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Citation - WoS: 34
Citation - Scopus: 38
Results in Wt-Distance Over B-Metric Spaces
(Mdpi, 2020) Chifu, Cristian; Karapinar, Erdal
In this manuscript, we introduce Meir-Keeler type contractions and Geraghty type contractions in the setting of the wt-distances over b-metric spaces. We examine the existence of a fixed point for such mappings. Under some additional assumption, we proved the uniqueness of the found fixed point.
Citation - WoS: 201
Citation - Scopus: 178
On the Solution of a Boundary Value Problem Associated With a Fractional Differential Equation
(Wiley, 2024) Aksoy, Umit; Karapinar, Erdal; Erhan, Inci M.; Adiguzel, Rezan Sevinik; Sevinik Adigüzel, Rezan
The problem of the existence and uniqueness of solutions of boundary value problems (BVPs) for a nonlinear fractional differential equation of order 2 < alpha <= 3 is studied. The BVP is transformed into an integral equation and discussed by means of a fixed point problem for an integral operator. Conditions for the existence and uniqueness of a fixed point for the integral operator are derived via b-comparison functions on complete b-metric spaces. In addition, estimates for the convergence of the Picard iteration sequence are given. An estimate for the Green's function related with the problem is provided and employed in the proof of the existence and uniqueness theorem for the solution of the given problem. Illustrative examples are presented to support the theoretical results.

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