DOI: 10.24193/fpt-ro.2020.2.45

Authors: G. Sankara Raju Kosuru

Abstract: In this paper we consider the following system of differential equations, where f, g are bounded L¹ functions defined on a rectangle in ℝ². We give sufficient conditions for the existence of two functions φ and ψ, on an interval I containing x₀, such that for all x ∈ I. To establish the same, we introduce a notation of c-cyclic contractive mapping and prove the existence of best proximity pairs for such a mapping.

Key Words and Phrases: Contraction, best proximity points, system of differential equations.

2010 Mathematics Subject Classification: 47H10, 54H25.

Published on-line: July 1st, 2020.

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