Cauchy sequences and a Meir-Keeler type fixed point theorem in partial metric spaces.

Abstract

In this paper we prove some new conditions for Cauchy sequences by using the diameter of orbit in partial metric spaces. A fixed point theorem for Meir-Keeler type contractions in this space is established.

Some New Results on Equivalent Cauchy Sequences and Their Applications to Meir-Keeler Contraction in Partial Rectangular Metric Space

“…In [17] and [18], are proved some conditions for equivalent Cauchy sequences and Cauchy sequences in partial metric spaces.…”