In this paper, we prove a common fixed point theorem for noncompatible maps in probabilistic metric space using implicit relation. Our result does not require either the completeness of the space or continuity of the maps. Full text

A criterion for a spacelike hypersurface in a conformally stationary spacetime to be a Cauchy hypersurface is given. The criterion is based on the forward and the backward completeness of a non-reversible Finsler metric associated to the hypersurface.

‎Inspired by the work of Suzuki in‎ ‎[T. Suzuki‎, ‎A generalized Banach contraction principle that characterizes metric completeness‎, Proc‎. ‎Amer‎. ‎Math‎. ‎Soc. ‎136 (2008)‎, ‎1861--1869]‎, ‎we prove a fixed point theorem for contractive mappings‎ ‎that generalizes a theorem of Geraghty in [M.A‎. ‎Geraghty‎, ‎On contractive mappings‎, ‎Proc‎. ‎Amer‎. ‎Math‎. ‎Soc., ‎40 (1973)‎, ‎604--608]‎an...

A gradient Ricci soliton is a triple (M, g, f) satisfying Rij +∇i∇jf = λgij for some real number λ. In this paper, we will show that the completeness of the metric g implies that of the vector field ∇f .

In this paper, we prove several fixed point theorems, which are generalizations of the Banach contraction principle and Kannan’s fixed point theorem. Further we discuss a characterization of metric completeness.

1 I n t r o d u c t i o n Logic-based methods for representing and reasoning about temporal information have proved to be highly beneficial in the area of formal specifications. In this paper we consider their application to the specification of real-t ime systems. Timing properties play a major role in the specification of reactive and concurrent software systems that operate in real-time. The...