Generalized Cyclic p-Contractions and p-Contraction Pairs Some Properties of Asymptotic Regularity Best Proximity Points, Fixed Points

This paper studies a general p-contractive condition of self-mapping T on X, where X ,d is either metric space or dislocated space, which combines the contribution to upper-bound dTx , Ty, x and y are arbitrary elements in weighted combination distances dx,y dx,Tx,dy,Ty,dx,Ty,dy,Tx, dx,Tx−dy,Ty dx,Ty−dy,Tx. The asymptotic regularity convergence Cauchy sequences unique fixed point also discussed if X,d complete. Subsequently, T, S generalized cyclic p-contraction pairs pair non-empty, general, disjoint subsets X. proposed contraction involves several associated with S-pair. Some properties demonstrated are: (a) relevant best proximity points both sets proved; (b) involved closed convex, norm induced, uniformly convex Banach space. It can be pointed out that metric-like (or metric) possess symmetry property since their respective distance values for any given corresponding identical after exchanging roles elements.