On the Best Proximity Points for p–Cyclic Summing Contractions

Abstract

<jats:p>We present a condition that guarantees the existence and uniqueness of fixed (or best proximity) points in complete metric space (or uniformly convex Banach spaces) for a wide class of cyclic maps, called p–cyclic summing maps. These results generalize some known results from fixed point theory. We find a priori and a posteriori error estimates of the fixed (or best proximity) point for the Picard iteration associated with the investigated class of maps, provided that the modulus of convexity of the underlying space is of power type. We illustrate the results with some applications and examples.</jats:p>

On the Admissibility of the Fixed Points Set of a Mapping with Respect to Another Mapping

“…Some extensions and generalizations of the obtained result in [5] can be found in [6][7][8][9][10][11][12] (see also the references therein). Some recent results related to fixed point theory in partial metric spaces can be found in [13][14][15][16] (see also the references therein).…”