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The goal of this research article is to study some fixed point results in dislocated quasi metric spaces. These results are proved for certain generalized contraction conditions involving linear and rational expressions. Our results extend and generalize some of the well-known fixed point results of the literature available in fixed point theory. Suitable examples of the established results are also given. [ABSTRACT FROM AUTHOR]

Recently, the fixed-point theorem for fuzzy contractive mappings has been investigated within the framework of intuitionistic fuzzy metric-like spaces. This interesting topic was explored through the utilization of G-Cauchy sequences as defined by Grabiec. The aim of this study is to enhance the aforementioned results in a few aspects. Initially, the proof of the fixed-point theorem is simplified and condensed, allowing for potential generalization to papers focusing on similar fixed-point analyses. Furthermore, instead of G-Cauchy sequences, the classical Cauchy sequences proposed by George and Veeramani are examined, incorporating an additional condition on the fuzzy metric. Within this context, a solution to an old unresolved question posed by Gregory and Sapena is provided. The findings are reinforced by relevant examples. Finally, the introduced fuzzy metrics are applied to the field of image processing. [ABSTRACT FROM AUTHOR]

In the framework of Gb-metric spaces, we introduce the concept of a generalized Ćirić-type contraction and obtain several fixed-point theorems for this contraction. First, we present a significant lemma, which is used to ensure that the Picard sequence is a Cauchy sequence. Using this lemma, we establish three fixed-point theorems satisfying different conditions. Second, we construct new examples to illustrate our results. As applications, we deduce the famous Ćirić fixed-point theorem in terms of b-metric spaces using our results. In addition, we obtain Reich-type contraction fixedpoint theorems in such a space using the aforementioned lemma. Our results improve and complement many recent findings. In particular, we substantially enlarge the range of the contraction constant in our results. Finally, we consider the existence and uniqueness of solutions for integral equation applying our new results. [ABSTRACT FROM AUTHOR]

This paper is devoted to showing the relevance of the notion of completeness used to establish a fixed point theorem in fuzzy metric spaces introduced by Kramosil and Michalek. Specifically, we show that demanding a stronger notion of completeness, called p-completeness, it is possible to relax some extra conditions on the space to obtain a fixed point theorem in this framework. To this end, we focus on a fixed point result, proved by Mihet for complete non-Archimedean fuzzy metric spaces (Theorem 1). So, we define a weaker concept than the non-Archimedean fuzzy metric, called t-strong, and we establish an alternative version of Miheţ's theorem for p-complete t-strong fuzzy metrics (Theorem 2). In addition, an example of t-strong fuzzy metric spaces that are not non-Archimedean is provided. [ABSTRACT FROM AUTHOR]

The purpose of this work is to define the generalized b-Menger spaces and prove a fixed point theorem in this new setting. As application, we establish the existence and uniqueness of a solution for Volterra type integral equation. Our results extend and generalize the existing results in literature. [ABSTRACT FROM AUTHOR]

S-metric space is a relatively new concept in the literature and currently there is much attention being given to the generalization of S-metric spaces and fixed point theory in these spaces. Recently, the concept of S-Menger spaces was introduced in the literature as a generalization of both S-metric spaces and Menger spaces. Combinations of Banach and Kannan type contractions are very much important to find fixed point results and there are very few works on S-metric spaces that includes both of these type contractions. In this paper, we present a fixed point result in S-Menger spaces that includes both Banach type contractions and Kannan type contractions. We have also deduced some corollaries from our result and provided examples to validate our work. [ABSTRACT FROM AUTHOR]

Partial metrics constitute a generalization of classical metrics for which self-distance may not be zero. They were introduced by S.G. Matthews in 1994 in order to provide an adequate mathematical framework for the denotational semantics of programming languages. Since then, different works were devoted to obtaining counterparts of metric fixed-point results in the more general context of partial metrics. Nevertheless, in the literature was shown that many of these generalizations are actually obtained as a corollary of their aforementioned classical counterparts. Recently, two fuzzy versions of partial metrics have been introduced in the literature. Such notions may constitute a future framework to extend already established fuzzy metric fixed point results to the partial metric context. The goal of this paper is to retrieve the conclusion drawn in the aforementioned paper by Haghia et al. to the fuzzy partial metric context. To achieve this goal, we construct a fuzzy metric from a fuzzy partial metric. The topology, Cauchy sequences, and completeness associated with this fuzzy metric are studied, and their relationships with the same notions associated to the fuzzy partial metric are provided. Moreover, this fuzzy metric helps us to show that many fixed point results stated in fuzzy metric spaces can be extended directly to the fuzzy partial metric framework. An outstanding difference between our approach and the classical technique introduced by Haghia et al. is shown. [ABSTRACT FROM AUTHOR]

