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In this publication, our objective was to introduce and establish the concepts of KGm-contraction and generalized (a, KGm)-contraction in complete Gm-metric spaces, which led to the discovery of novel fixed points, coincidence points, and common fixed points. Additionally, we demonstrated the usefulness of our main results by applying it to the investigation of the integral equation. Also, we presenting a noteworthy example demonstrating the practicality of our primary hypothesis. [ABSTRACT FROM AUTHOR]

The main objective of this manuscript is to define the concepts of F-(⋏,h)-contraction and (α , η) -Reich type interpolative contraction in the framework of orthogonal F -metric space and prove some fixed point results. Our primary result serves as a cornerstone, from which established findings in the literature emerge as natural consequences. To enhance the clarity of our novel contributions, we furnish a significant example that not only strengthens the innovative findings but also facilitates a deeper understanding of the established theory. The concluding section of our work is dedicated to the application of these results in establishing the existence and uniqueness of a solution for a fractional differential equation of anomalous diffusion. [ABSTRACT FROM AUTHOR]

The aim of the present research work is to investigate the solution of Urysohn integral equation by common fixed point result in the setting of complex valued b-metric space. To obtain the objective, we used a generalized rational contraction involving control functions and a pair of self-mappings. In this way, we generalize some well-known results of literature. Some non-trivial examples are also flourished to demonstrate the innovation of our principal result. [ABSTRACT FROM AUTHOR]

The aim of the present research article is to solve the system of linear equations using common fixed point theorems in the context of bicomplex valued metric spaces. To obtain our main objective, we introduce generalized contractive conditions in bicomplex valued metric spaces and establish common fixed point theorems for self mappings. We also give a significant example to demonstrate the legitimacy of the given theorems. [ABSTRACT FROM AUTHOR]

The purpose of this article is to investigate the existence of solutions for Urysohn integral equations. To achieve our objectives, we take advantage of common fixed point results for self-mappings satisfying a generalized contraction involving control functions of two variables in the context of complex valued metric spaces. We also supply a non-trivial example to show the validity of obtained results. [ABSTRACT FROM AUTHOR]

The aim of this paper is to define a Berinde type ( ρ , μ)- ϑ contraction and establish some fixed point results for self mappings in the setting of complete metric spaces. We derive new fixed point results, which extend and improve some results in the literature. We also supply a non trivial example to support the obtained results. Finally, we investigate the existence of solutions for the nonlinear fractional differential equation. [ABSTRACT FROM AUTHOR]

Jleli and Samet introduced the notion of F-metric space as a generalization of traditional metric space and proved Banach contraction principle in the setting of these generalized metric spaces. The aim of this article is to utilize F-metric space and establish some common α-fuzzy fixed point theorems for rational (β-ϕ)-contractive conditions. Our results extend, generalize and unify some wellknown results in the literature. As application of our main result, we discuss the solution of fuzzy integrodifferential equations in the setting of a generalized Hukuhara derivative. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of a generalized (α, ΘF)-contraction in the context of an orthogonal F-complete metric space and obtain some new fixed point results for this newly introduced contraction. A nontrivial example is also provided to satisfy the validity of the established results. As consequences of our obtained results, we derive the leading results in [Fixed Point Theory Appl., 2015,185, 2015] and [Symmetry, 2020, 12,832]. As an application, we investigate the existence and uniqueness of the solution for a nonlinear fractional differential equation. [ABSTRACT FROM AUTHOR]

The aim of this article is to obtain common fixed points of locally contractive mappings in the setting of bicomplex valued metric spaces. Our investigations generalize some conventional theorems of literature. Furthermore, we supply a significant example to manifest the authenticity of the proved results. As an application, we solve the solution of the integral equation by using our main result. [ABSTRACT FROM AUTHOR]

The aim of this article is to obtain common fixed point results on complex-valued extended b-metric spaces for rational contractions involving control functions of two variables. Our theorems generalize some famous results in the literature. We supply an example to show the originality of our main result. As an application, we develop common fixed point results for rational contractions involving control functions of one variable in the class of complex-valued extended b-metric spaces. [ABSTRACT FROM AUTHOR]

The aim of this article is to obtain common fixed point results for generalized contractions involving control functions of two variables in the context of F-metric spaces. We also furnish an example to show the originality of our main result. Some results in the context of F-metric space equipped with a directed graph G are also established. As an application, we discuss the existence of solution to nonlinear neutral differential equation. [ABSTRACT FROM AUTHOR]

