In this article, in a generalized metric space, we will focus on new types of sequences. We introduce three kinds Cauchy sequences and study their significance spaces. Also, give several interesting properties these

in this paper, we prove a fixed point theorem for a pair of generalized weakly contractive mappings in complete partial metric spaces. the theorems presented are generalizations of very recent fixed point theorems due to abdeljawad, karapinar and tas. to emphasize the very general nature of these results, we illustrate an example.

In this paper, we will establish some xed point results for two pairs of self mappings satisfying generalized contractive condition by using a new concept as weak subsequential continuity with compatibility of type (E) in metric spaces, as an application the existence of unique common solution for a system of functional equations arising in system programming is proved.

In this paper, we first introduce some types of generalized $alpha$-Meir-Keeler contractions in $b$-metric-like spaces and then we establish some fixed point results for these types of contractions. Also, we present a new fixed point theorem for a Meir-Keeler contraction through rational expression. Finally, we give some examples to illustrate the usability of the obtained results.

We prove a set of fixed point theorems for mappings with ϕ-contractive iterate at a point in a class of generalized metric spaces. This is a generalization of some well-known results for Guseman and Matkowski types of fixed point results in metric and generalized metric spaces.