Cone D-metric Spaces and Some Fixed Point Theorems

Zahir Mazlumi Nezhad, Hossein Lakzian

Abstract

In this paper, we introduce and study the concept of cone D-metric spaces, in which the cone does not need to be normal. Using this new notion we prove several fixed point theorems, which are generalizations of fixed point theorems by Ume [J.S. Ume, Remarks on nonconvex minimization theorems and fixed point theorems in complete D-metric spaces, Indian J. Pure Appl. Math. 32 (1) (2001) 25–36], Rhoades [B.E. Rhoades, A fixed point theorem for generalized metric spaces, Pacific J. Math. 10 (1960) 637–675] and Dhage [B.C. Dhage, Generalized metric spaces and mapping with fixed point, Bull. Calcutta Math. Soc. 84 (1992) 329–336].