The purpose of this article is to establish some common fixed point results for generalized contractions including some precise control functions of two variables in the setting of controlled metric spaces. As consequences of our leading results, we derive common fixed point and fixed point results for contractions with control functions of one variable and constants. We also discuss controlled metric spaces endowed with a graph and obtain some common fixed point results in this newly introduced space. As an application of our leading result, we examine the solution of a Fredholm type integral equation. [ABSTRACT FROM AUTHOR]

The aim of this paper is to construct a fractal of generalized Θ-Hutchinson Operator with the help of a finite family of Θ-contraction mappings, a class of mappings more general than contractions, defined on a complete metric space. Our results unify, generalize and extend various results in the existing literature. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce the notion of Perov–Ćirić–Prešić-type Θ -contractions and to obtain some generalized fixed point theorems in the setting of vector-valued metric spaces. We derive some fixed point results as consequences of our main results. A nontrivial example is also provided to support the validity of our established results. As an application, we investigate the solution of a semilinear operator system in Banach space. [ABSTRACT FROM AUTHOR]

The purpose of this article is to introduce locally α - ζ -multivalued contraction and rational Ćirić type α - ζ -multivalued contraction in the context of F -metric spaces and prove some endpoint results. We provide a nontrivial example to show the authenticity of our main result. Our results generalize some well-known results of literature. We also present some endpoint results in both graphic F -metric spaces and ordered F -metric spaces. As an application of our main result, we investigate the solution of an integral equation. [ABSTRACT FROM AUTHOR]

In this article, we introduce Reich type contractions and (α , F)-contractions in the class of controlled metric spaces and establish some new related fixed point theorems. Our results are generalizations of some known results of literature. Some examples and certain consequences are given to illustrate significance of presented results. [ABSTRACT FROM AUTHOR]

In this paper, we establish some new fixed point theorems for multivalued mappings in the context of metric spaces. Some special cases are also discussed to derive some well known results of the literature. Finally, one example is also presented to verify the effectiveness and applicability of our main results. [ABSTRACT FROM AUTHOR]

In this manuscript, we study the existence of common α- fuzzy fixed points for fuzzy mappings via F-contractions on a metric space. We obtain some common fixed points of fuzzy (multivalued) mappings satisfying an F-contraction associated with the σ∞ (Hausdorff) metric. In closing, we provide an application of our results. [ABSTRACT FROM AUTHOR]

The aim of this paper is to define ... and establish some new fixed point theorems in the setting of left K-complete T1-quasi metric space. Our theorems generalize, extend, and unify several results of literature. [ABSTRACT FROM AUTHOR]

Jleli and Samet [J. Fixed Point Theory Appl. (2018) 20:128] introduced a new metric space named as F-metric space. They established a new version of the Banach contraction principle in the setting of this generalized metric spaces. The aim of this article is to define rational contraction and obtain some fixed point theorems in the context of F-metric spaces. Our results extend, generalize and unify several known results in the literature. [ABSTRACT FROM AUTHOR]

In this paper we obtain the common fuzzy fixed points of fuzzy mappings satisfying Θ-contraction in a metric space. In the process, we generalize several well known recent and classical results. Finally, we provide an example and application to theoretical computer science to show the significance of the investigation of this paper. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce α-generalized multi-valued contractions in cone metric spaces over Banach Algebras with solid cones and show the existence of fixed points of these contractions in this context. Our results generalize and extend several known results in metric and cone metric spaces given by some authors. Also, we give one example to illustrate significance of the main result in this paper. [ABSTRACT FROM AUTHOR]

The aim of this research article is to define locally rational contractions concerning control functions of one variable in the background of F -metric spaces and establish common fixed point results. We also introduce ( α ∗ - ψ) -contractions and generalized ( α ∗ , ψ , δ F ) -contractions in F -metric spaces and obtain fixed points of multifunctions. A non trivial example is also furnished to manifest the originality of the fundamental result. As application, we investigate the solution of nonlinear neutral differential equation. The aim of this research article is to define locally rational contractions concerning control functions of one variable in the background of -metric spaces and establish common fixed point results. We also introduce ( - -contractions and generalized ( , -contractions in -metric spaces and obtain fixed points of multifunctions. A non trivial example is also furnished to manifest the originality of the fundamental result. As application, we investigate the solution of nonlinear neutral differential equation. [ABSTRACT FROM AUTHOR]

The aim of this paper is to obtain some common α-fuzzy fixed point theorems under generalized Θ-contraction in the setting of complete metric space. In this way, we generalize various results of literature including the main result of Hancer et al. (Fixed Point Theory, 18 (2017), 229-236). We also provide an example to show the significance of the results investigated in this paper. [ABSTRACT FROM AUTHOR]

