Search results for "Strictly convex Banach space"
showing 3 items of 3 documents
A New Extension of Darbo's Fixed Point Theorem Using Relatively Meir-Keeler Condensing Operators
2018
We consider relatively Meir–Keeler condensing operators to study the existence of best proximity points (pairs) by using the notion of measure of noncompactness, and extend a result of Aghajani et al. [‘Fixed point theorems for Meir–Keeler condensing operators via measure of noncompactness’, Acta Math. Sci. Ser. B35 (2015), 552–566]. As an application of our main result, we investigate the existence of an optimal solution for a system of integrodifferential equations.
Cyclic (noncyclic) phi-condensing operator and its application to a system of differential equations
2019
We establish a best proximity pair theorem for noncyclic φ-condensing operators in strictly convex Banach spaces by using a measure of noncompactness. We also obtain a counterpart result for cyclic φ-condensing operators in Banach spaces to guarantee the existence of best proximity points, and so, an extension of Darbo’s fixed point theorem will be concluded. As an application of our results, we study the existence of a global optimal solution for a system of ordinary differential equations.
A best proximity point approach to existence of solutions for a system of ordinary differential equations
2019
We establish the existence of a solution for the following system of differential equations (y x ′′((t t ) ) = = g f ((t t ,y x ((t t )) )) ,y x ((t t 0 0) ) = = x x *** in the space of all bounded and continuous real functions on [0, +∞[. We use best proximity point methods and measure of noncompactness theory under suitable assumptions on f and g. Some new best proximity point theorems play a key role in the above result.