Orbital completeness and fixed points of (δ, k)−weak contractions

Abstract

Extension of Ciric’s (Proc. Amer. Math. Soc. N0. 45 (1974), 267 - 273) asymptotic fixed point theorem for quasi-contractions in T−orbitally complete metric spaces is obtained for the class of (δ, k)−weak contractions studied by Berinde (Carpath. J. Math. 19(1):7-22, 2003; Nonlinear Anal. Forum 9(1): 43-53, 2004). Our results are significant extensions of those of Ciric and Berinde mentioned above and numerous others in literature.