The aim of this article is to obtain common fixed points of set mappings defined on a family of sets endowed with a graph satisfying Θ-contraction. Our results generalize and extend various results in the existing literature. We also provide some non trivial examples to support the validity of our main results. Some applications to the construction of common fixed points of set mappings in ε-chainable metric space are also discussed. [ABSTRACT FROM AUTHOR]

Motivated by the recent work of Liu and Xu, we establish a generalized fixed point theorem for multivalued mapping in the setting of G-cone metric spaces over Banach algebra without assuming the normality of the underlying cone. Our results generalize and extend some known results of G-metric and G-cone metric spaces. An example and certain consequences are presented to illustrate significance of proved results. [ABSTRACT FROM AUTHOR]

The aim of this article is to study the cone b-metric spaces over Banach Algebra with solid cones and establish some fixed points of multivalued mappings in this setting. Our results generalize and extend several known results of metric, cone metric and cone b-metric spaces. An example and certain consequences are presented to illustrate significance of established results. [ABSTRACT FROM AUTHOR]

The aim of this paper is to establish some existence theorems for coupled fixed points ofϴ-type contractive operator in metric spaces endowed with a directed graph. Our results unify, generalize and extend various results related with G-contraction for a directed graph G. We also provide an application to some nonlinear integral system equations to support the results. [ABSTRACT FROM AUTHOR]

The purpose of this article is to establish the existence of common fixed points of multivalued-contraction mappings on a metric space endowed with a graph. Presented theorems are generalizations of recent fixed point theorems due to Hussain et al. [Fixed Point Theory and Applications (2015)2015:185]. An example is also given to support our generalized result. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce the notion of generalized Hausdorff distance function on Gb-cone metric spaces and exploit it to study some fixed point results in the setting of Gb-cone metric spaces without the assumption of normality. These results improve and generalize some important known results. Some illustrative examples are also furnished to highlight the realized improvements. [ABSTRACT FROM AUTHOR]

The aim of this article is to introduce new family of functions M(S; T) and N(S; T) and obtain some new common fixed point theorems in the context of multiplicative metric spaces. The established results carry some well known results from the literature to multiplicative metric space. [ABSTRACT FROM AUTHOR]

The purpose of this article is to generalize common fixed point theorems under contractive condition involving rational expressions on a complete complex-valued metric space. Obtained results in this article extend, generalize, and improve wellknown comparable results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we define new notions called (g-F) contractions and generalize Mizoguchi-Takahashi contractions for complete G-metric spaces and we establish some new coincidence points and common fixed point results. Our results unify and generalize various known comparable results from the current literature. An example and application are given to illustrate the usability of the main results. [ABSTRACT FROM AUTHOR]

The aim of this article is to study JS-contractions and to establish some new common fixed point theorems for these contractions in the setup of complete metric spaces. Presented theorems are generalizations of recent fixed point theorems due to Hussain et al. [Fixed Point Theory and Applications (2015) 2015:185]. An example is also given to support our generalized result. [ABSTRACT FROM AUTHOR]

Remarkable feature of contractions is associated with the concept Mizoguchi-Takahashi function. For the purpose of extension and modification of classical ideas related with Mizoguchi-Takahashi contraction, we define generalized Mizoguchi-Takahashi G-contractions and establish some generalized fixed point theorems regarding these contractions in this paper. Some applications to the construction of a fixed point of multivalued mappings in ε-chainable metric space are also discussed. [ABSTRACT FROM AUTHOR]

Javahernia et al. [Fixed Point Theory and Applications 2014, 2014:195] introduced the concept of generalized Mizoguchi-Takahashi type contractions and established some common fixed point results for such contractions. In this paper, we define the notion of generalized α* - Mizoguchi-Takahashi type contractions and obtain some new fixed point results which generalize various results existing in literature. An example is included to show that our results are genuine generalization of the corresponding known results. [ABSTRACT FROM AUTHOR]

In this paper, owing to the concept of F-contraction, we define two new classes of functions $M(S,T)$ and $N(S,T)$, and we prove some new fixed point results for single-valued and multivalued mappings in complete metric spaces. Our results extend, generalize and unify several known results in the literature. We include an example to show that the generalization is proper. [ABSTRACT FROM AUTHOR]

We recall the concepts of {α, ξ}-contractive and α-admissible mappings on complete metric spaces to state related fixed point theorems. In this paper, we obtain some fixed point results for {α, ξ}-expansive locally contractive mappings in complete metric spaces. The contractiveness of the mapping is only on a closed ball instead of the whole space. Our results unify, generalize, and complement various well-known comparable results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we extend the coupled coincidence point theorems for a mixed g-monotone operator obtained by Alotaibi and Alsulami [Fixed Point Theory Appl. (2011), article ID 44], by weakening the involved contractive condition. Two examples are given to illustrate the effectiveness of our generalizations. Our result also generalizes some recent results announced in the literature. Moreover, some applications to integral equations are presented. [ABSTRACT FROM AUTHOR]

