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In this paper, we define g-convergence and g-Cauchy of double sequences in g-metric spaces. Also we prove that g-limit is unique and every g-convergent double sequence is a g-Cauchy sequence. Additionally g-statistical convergence of double sequences is introduced and the theorem giving the relationship between statistical convergence and strongly Cesáro summability in a g-metric space is demonstrated. Further, we put forward the notations of g-lacunary statistical convergence and g-strongly lacunary convergence of double sequences and we also present some inclusion theorems. [ABSTRACT FROM AUTHOR]

The aim of this paper is to define the concepts of remotest points and approximate remotest points in G-metric spaces and obtain some existence results on these concepts. In particular, we define G-remotest points and G - ϵ-approximate remotest points by considering a cyclic map and prove some results in G-metric spaces. [ABSTRACT FROM AUTHOR]

In this article, we provide a fixed point theory for Generalized Neutrosophic Metric Spaces (GNMS) and present generalized ((ψ - φ)- contracting principle. Numerous modern fixed point concepts have been generalized as well as extended by what we have found. We support our argument with a specific example. [ABSTRACT FROM AUTHOR]

Sedghi et al. (Mat. Vesn. 64(3):258-266, 2012) introduced the notion of a S-metric as a generalized metric in 3-tuples $S:X^{3} \rightarrow[0,\infty)$, where X is a nonempty set. The aim of this paper is to introduce the concept of an n-tuple metric $A: X^{n} \rightarrow[0,\infty)$ and to study its basic topological properties. We also prove some generalized coupled common fixed point theorems for mixed weakly monotone maps in partially ordered A-metric spaces. Some examples are presented to support the results proved herein. Our results generalize and extend various results in the existing literature. [ABSTRACT FROM AUTHOR]

The aim of this paper is to define the concepts of remotest points and approximate remotest points in G-metric spaces and obtain some existence results on these concepts. In particular, we define G-remotest points and G-ϵ-approximate remotest points by considering a cyclic map and prove some results in G-metric spaces.

In this paper first of all, we introduce the mapping : [0;1) X [0;1) R,called the simulation function and the notion of Z-contraction with respect to which generalize several known types of contractions. Secondly, we prove certain xed point theorems using simulation functions in G-Metric spaces. An example is also given to support our result.

In this paper, we use the concepts of (A;B)-weakly increasing mappings and altering distance functions to establish new contractive conditions for the pair of mappings in the setting of G-metric spaces. Many Fixed and common Fixed point results in the setting of G{metric spaces are formulated. Note that our new contractive conditions can't be reduces to contractive conditions in standard metric spaces.

In the following article we have introduced generalized multivalued α-ψ-contractive type mappings and multi-valued (θ, L)-weakly contractive mappings in G-metric spaces and have established common fixed point results for the concerned contractive mappings. We have also proved some coincidence point theorems for multivalued G-α-admissible mappings and relations. Some examples are also included in the support of these results. Our results can not be derived directly from fixed point theorems on metric or qusai-metric spaces as discussed by Jleli et al. in [21] and Azam et al. in [9]. An interesting application is also added to evaluate the solution of hyperbolic differential inclusion. [ABSTRACT FROM AUTHOR]