Abstract
PurposeThis paper aims to prove some fixed-point theorems for a general class of mappings in modular G-metric spaces. The results of this paper generalize and extend several known results to modular G-metric spaces, including the results of Mutlu et al. [1]. Furthermore, the authors produce an example to demonstrate the applicability of the results.Design/methodology/approachThe results of this paper are theoretical and analytical in nature.FindingsThe authors established some fixed-point theorems for a general class of mappings in modular G-metric spaces. The results generalize and extend several known results to modular G-metric spaces, including the results of Mutlu et al. [1]. An example was constructed to demonstrate the applicability of the results.Research limitations/implicationsAnalytical and theoretical results.Practical implicationsThe results of this paper can be applied in science and engineering.Social implicationsThe results of this paper is applicable in certain social sciences.Originality/valueThe results of this paper are new and will open up new areas of research in mathematical sciences.
Highlights
In search for the generalization of classical metric spaces, in 1966, Gahler [2], introduced the concept of 2-metric spaces and proved that its results exists
To ameliorate the drawbacks about D-metric spaces, Mustafa and Sims [5] introduced a generalization of metric spaces, which they called G-metric spaces and proved some fixed-point theorems, and in [6], Mustafa et al proved some fixed-point results on complete G-metric spaces
Our intention in this paper is to extend the fixed-point theorem of Mutlu et al [1] from the setting of modular metric spaces to modular G-metric spaces
Summary
In search for the generalization of classical metric spaces, in 1966, Gahler [2], introduced the concept of 2-metric spaces and proved that its results exists. Dhage [3] extend the work in [2] in which D-metric spaces were introduced. These authors claimed that their results generalized the concept of metric spaces. In 2003, Mustafa and Sims [4] claimed that the fundamental topological properties of D-metric spaces introduced by Dhage [3] were incorrect. To ameliorate the drawbacks about D-metric spaces, Mustafa and Sims [5] introduced a generalization of metric spaces, which they called G-metric spaces and proved some fixed-point theorems, and in [6], Mustafa et al proved some fixed-point results on complete G-metric spaces. Data availability: The data used to support the findings of this study are included within the article
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