We obtained some generalized common fixed point results in the context of complex valued metric spaces. Moreover, we proved an existence theorem for the common solution for two Urysohn integral equations. Examples are presented to support our results. [ABSTRACT FROM AUTHOR]

The aim of this paper is to obtain some common fixed point theorems for generalized contractions involving certain control functions in controlled metric space and derive some generalized fixed point results as a consequence of our main results. We also prove some common fixed point theorems in controlled metric spaces endowed with a graph. Our results will generalize and amend many famous results from the literature. We also provide an example to show the authenticity of the established results. As an application of our main result, we investigate the solution of integral equations. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of multivalued contractiv emappings in complex valuedmetric space and prove common fixed point theorems for two multivalued contractive mappings in complex valued metric spaces without using the notion of continuity. Our results improve and extend the results of Azam et al. (2011). [ABSTRACT FROM AUTHOR]

We obtain some common fixed point results for single as well as set valued mappings involving certain rational expressions in complete partial metric spaces. In the process, we generalize various results of the literature. Two examples are also included to illustrate the fact that our results cannot be obtained from the corresponding results in metric spaces. [ABSTRACT FROM AUTHOR]

We define the notion of α*-Ψ-contractive mappings for cone metric space and obtain fixed points of multivalued mappings in connection with Hausdorff distance function for closed bounded subsets of cone metric spaces. We obtain some recent results of the literature as corollaries of our main theorem. Moreover, a nontrivial example of α*-Ψ-contractive mapping satisfying all conditions of our main result has been constructed [ABSTRACT FROM AUTHOR]

We introduce and study the notion of common coupled fixed points for a pair of mappings in complex valued metric space and demonstrate the existence and uniqueness of the common coupled fixed points in a complete complex-valuedmetric space in view of diverse contractive conditions. In addition, our investigations are well supported by nontrivial examples. [ABSTRACT FROM AUTHOR]

In this article, we define the C*-algebra-valued Gb-metric spaces and prove the existence and uniqueness of some fixed point theorems for self mappings with contractive conditions on complete C*-algebra-valued Gb-metric spaces. As an application of our result, we establish an existing result for a differential equation in a C*-algebra-valued Gb-metric space. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to introduce the ( α , β )-type ϑ -contraction, ( α , β )-type rational ϑ -contraction, and cyclic ( α - ϑ ) contraction. Based on these definitions we prove fixed point theorems in the complete metric spaces. These results extend and improve some known results in the literature. As an application of the proved fixed point Theorems, we study the existence of solutions of an integral boundary value problem for scalar nonlinear Caputo fractional differential equations with a fractional order in (1,2). [ABSTRACT FROM AUTHOR]

Best proximity point theorem furnishes sufficient conditions for the existence and computation of an approximate solution ω that is optimal in the sense that the error σ (ω , J ω) assumes the global minimum value σ (θ , ϑ) . The aim of this paper is to define the notion of Suzuki α - Θ -proximal multivalued contraction and prove the existence of best proximity points ω satisfying σ (ω , J ω) = σ (θ , ϑ) , where J is assumed to be continuous or the space M is regular. We derive some best proximity results on a metric space with graphs and ordered metric spaces as consequences. We also provide a non trivial example to support our main results. As applications of our main results, we discuss some variational inequality problems and dynamical programming problems. [ABSTRACT FROM AUTHOR]

The aim of this study is to investigate the existence of solutions for the following Fredholm integral inclusion φ (t) ∈ f (t) + ∫ 0 1 K (t , s , φ (s)) ϱ s for t ∈ [ 0 , 1 ] , where f ∈ C [ 0 , 1 ] is a given real-valued function and K : [ 0 , 1 ] × [ 0 , 1 ] × R → K c v (R) a given multivalued operator, where K c v represents the family of non-empty compact and convex subsets of R , φ ∈ C [ 0 , 1 ] is the unknown function and ϱ is a metric defined on C [ 0 , 1 ] . To attain this target, we take advantage of fixed point theorems for α -fuzzy mappings satisfying a new class of contractive conditions in the context of complete metric spaces. We derive new fixed point results which extend and improve the well-known results of Banach, Kannan, Chatterjea, Reich, Hardy-Rogers, Berinde and Ćirić by means of this new class of contractions. We also give a significantly non-trivial example to support our new results. [ABSTRACT FROM AUTHOR]