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A New Kind Of $F$-Contraction And Some Best Proximity Point Results For Such Mappings With An Application, Hakan Şahi̇n
A New Kind Of $F$-Contraction And Some Best Proximity Point Results For Such Mappings With An Application, Hakan Şahi̇n
Turkish Journal of Mathematics
In this paper, we aim to present a new and unified way, including the previously mentioned solution methods, to overcome the problem in [7] for closed and bounded valued $F$-contraction mappings. We also want to obtain a real generalization of fixed point results existing in the literature by using best proximity point theory. Further, considering the strong relationship between homotopy theory and various branches of mathematics such as category theory, topological spaces, and Hamiltonian manifolds in quantum mechanics, our objective is to present an application to homotopy theory of our best proximity point results obtained in the paper. In this …
Nonunique Best Proximity Point Results With An Application To Nonlinear Fractional Differential Equations, Mustafa Aslantaş
Nonunique Best Proximity Point Results With An Application To Nonlinear Fractional Differential Equations, Mustafa Aslantaş
Turkish Journal of Mathematics
In this paper, we point out an error in proving famous Achari type nonunique fixed point results. Also, we prove some best proximity point results in $b$ -metric spaces by introducing new concepts. Hence, we develop some results existing in the literature. Finally, we give a result for the existence of the solution of nonlinear fractional differential equations.