In this paper, we introduce an interesting extension of the b-metric space called b-metric-like space. We investigate some contraction mapping in partial b-metriclike space and prove the existence of fixed point of this mapping in partial b-metric-like space under some conditions. [ABSTRACT FROM AUTHOR]

In this paper, we have established some new results by extending some existing theorems in the setting of Digital Metric Space. We also proved some results in Digital Metric Space which were established earlier in the context of Complete Metric Space by different authors. [ABSTRACT FROM AUTHOR]

Introduction/purpose: This paper considers, generalizes and improves recent results on fixed points in rectangular metric spaces. The aim of this paper is to provide much simpler and shorter proofs of some new results in rectangular metric spaces. Methods: Some standard methods from the fixed point theory in generalized metric spaces are used. Results: The obtained results improve the well-known results in the literature. The new approach has proved that the Picard sequence is Cauchy in rectangular metric spaces. The obtained results are used to prove the existence of solutions to some nonlinear problems related to chemical sciences. Finally, an open question is given for generalized contractile mappings in rectangular metric spaces. Conclusions: New results are given for fixed points in rectangular metric spaces with application to some problems in chemical sciences. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study a common fixed point results in dislocated quasi metric spaces. We will prove common fixed point results for some new types of contractile conditions which generalize, modify and unify some existing well known fixed point results in the literature. Moreover, a particular example is given here to elucidate the usability of our establish results. We have noticed that by using our results some fixed point theorems in the context of dislocated quasi metric spaces can be deduced. [ABSTRACT FROM AUTHOR]

Introduction/purpose: This paper establishes some new results of Piri–Kumam–Dung-type mappings in a complete metric space.Тhe goal was to improve the already published results. Methods: Using the property of a strictly increasing function as well as the known Lemma formulated in (Radenović et al, 2017), the authors have proved that a Picard sequence is a Cauchy sequence. Results: New results were obtained concerning the F – contraction mappings of S in a complete metric space. To prove it, the authors used only property (W1). Conclusion: The authors believe that the obtained results represent a significant improvement of many known results in the existing literature. [ABSTRACT FROM AUTHOR]

In this paper we have established a fixed point theorem in 2-metric space, using a more general rational type contraction. Here we have extended the result of Olatinwo et. al [14] in 2-metric space. [ABSTRACT FROM AUTHOR]

This paper consists of several fixed point theorems in the fuzzy b-metric spaces. As an important result, we give a sufficient condition for a sequence to be Cauchy in the fuzzy b-metric space. Thus we simplify the proofs of many fixed point theorems in the fuzzy b-metric spaces with the well-known contraction conditions. [ABSTRACT FROM AUTHOR]

The reason of this paper is to earn fixed point theorem on six metric spaces using contractive type mapping. This theorem generalizes the results given in [7]. [ABSTRACT FROM AUTHOR]

We consider the dislocated quasi metric spaces satisfying certain rational inequalities. We therefore establish some new results related to fixed points. In order to illustrate the existence of the fixed points, we construct some examples in this paper. [ABSTRACT FROM AUTHOR]

In this paper are given some features and important results in the fuzzy metric space. The results that are presented are related to the fixed point in the fuzzy metric space. The theorems which are elaborated provide the existence and uniqueness of the fixed point in the complete fuzzy metric space. The proof of which is done by using Cauchy sequence. Also are given results for the fixed point in the compact fuzzy metric spaces. All these results are explained by concrete examples that once also present their application. [ABSTRACT FROM AUTHOR]

In this paper, we present a new class of pseudo Picard operators in the setting of generalized metric spaces introduced recently in [M. JLELI AND B. SAMET: A generalized metric space and related fixed point theorems, Fixed Point Theory Appl., (2015) 2015:61]. An example is provided to illustrate the main result. [ABSTRACT FROM AUTHOR]

In this paper some fixed point theorems for two pairs of absorbing mappings satisfying an implicit relation are proved, which extend Theorem 5 [21] to two pairs of mappings. As application, a general fixed point theorem for a sequence of mappings in partial metric spaces is obtained. [ABSTRACT FROM AUTHOR]

