On metric type spaces and fixed point theorems

Abstract

In this article, we discuss some fixed point theorems in metric type spaces. The need to define such space came from the properties obtain on cone metric spaces and the connection between the two notions is clearly explained in [1]. In particular, we show that most of the new results are merely copies of the classic ones.

Fixed points of rational type contractions in G-metric spaces

“…

In this article, we prove some fixed point theorems in metric type spaces. This article is just a generalization some results previously proved in [3]. In particular, we give some coupled common fixed points theorems under weak contractions.

…”

“…Some topological properties concerning metric type spaces can be read in [3]. We recall some of these results, as we will make use of them.…”

“…Due to its importance, several authors have obtained many interesting extensions and generalizations, from single fixed point to coupled fixed point. In [3], Olaniyi et al gave a brief justification on the origin of metric type space and considered it as a suitable framework to generalize some fixed point theorems. Metric type spaces generalize the notion of metric spaces, even if both structures are very close .…”

“…We also give coupled fixed point results. For the convenience of the reader, we shall recall some definitions but for a detailed exposé of the definition and examples, the interested reader is referred to [3].…”

New Contractive Conditions for Maps in G-metric Type Spaces

“…The method builds on the convergence of an appropriate series of coefficients. Recent and similar work can also be read in [1,5,6,7,8].…”