Various generalizations of metric spaces and fixed point theorems (original) (raw)

2014, Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas

There have been many attempts to generalize the definition of a metric space in order to obtain possibilities for more general fixed point results. In this paper, we give a survey of recent results on reducing fixed point theorems on generalized metric spaces to fixed point theorems on metric spaces and then investigate this fact in other generalized metric spaces. We show that many generalized metric spaces are topologically equivalent to certain metric spaces or to previously generalized metric spaces. Also, the fixed point theory in these generalized metric spaces may be a consequence of the fixed point theory in certain metric spaces or in previously generalized metric spaces.

A Generalized Metric Space and Related Fixed Point Theorems

We introduce a new concept of generalized metric spaces and extend some well-known related fixed point theorems including Banach contraction principle, Ćirić's fixed point theorem, a fixed point result due to Ran and Reurings, and a fixed point result due to Nieto and Rodríguez-López. This new concept of generalized metric spaces and extend some well-known related fixed point theorems recover various topological spaces including standard metric spaces, b-metric spaces, dislocated metric spaces, and modular spaces.

On some fixed point theorems in generalized metric spaces

Fixed Point Theory and Applications

In this paper, we obtain some generalizations of fixed point results for Kannan, Chatterjea and Hardy-Rogers contraction mappings in a new class of generalized metric spaces introduced recently by Jleli and Samet (Fixed Point Theory Appl. 2015:33, 2015).

Two fixed point theorems in generalized metric spaces

International Journal of Advanced Statistics and Probability, 2016

In this paper, we prove there exists a coupled fixed point for a set-valued contraction mapping defined on X× X , where X is incomplete ordered G-metric. Also, we prove the existence of a unique fixed point for single valued mapping with respect to implicit condition defined on a complete G-metric.

On Fixed Point Theorems in Complete Metric Space

Journal of Computer and Mathematical Sciences

In this paper, some theorems concerning the existence and uniqueness of fixed point in complete metric space are established. The results of the continuity clause we reached are introduced and some of the results we obtained are circulated.

Some Common Fixed Point Theorems in Metric Spaces Under a Different Set of Conditions

The purpose of this paper is to prove some new common fixed point theorems in metric spaces for weakly compatible mapping satisfying an implicit relation under a different set of conditions, which unify and generalize most of the existing relevant fixed point theorems. While proving our results, we utilize an implicit function due to Popa et al. [Using implicit relations to prove unified fixed point theorems in metric and 2-metric spaces. Bull. Malays. Math. Sci. Soc. (2) 33 (1) (2010), 105-120] keeping in view their unifying power. Our results improve some recent results contained in Imdad and Ali [Jungck's common fixed point theorem and (E.A) property. Acta Math. Sinica, Eng. Ser. 24(1) (2008), 87-94]. Some related results and illustrative examples to highlight the realized improvements are also furnished.

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