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The probabilistic cone b-metric space is a novel concept that we describe in this study along with some of its fundamental topological properties and instances. We also established the fixed point theorem for the probabilistic nonlinear Banach contraction mapping on this kind of spaces. Many prior findings in the literature are generalized and unified by our findings. In order to illustrate the basic theorem in ordinary cone b-metric spaces, some related findings are also provided with an application to integral equation. [ABSTRACT FROM AUTHOR]

We establish some common coupled fixed point theorems for hybrid pair of mappings under generalized weak contraction on a non complete metric space, which is not partially ordered. As an application, we study the existence and uniqueness of the solution to an integral equation and also give an example to show the fruitfulness of our results. The results we obtain generalize, extend and improve several classical results in the literature in metric spaces. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of an orthogonal neutrosophic rectangular metric space and prove fixed point theorems. We extend some of the well-known results in the literature. As applications of the main results, we apply our main results to show the existence of a unique solution. [ABSTRACT FROM AUTHOR]

In this article, we define a new space named the modular-like space with its related concepts to prove the existence of a fixed point and a point of coincidence for mappings on this space. Also, we defined Ćirić-Reich-Rus type weakly contractive mappings on modular-like spaces and discussed some conditions that guarantee the existence of the fixed points for these kind of mappings. Some examples are also provided to elaborate the usability of our main results. It is worth mentioning that a modular-like space is a generalization of a modular space, thus our theorems are more general and applicable than the fixed point theorems on modular spaces. [ABSTRACT FROM AUTHOR]

Here, some fixed point theorems in partially ordered spaces are proved. As an application, the existence of a solution of an integral equation is obtained. [ABSTRACT FROM AUTHOR]

In this article we have introduced a metric named complex valued controlled metric type space, more generalized form of controlled metric type spaces. This concept is a new extension of the concept complex valued b-metric type space and this one is different from complex valued extended bmetric space. Using the idea of this new metric, some fixed point theorems involving Banach, Kannan and Fisher contractions type are proved. Some examples togetheran application are described to sustain our primary results. [ABSTRACT FROM AUTHOR]

In this paper, parallel to the ideas based on Ahmadullah et al. [4, 5, 6], and Eke et al. [18], we prove the existence and uniqueness of the common fixed point for a pair of self-mappings employing (E. A.)-property in metric-like spaces for implicit contractive mappings related to binary relation. Henceforth, results obtained will be verified with the help of illustrative examples. As an application of the results, we solve two boundary value problems of the second-order differential equation. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce several generalized F-contractions in b-metric-like spaces and establish some fixed point theorems for such contractions. Moreover, some nontrivial examples are given to illustrate the superiority of our results. In addition, as an application, we find the existence and uniqueness of a solution to a class of integral equations in the context of b-metric-like spaces. [ABSTRACT FROM AUTHOR]

The purpose of this manuscript is to demonstrate the existence and uniqueness of triple fixed-point results for Geraghty-type contractions in ordinary metric spaces with binary relations. Moreover, the well-posedness of the tripled fixed point problem is investigated. Consequently, α -dominated mapping on such space is discussed. Ultimately, to promote our paper, some illustrative examples are derived, and the existence of the solution to a system of differential equations is obtained as an application. [ABSTRACT FROM AUTHOR]

In this paper, we establish some results on the existence and uniqueness of common fixed point theorems in partially ordered Ab -metric spaces. Examples and application also are presented in support of the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, we present new nonlinear contractions based on altering distances and prove the existence and uniqueness of fixed points for cyclic operators. We prove here very interesting fixed point theorems in which we combine and extend the contractive conditions of Banach, Kannan, Chatterjea, and of many others. Our results shall serve as generalized versions of many fixed point results proved in the literature. Examples and application to integral equations that exploits Jensen inequality are given to illustrate the analysis and theory and validate our proved results. [ABSTRACT FROM AUTHOR]

In this paper, we prove fixed point theorem for F-contractions mappings in ordered partial metric space with an application to the integral equation. This paper will generalise the theorem proven by Imdad et al. to an ordered partial metric space. We also provided an illustrative example and application to integral equations to validate the results. [ABSTRACT FROM AUTHOR]