In this paper, using the concept of w-distance we prove some results on the existence of fixed points for contractive type operators, namely; (α, µ)-ψ-contractive operators. Applications are also presented. Our results improve and generalize a number of known results of fixed point theory including the recent results of Guran and Bota [Guran, L. and Bota, M.-F., Ulam-Hyers Stability Problems for Fixed Point Theorems concerning α-ψ-Type Contractive Operators on KST-Spaces, Submitted in press.] and Ansari [Ansari, A. H. and Shukla, S., Some fixed point theorems for ordered F-(F, h)-contraction and subcontractions in θ-f-orbitally complete partial metric spaces, J. Adv. Math. Stud., 9 (2016), No. 1, 37-53]. [ABSTRACT FROM AUTHOR]

We use results from theory of nonexpansive mappings to unify and deduce the recent results of Lin and Takahashi (Positivity 16:429-453, 2012) and of Takahashi (J Optim Theory Appl 157:781-802, 2013). [ABSTRACT FROM AUTHOR]

We introduce a new concept of α-fuzzy H-contractive mapping which is essentially weaker than the class of fuzzy contractive mapping and stronger than the concept of α-ϕ-fuzzy contractive mapping. For this type of contractions, the existence and uniqueness of fixed point in fuzzy M-complete metric spaces is also established. [ABSTRACT FROM AUTHOR]

We introduce the concept of semicompleteness on semimetric space, which is weaker than completeness. We prove fixed point theorems for contractions in semicomplete semimetric spaces. Also, we generalize Jachymski-Matkowski-Świątkowski's fixed point theorem in semimetric spaces. [ABSTRACT FROM AUTHOR]

The purpose of this article is to introduce a new class of b-Reichtype multi-valued contraction on complete b-metric spaces endowedwith a graph satisfying the g-graph preserving condition and obtaifixed point results for such classes of contractions. Our results-generalize and extend several well known comparable results. Some-examples are given to illustrate the usability of our results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of generalised S -- β -- ψ contractive type mappings. For these mappings we prove some fixed point theorems in the setting of S-metric space. [ABSTRACT FROM AUTHOR]

In this paper, we discuss unique fixed point results for mappings satisfying contractive condition via C-class functions for a complete dislocated Gd-metric space. Example is also given which shows the novelty of our work. Our results improve/generalize several well known recent and classical results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the existence and uniqueness of a fixed point of certain contraction via auxiliary functions in the context of complete Branciari metric spaces endowed with a transitive binary relation. Our results unify and extend some existing fixed point results in the related literature. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the existence and uniqueness of a fixed point in a dislocated quasi-metric space. Several fixed point theorems for distinct type of contractive conditions are presented that generalize, extend, and unify a number of related results reported in the literature. Illustrative examples are provided. [ABSTRACT FROM AUTHOR]

Inspired by the concept of Sb-metric spaces which was introduced by Souayah and Mlaiki in [8]. In this paper, we define complex valued Sb-metric spaces. Along with the topology of this space, we prove very interesting fixed point theorems. Examples are also given as a support of our results. [ABSTRACT FROM AUTHOR]

Using the concept of generalized contraction, some fixed point theorems are investigated in the context of right and left dislocated b-metric spaces. We have proved φ-contraction and Reich type contraction in right and left dislocated b-metric spaces. [ABSTRACT FROM AUTHOR]

Two generalized types of b-dislocated metric spaces are introduced and some interesting properties and examples of these new spaces are dis- cussed. Some fixed point results are also investigated in these new spaces. The presented work generalizes some well-known results from the existing lit- erature. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to prove common fixed point theorems for two operators without the assumption of continuity on a set endowed with vector-valued b-metric and we also study the case of two vector-valued b-metrics. The well-posedness of the fixed point problem is also discussed and an application is presented for systems of operator equations in complete b-normed vector space. Our results improve and generalize theorems 2 and 5 of M. Boriceanu [5]. [ABSTRACT FROM AUTHOR]

Very recently, in order to unify the notions of fuzzy metric space and metric-like space, Shukla and Abbas introduced the concept offuzzy metric-like spaceand proved some fixed-point results in this setting. In this article, we modify the notion of Cauchy sequence and completeness to generalize their results. Thus, we extend their theorems to a more general framework, which is also appropriate to generalize some recent, well-known results in this line of research. Furthermore, several examples are presented to illustrate the significance of our results. [ABSTRACT FROM PUBLISHER]

In this paper we give a fixed point theorem in the context of fuzzy metric spaces in the sense of George and Veeramani. As a consequence of our result we obtain a fixed point theorem due to D. Mihet and generalize a fixed point theorem due to D. Wardowski. Also, we answer in a positive way to a question posed by D. Wardowski, and solve partially an open question on Cauchyness and contractivity. [ABSTRACT FROM AUTHOR]

