Abstract
In the present work, we consider the best proximal problem related to a coupled mapping, which we define using control functions and weak inequalities. As a consequence, we obtain some results on coupled fixed points. Our results generalize some recent results in the literature. Also, as an application of the results obtained, we present the solution to a system of a coupled Fredholm nonlinear integral equation. Our work is supported by several illustrations.
Highlights
The idea of weak contraction in Hilbert spaces given by Alber et al [4] and extended by Rhoades [3]
We investigate the coupled proximity point in ordered metric spaces associated with a weak inequality
We provide a suitable illustration which satisfies the coupled best proximity point result
Summary
The contraction mapping principle is one of the pioneering ideas of mathematics associated with physical as well as mathematical endeavors. Many discussions related with the existence of fixed point through the consideration of order relation with the underneath metric and of best approximation are investigated in [2,20,27,28,29,30,31,32,33,34,35,36,37,38]. Contraction mapping procedures have been continuously employing in differential equations and integral equations as cornerstone instruments to prove the existence of related solutions (see [39,40,41]). We investigate the coupled proximity point in ordered metric spaces associated with a weak inequality. We provide a suitable illustration which satisfies the coupled best proximity point result
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