Fixed point theory is one of the most important theories and has been studied extensively by researchers in many disciplines. One of these studies is its application to integral equations. In this work, we have shown that the iteration method given in [30] converges to the solution of the more general Volterra integral equation in two variables by using Bielecki's norm. Also, a data dependence result for the solution of this integral equation has been proven. [ABSTRACT FROM AUTHOR]

We establish a common fixed point theorem satisfying a weak ψ--ψ contraction on partially ordered non-Archimedean fuzzy metric spaces. In the process, some multidimensional common fixed point results are derived from our main results. As an application, we study the existence of the solution to an integral equation and also give an example to show the usefulness of the obtained results. Our results generalize, extend and improve several well-known results of the existing literature. [ABSTRACT FROM AUTHOR]

The main aim of this article is to study the existence and uniqueness of fixed point for isotone mappings of any number of arguments under contraction mapping principle on a complete metric space endowed with a partial order. As an application of our result, we have studied the existence and uniqueness of the solution to an integral equation. The results we have obtaied will generalize, extend and unify several classical and very recent related results in the literature in metric spaces. [ABSTRACT FROM AUTHOR]

The objective of this article is to investigate the Ulam-Hyres stability and Ulam-Hyres-Rassias stability for some general integral equations f(x) = ∫E F(x,f(x))dx, x ∈ E, where E is a nonempty set of a Banach space. The main tool used in the analysis is a recent fixed point theory. In this way, we obtain results in 2-Banach Spaces. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of Su-type contractive mapping and establish fixed point theorems for such mappings in the setting of ordered extended partial b-metric space. We also develop an application for Fredholm type integral equations to validate our main result and a non-trivial example is given to elucidate our work. [ABSTRACT FROM AUTHOR]

In this note, the notion of a mixed weakly monotone pair of mappings is invoked to prove some coupled common fixed point theorems in partially ordered b-metric spaces. Results proved in this note are authenticated by some innovative examples. Demonstrative surfaces leading to better understanding of calculation done. Moreover as an application our results are utilized to establish existence of solutions of system of integral equations which is also substantiated by an example. [ABSTRACT FROM AUTHOR]

In this paper, a concept of C*-algebra-valued modular metric space is introduced which is a generalization of a modular metric space of Chistyakov (Folia Math. 14 (2008), 3-25). Next, some common fixed point theorems are proved for generalized contraction type mappings on such spaces. Also, to support of our results an application is provided for existence and uniqueness of solution for a system of integral equations. [ABSTRACT FROM AUTHOR]

In this paper we discuss the application of the non-unique fixed point theorem of Ćirić to nonlinear Fredholm integral equations. We establish an existence theorem for the solutions of such integral equations and apply the theorem to particular examples. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and define a concept of -operator pair as a pair of non-commuting mappings in a C*-algebra-valued modular metric space. Next, some common fixed point theorems are established for such mappings. Also, to support and elaborate our results, some examples are given and an application is provided for a system of integral equations. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a notion of hybrid pair (f; T), which is α*-admissible with respect to η for generalized multivalued Geraghty F-contraction mappings and obtain coincidence and common fixed point results for such mappings. We provide some examples to support our results and give applications to dynamic programming and integral equations. Our results provide extension as well as substantial generalizations and improvements of several well known results in the existing comparable literature. [ABSTRACT FROM AUTHOR]

In this article, following the approach of F-contractions, we establish a common fixed point theorem for a pair of self-mappings satisfying F-contraction of rational type in complete metric spaces. An example is constructed to illustrate this result. An application to system of integral equations is presented. [ABSTRACT FROM AUTHOR]

A new concept of set-valued Mizoguchi-Takahashi G-contractions is introduced in this paper and some fixed point theorems for such mappings in b-metric spaces endowed with directed graphs are established under some suffcient conditions. Our results improve and extend those of [20] and [24]. We also give some examples supporting our main results. As an applications, we prove the existence of fixed points for multivalued mappings satisfying generalized MT-contractive condition in ϵ-chainable b-metric spaces and the existence of a solution for some integral equations. [ABSTRACT FROM AUTHOR]

