In this paper, we discuss the existence and uniqueness of fixed points for $G$-asymptotic contractions in metric spaces endowed with a graph. The result given here is a new version of Kirk's fixed point theorem for asymptotic contractions in metric spaces endowed with a graph. The given result here is a generalization of fixed point theorem for asymptotic contraction from metric s paces to metr...

Abstract. In this paper, we introduce contractive conditions of integral type in the setting of dislocated quasi b-metric spaces. Using contractive conditions of integral type, we have presented a fixed point theorem in the framework of dislocated quasi b-metric spaces. Our established result generalize and extend various fixed point theorems of the literature in the context of dislocated quasi...

The main purpose of this research is to extend some fixed point results in orthogonal metric spaces. For this purpose, first, we investigate new mappings in this spaces. We introduce the new notions of functions. Then by using it, we define contractive mappings and then we establish and prove some fixed point theorems for such mappings in orthogonal metric spaces. Then by utilizing examples of ...

In this work‎, ‎we formulate Chatterjea contractions using graphs in metric spaces endowed with a graph ‎‎and‏ ‎‎‎‎investigate ‎the ‎existence‎ ‎of ‎fixed ‎points ‎for such mappings ‎under two different hypotheses‎. We also discuss the uniqueness of the fixed point. The given result is a generalization of Chatterjea's fixed point theorem from metric spaces to metric spaces endowed with a graph.

In this paper, we introduce a new class of implicit functions and also common property (E.A) in modified intuitionistic fuzzy metric spaces and utilize the same to prove some common fixed point theorems in modified intuitionistic fuzzy metric spaces besides discussing related results and illustrative examples. We are not aware of any paper dealing with such implicit functions in modified intuit...

The existing literature of fixed point theory contains many results enunciating fixed point theorems for self-mappings in metric and Banach spaces. Recently, Huang and Zhang [4] introduced the concept of cone metric spaces which generalized the concept of the metric spaces, replacing the set of real numbers by an ordered Banach space, and obtained some fixed point theorems for mapping satisfyin...

In this paper, we present some fixed and coincidence point theorems for hybrid rational Geraghty contractive mappings in partially ordered $b$-metric spaces. Also, we derive certain coincidence point results for such contractions. An illustrative example is provided here to highlight our findings.

In this paper, we discuss the existence and uniqueness of points of coincidence and common fixed points for a pair of self-mappings satisfying some generalized contractive type conditions in $b$-metric spaces endowed with graphs and altering distance functions. Finally, some examples are provided to justify the validity of our results.

For a class of fuzzy metric spaces (in the sense of George and Veeramani) with an H-type t-norm,  we present a method to construct a metric on a  fuzzy metric space. The induced metric space shares many important properties with the given fuzzy metric space.  Specifically, they generate the same topology, and have the same completeness. Our results can give the constructive proofs to some probl...

In this paper, we propose a new definition of intuitionistic fuzzyquasi-metric and pseudo-metric spaces based on intuitionistic fuzzy points. Weprove some properties of intuitionistic fuzzy quasi- metric and pseudo-metricspaces, and show that every intuitionistic fuzzy pseudo-metric space is intuitionisticfuzzy regular and intuitionistic fuzzy completely normal and henceintuitionistic fuzzy nor...