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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 principal object of this paper is to present new contractive type condition for mappings defined on G-metric spaces. Further, we prove some new fixed point theorems concerning these mappings in G-metric space. Particular cases and examples to illustrate and support our results are also considered. Our findings extend and unify a known results. [ABSTRACT FROM AUTHOR]

The purpose of this paper is threefold. Firstly, recognizing the concept of Piri and Kumam (Fixed Point Theor Appl 210, 2014), we define generalized F-contractive mappings in the framework of G-metric spaces and by employing this, some fixed point theorems in the structure of G-metric spaces are established that can not be obtained from the existing results in the context of allied metric spaces and do not meet the remarks of Samet et al. (Int J Anal. Article ID 917158, 2013) and Jleli et al. (Fixed Point Theor Appl 210, 2012). Infact, we utilize the pattern, mentioned in Karapinar and Agrawal (Fixed Point Theor Appl 154, 2013), a counter paper to remarks of Samet et al. (Int J Anal. Article ID 917158, 2013) and Jleli et al. (Fixed Point Theor Appl 210, 2012). Secondly, in the setting of G-metric spaces, certain fixed point results for integral inequalities under generalized F-contraction are presented. Finally, as an application, our results are utilized to establish the existence and uniqueness of solution the equations arising in Oscillation of a spring. In the sequel, another application is given to set-up the existence and uniqueness of solution of functional equations occurring in dynamic programming. Our investigations are also authenticated with the aid of some appropriate and innovative examples. [ABSTRACT FROM AUTHOR]

In this paper, we obtain unique common fixed point theorems for six weakly compatible mappings in intuitionistic generalized fuzzy metric spaces. [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 paper, we establish some fixed point theorems with the help of α-admissible mapping satisfying (ψ,Φ) contractive condition of integral type in Gb-metric space. Our results are supported by examples. [ABSTRACT FROM AUTHOR]

In this paper we introduce the concept of the best triplex common proximity point in G-metric space (X;G), as extension of the best proximity point in metric spaces. Also we provide sufficient conditions for the existence of a unique best triplex common proximity point for some mappings in complete G-metric spaces. At the end, we show that some of this results are extension of the best proximity point theorems in metric spaces. [ABSTRACT FROM AUTHOR]

In this paper we prove some common fixed point theorems for self mappings of cyclic form using the concept of generalized-distance mappings that was introduced by K. Abodaya et.al. [1] in a complete Gb-metric space in sense of A. Aghanjani et.al. [2]. [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]

Banach's contraction mapping principle is remarkable in its simplicity, yet it is perhaps the most widely applied fixed point theorem in all of analysis with special applications to the theory of differential and integral equations. Because the underlined space of this theorem is a metric space, the theory that developed following its publication is known as the metric fixed point theory. Over the last one hundred years, many people have tried to generalize the definition of a metric space. In this paper, we survey the most popular generalizations and we discuss the recent uptick in some generalizations and their impact in metric fixed point theory. [ABSTRACT FROM AUTHOR]

In this paper, we prove several fixed point results for mappings of Caristi type in the setting of G-metric spaces. [ABSTRACT FROM AUTHOR]

In this paper, we prove fixed point theorem for a contractive map-ping which satisfy property P in Gb-metric space. Our results are supported by an example. [ABSTRACT FROM AUTHOR]

In this paper we extend some results of fixed points for asymptotically regular mappings on a complete G-metric spaces by using new approach. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notions of G-uniform continuity and G-Cauchy continuity of a function defined from one generalized metric space to another generalized metric space. Also, we investigate the relationships between these two types continuity and ordinary continuity. Further, we give some special properties of G-Cauchy sequences and G-totally bounded sets. [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 2006, Mustafa and Sims [18-19] introduced an improved version of the generalized metric space structure which they called G-metric spaces and in 2011; Berinde and Borcut [11] introduced the concept of triple fixed point. The intent of this paper is to establish some tripled fixed point theorems for mappings having mixed monotone property under nonlinear type contractions depended on another function in the framework of a G-metric space X enclosed with partial order. The presented results generalize, improve and extend corresponding results of H. Aydi et al. [13] (Tripled Fixed Point Results in Generalized Metric Spaces" Journal of Applied Mathematics Volume 2012, Article ID 314279, 10 pages, doi:10.1155/2012/314279). Moreover, some examples are provided to illustrate the usability of the obtained results. [ABSTRACT FROM AUTHOR]

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]