*Correspondence: [email protected] 3Department of Mathematics, GDCW, Bosan Road, Multan, Pakistan Full list of author information is available at the end of the article Abstract In this paper, we first introduce a cyclic generalized contraction map in metric spaces and give an existence result for a best proximity point of such mappings in the setting of a uniformly convex Banach space. Then we...

Meir and Keeler in 1 considered an extension of the classical Banach contraction theorem on a complete metric space. Kirk et al. in 2 extended the Banach contraction theorem for a class of mappings satisfying cyclical contractive conditions. Eldred and Veeramani in 3 introduced the following definition. Let A and B be nonempty subsets of a metric space X. A map T : A ∪ B → A ∪ B, is a cyclic co...

The significance of fixed-point theory stems from the fact that it furnishes a unified approach and constitutes an important tool in solving equations which are not necessarily linear. On the other hand, if the fixed-point equation Tx = x does not possess a solution, it is contemplated to resolve a problem of finding an element x such that x is in proximity to Tx in some sense. Best proximity p...

*Correspondence: [email protected] 2Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia Full list of author information is available at the end of the article Abstract Given a non-self mapping from A to B, where A and B are subsets of a metric space, in order to compute an optimal approximate solution of the equation Sx = x, a best proximit...

In this paper, we present a new class of cyclic (noncyclic) α-ψ and β-ψ condensing operators survey the existence best proximity points (pairs) as well coupled in setting reflexive Busemann convex spaces. Then an application main result to study optimal solution for system differential equations is demonstrated.