Theoretical Mathematics & Applications

Theorems On Best Proximity Points For Generalized Rational Proximal Contractions

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• Abstract

  If the fixed point equation Tx = x does not posses a solution, then the natural interest is to find an element x € X such that x is in proximity to Tx in some sense. In other words, we would like to get a desirable estimate for the quantity d(x; Tx) . In this paper, we prove best proximity point theorems for generalized rational proximal contraction of the first and second kinds. We also prove a best proximity point theorem for nonself mapping for generalized rational proximal contraction of the first and second kinds without assuming the continuity. Our results unify, generalize various known comparable results from the current literature [6, 7] .