The aim of this paper is to establish fixed point results for semi fixed α*-admissible multivalued mappings satisfying generalized locally α*-ψ-contractive conditions in complete dislocated metric space. As an application, we derive some new fixed point theorems for preordered metric space and metric space endowed with a graph. Example has been constructed to demonstrate the novelty of our results. Our results unify, extend and generalize several comparable results in the existing literature. [ABSTRACT FROM AUTHOR]

The paper is mainly devoted to fixed point theorems. More general versions of important theorems of Matkowski, Romaguera, Takahashi, Brøndsted, and Banach are proved. Also, Ekeland's variational principle is extended. On the way to the main results, short proofs of crucial properties of partial metric spaces are proposed. In addition, the notion of kernel of partial metric is suggested together with a standard method of proving fixed point theorems. We also supply a useful criterion for Cauchy sequences. [ABSTRACT FROM AUTHOR]

The intrinsic flexibility of probabilistic metric spaces makes it possible to extend the idea of contraction mapping in several inequivalent ways, one of which being the C-contraction. Cyclic contractions are another type of contractions used extensively in global optimization problems. We introduced here p-cyclic contractions which are probabilistic C-contraction types. It involves p numbers of subsets of the spaces and involves two control functions for its definitions. We show that such contractions have fixed points in a complete probabilistic metric space. The main result is supported with an example and extends several existing results. [ABSTRACT FROM AUTHOR]

In the present article we study distinct metrical structures guaranteeing the existence of fixed points for a given mapping (Propositions 3.4 and 5.9, Theorems 4.1 and 7.3, Corollaries 2.1, 3.3, 4.4, 4.7, 5.10, 6.12, 6.13). Some examples are proposed (Examples 1.4, 4.9, 6.12). [ABSTRACT FROM AUTHOR]

In the present paper, we introduce a new concept of (õ, Fd)-contraction on quasi metric space. Then we provide some new fixed point theorems for such type mappings on left K, left M and left Smyth-complete quasi metric spaces. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to generalize fixed point theorems introduced by Jleli et al. (J. Inequal. Appl. 2014:38, ) by using the concept of triangular α-orbital admissible mappings established in Popescu (Fixed Point Theory Appl. 2014:190, ). Some examples are given here to illustrate the usability of the obtained results. [ABSTRACT FROM AUTHOR]

We use the gauge function introduced by Fang to gain a fixed point result in probabilistic G-metric spaces. Our work extends some existing results. Moreover, our result is supported with an example. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to obtain some results on existence of fixed points for contractive mappings in fuzzy metric spaces using control function. We prove our results on fuzzy metric spaces in the sense of George and Veeramani. Our results mainly generalize and extend the result of various authors, announced in the literature. As an application, a consequence theorem of integral type contraction is given in support of our result. [ABSTRACT FROM AUTHOR]

A fixed point theorem in generalized quasi-metric spaces is proved. The obtained result extends in generalized quasi-metric spaces the Ciric's fixed point theorem on quasi-contraction mapping. An example shows that the main theorem of this paper provides a larger class of mappings than the Ciric's fixed point theorem. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to present a fixed point theorem using a contractive condition of rational type in the context of ordered partial metric spaces. [ABSTRACT FROM AUTHOR]

In this paper, we have studied some fixed point theorems on complete G- metric spaces. [ABSTRACT FROM AUTHOR]

In this article, we generalize, improve, unify and enrich some results for Jaggi- W -contraction-type mappings in the framework of b-metric-like spaces. Our results supplement numerous methods in the existing literature, and we created new approach to prove that a Picard sequence is Cauchy in a b-metric-like space. Among other things, we prove Wardowski's theorem, but now by using only the property (W 1). Our proofs in this article are much shorter than ones in recently published papers. [ABSTRACT FROM AUTHOR]

The fixed point theorems in so-called pre-metric spaces is investigated in this paper. The main issue in the pre-metric space is that the symmetric condition is not assumed to be satisfied, which can result in four different forms of triangle inequalities. In this case, the fixed point theorems in pre-metric space will have many different styles based on the different forms of triangle inequalities. [ABSTRACT FROM AUTHOR]

The aim of our paper is to present a new class of functions and to define some new contractive mappings in b-metric spaces. We establish some fixed point results for these new contractive mappings in b-metric spaces. Furthermore, we extend our main result in the framework of b-metric-like spaces. Some consequences of main results are also deduced. We present some examples to illustrate and support our results. We provide an application to solve simultaneous linear equations. In addition, we present some open problems. [ABSTRACT FROM AUTHOR]