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The purpose of this research article is to point out some fallacies in the statements of the main results of Rao et al. [Bull. Maths. Stat. Res] and Berrah et al. [AIMS Mathematics, 4(3)(2023), 1019{1033] and give a genuine contractive condition in the framework of complex valued b-metric spaces. We also introduce interpolative rational contractions in complex valued b-metric spaces and prove some fixed point results for such contractions. A non-trivial example is also provided to demonstrate the validity of obtained theorems. As an application, we investigate the existence of solutions for integral equations. [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 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 main objective of this article is to introduce the notion of α , ⊥ F -contraction in the setting of orthogonal F -metric space and present some new fixed point results in such newly introduced space. We also furnish an example to manifest the originality of the obtained results. As application of our foremost result, we look into the solution of a nonlinear fractional differential equation. [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]

The purpose of this paper is to define a rational orbitally (Θ , δ b )-contraction and prove some new results in the context of b -metric spaces. Our results extend, generalize, and unify some known results in the literature. As application of our main result, we investigate the solution of Fredholm integral inclusion. We also provide an example to substantiate the advantage and usefulness of obtained results. [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]

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]

The purpose of this article is to define Dass and Gupta's contraction in the context of F-metric spaces and obtain some new fixed point theorems to elaborate, generalize and synthesize several known results in the literature including Jleli and Samet [M. Jleli, B. Samet, J. Fixed Point Theory Appl., 20 (2018), 20 pages] and Dass and Gupta [B. K. Dass, S. Gupta, Indian J. Pure Appl. Math., 6 (1975), 1455-1458]. Also we have provided a non trivial example to validate our main result. [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 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 aim of this paper is to extend the result of [M. Jleli, B. Samet, J. Inequal. Appl., 2014 (2014), 8 pages] by applying a simple condition on the function Θ. With this condition, we also prove some fixed point theorems for Suzuki-Berinde type Θ-contractions which generalize various results of literature. Finally, we give one example to illustrate the main results in this paper. [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]

In this article, we introduce a new type of contraction and prove certain coincidence point theorems which generalize some known results in this area. As an application, we derive some new fixed point theorems for F-contractions. The article also includes an example which shows the validity of our main result and an application in which we prove an existence and uniqueness of a solution for a general class of Fredholm integral equations of the second kind. [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]

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]

This paper is designed to display some results which generalize the recent results that cannot be established from the corresponding results in other spaces and do not satisfy the remarks of Jleli et al. (Fixed Point Theor Appl. 210, 2012) and Samet et al. (Int. J. Anal. Article ID 917158, 2013). We obtain unique fixed-point for mapping satisfying β - ψ ˇ contraction only on a closed G d ball in complete dislocated G d -metric space. An example is also discussed to shed light on the main result. [ABSTRACT FROM AUTHOR]

The aim of this article is to establish some fixed point results for fuzzy mappings and derive some corresponding multivalued mappings results of literature. For this purpose, we define some new and generalized contractions in the setting of b-metric spaces. As applications, we find solutions of integral inclusions by our obtained results. [ABSTRACT FROM AUTHOR]

The aim of this article is to introduce a new class of contraction-like mappings, called the almost multivalued ( Θ , δ b )-contraction mappings in the setting of b-metric spaces to obtain some generalized fixed point theorems. As an application of our main result, we present the sufficient conditions for the existence of solutions of Fredholm integral inclusions. An example is also provided to verify the effectiveness and applicability of our main results. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to define generalized ( α β - ψ) -contraction in the context of F -metric space and obtain some new fixed point results. As applications, we solve a nonlinear neutral differential equation with an unbounded delay ϑ / (ι) = − ρ 1 (ι) ϑ (ι) + ρ 2 (ι) L (ϑ (ι − ς (ι))) + ρ 3 (ι) ϑ / (ι − ς (ι)) , where ρ 1 (ι) , ρ 2 (ι) are continuous, ρ 3 (ι) is continuously differentiable and ς (ι) > 0 , for all ι ∈ R and is twice continuously differentiable. [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]