EXISTENCE OF FIXED POINTS AND BEST PROXIMITY POINTS OF p-CYCLIC BOYD-WONG CONTRACTIONS

Abstract

We introduce a new contraction map called p-cyclic Boyd-Wongcontraction, defined on the union of p (p ≥ 2) non empty subsets of ametric space. We give sufficient conditions for the existence of a uniquefixed point, best proximity point or periodic point for the map and aniterative method is used to approximate the fixed point and the bestproximate point.variable exponents where the right-hand side f is in L q(·) , q(·) : Ω → (1, +∞). The functional setting involves anisotropic Sobolev spaces with variable exponents as well as weak Lebesgue (Marcinkiewicz) spaces with variable exponents.