaces and establish common fixed point results for our presented mappings
Summary
Fixed point theory is one of applicable mathematical research fields. The obtained results in this field will apply to find solutions for integral equations, differential equations and matrix equations. Before starting the topic of this paper it is worth to recall some recent works in fixed point theory. Xu, Tang, Yang, and Srivastava (2016) obtained sharp estimates of the classical boundary Schwarz lemma involving the boundary fixed points for holomorphic functions which map the unit disk in C into itself. Srivastava, Bedre, Khairnar, and Desale (2014a, 2014b) obtained some hybrid fixed point theorems of Krasnoselskii type, which involve product of two operators in partially ordered normed linear spaces and applied their results to proving the existence of solutions for fractional integral equations under certain monotonicity conditions
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