In this paper we present Perov type fixed point theorems for contractive mappings in Gheorghius sense on spaces endowed with a family of vector valued pseudo-metrics. Applications to systems of integral equations are given to illustrate the theory. The examples also prove the advantage of using vector valued pseudo-metrics and matrices that are convergent to zero, for the study of systems of equations. [ABSTRACT FROM AUTHOR]

The main results of the paper concern the existence of fixed points of nonlinear F-contraction and the sum of this type of mapping with a compact operator. The results of Krasnosel’skii type are obtained with a usage of the Hausdorff measure of noncompactness and condensing mappings. The presented new tools give the possibility to verify the existence problems of the solutions for some classes of integral equations. [ABSTRACT FROM AUTHOR]

In this paper, we prove some common fixed point theorems for three self-mappings satisfying various new contractive conditions in complete G-metric spaces. We also discuss that these mappings are G-continuous on such a common fixed point. And a non-trivial example is provided to support our new result in the framework of nonsymmetric G-metric spaces. At the end of the results, we give an existence theorem for common solution of three integral equations. The results obtained in this paper differ from the recent relative results in literature. [ABSTRACT FROM AUTHOR]

The aim of this paper is to establish the structure of C*- algebra-valued b2-metric space and give some fixed point theorems for self-maps with contractive or expansive conditions on such spaces. As an application we investigate existence and uniqueness solution for a type of integral equation. [ABSTRACT FROM AUTHOR]

In this paper we extend Darbo's fixed point theorem in Banach spaces and obtain a tripled fixed point theorem. The technique of measure of noncompactness is the main tool in carrying out our proof. Finally, as an application of our results, we analyze the existence of solutions for a system of neutral differential equations. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to present a new class of generalized Berinde-type (&#951,ξ,ν,θ)-contractive in b-metric space and establish some fixed and common fixed point results for the class of mappings in partially ordered complete b-metric spaces. Our results generalize and extend several known results from the context of ordered metric spaces to the setting of ordered b-metric spaces. [ABSTRACT FROM AUTHOR]

In this paper, by using the Guo-Krasnoselskii theorem, we investigate the existence and nonexistence of positive solutions of a system of integral equation with parameters which can be seen as an effective generalization of various types of systems of boundary value problems for differential equation on continuous interval and time scales or fractional differential equations. We give a general approach of positive solutions to cover various systems of boundary value problems in a unified way, which avoids treating these problems on a case-by-case basis. Under some growth conditions imposed on the nonlinear term, we obtain explicit ranges of values of parameters with which the problem has a positive solution and has no positive solution, respectively. By giving some examples, we will show how our results may be applied to consider existence of positive solutions to a variety of system of boundary value problems of differential equations, differential equations on time scales or fractional differential equations. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of diagonal operator, we present the historical roots of diagonal operators and we give some fixed point theorems for this class of operators. Our approaches are based on the weakly Picard operator technique, difference equation techniques, and some fixed point theorems for multi-valued operators. Some applications to differential and integral equations are given. We also present some research directions. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of dualistic contraction of rational type. We prove some fixed point theorems for ordered mappings satisfying above mentioned contraction. We give examples to illustrate the importance of these results. We present an application of our fixed point result to show the existence of solution of integral equations. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of Menger PMT-spaces. Further, we prove common fixed point theorems in a complete Menger probabilistic metric type space and, by using the main result, we give applications on the existence and uniqueness of a solution for a class of integral equations. [ABSTRACT FROM AUTHOR]

We use a modification of Krasnoselskii's fixed point theorem introduced by Burton to show the periodicity and non-negativity of solutions for the nonlinear neutral differential equation with variable delay [ABSTRACT FROM AUTHOR]

In this paper, we use a modification of Krasnoselskii's fixed point theorem introduced by Burton (see [8] Theorem 3) to obtain stability results of the zero solution of totally nonlinear neutral differential equations with functional delay x' (t) = -a (t) h (x (t - τ (t))) + c (t) x' (t - τ (t)) + G(t, x (t) , x (t - τ (t))) : The stability of the zero solution of this equation provided that h (0) = G(t; 0; 0) = 0. The Caratheodory condition is used for the function G. [ABSTRACT FROM AUTHOR]

In this paper, based on [A. Razani, V. Rakočcević and Z. Goodarzi, Nonself mappings in modular spaces and common fixed point theorems, Cent. Eur. J. Math. 2 (2010) 357-366.] a fixed point theorem for non-self contraction mapping T in the modular space Xρ is presented. Moreover, we study a new version of Krasnoseleskii's fixed point theorem for S + T, where T is a continuous nonself contraction mapping and S is continuous mapping such that S(C) resides in a compact subset of Xρ, where C is a nonempty and complete subset of Xρ, also C is not bounded. Our result extends and improves the result announced by Hajji and Hanebally [A. Hajji and E. Hanebaly, Fixed point theorem and its application to perturbed integral equations in modular function spaces, Electron. J. Differ. Equ. 2005 (2005) 1-11]. As an application, the existence of a solution of a nonlinear integral equation on C(I, Lφ) is presented, where C(I, Lφ) denotes the space of all continuous function from I to Lφ, Lφ is the Musielak-Orlicz space and I = [0, b] ⊂ R. In addition, the concept of quasi contraction non-self mapping in modular space is introduced. Then the existence of a fixed point of these kinds of mapping without ∆2-condition is proved. Finally, a three step iterative sequence for non-self mapping is introduced and the strong convergence of this iterative sequence is studied. Our theorem improves and generalized recent know results in the literature. [ABSTRACT FROM AUTHOR]

In this paper we obtain some equivalences between cyclic contractions and non-cyclic contractions in the framework of b -metric spaces. Our results improve and complement several recent fixed point results for cyclic contractions in b -metric spaces established by George et al. (2015) and Nashine et al. (2014). Moreover, all the results are with much shorter proofs. In addition, an application to integral equations is given to illustrate the usability of the obtained results. [ABSTRACT FROM AUTHOR]

The aim of this paper to present fixed point results for single-valued operators in b-metric spaces. The case of scalar metric and the case of vector-valued metric approaches are considered. As an application, a system of integral equations is studied. [ABSTRACT FROM AUTHOR]

In this work, we discuss the existence of fixed points of monotone nonexpansive mappings defined on partially ordered Banach spaces. This work is a continuity of the previous works of Ran and Reurings, Nieto et al., and Jachimsky done for contraction mappings. As an application, we discuss the existence of solutions to an integral equations. [ABSTRACT FROM AUTHOR]

In this paper, we use a modification of Krasnoselskii's fixed point theorem introduced by Burton (see [6] Theorem 3) to obtain stability results of the zero solution of the totally nonlinear neutral differential equations with functional delay x' (t) = -a (t)h(x(t-τ(t))) + c (t)x' (t - τ(t)) + b (t)G(x (t), x (t - τ (t))). The stability of the zero solution of this equations provided that h (0) = G(0,0) = 0. [ABSTRACT FROM AUTHOR]

The main objective of the paper is to study the existence, uniqueness and other properties of solution of certain dynamic integral equation on time scales. The tools employed are based on the application of the Banach fixed point theorem and certain integral inequality with explicit estimates on time scales. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence and uniqueness of positive solutions for a class of nonlinear operator equations on ordered Banach spaces. Various applications are also considered to illustrate our obtained results (existence of solutions to quadratic integral equations with a linear modification of the argument, positive solution of second-order Neumann boundary value problem, and positive definite solutions of a class of nonlinear matrix equations). [ABSTRACT FROM AUTHOR]

In this paper we prove some coupled fixed point theorems for Geraghty-type mappings having mixed monotone property and depending on another function in G-metric spaces. Moreover, we prove the uniqueness of the coupled fixed point. Our results generalize several comparable results in the literature. We also give some examples to prove the validity of our results. At the end, application to a certain class of non-linear integral equations is also obtained. [ABSTRACT FROM AUTHOR]

Let T be a time scale which is unbounded above and below and such that 0 ϵ T. Let id - r : T → T be such that (id - r) (T) is a time scale. We use the contraction mapping theorem to obtain stability results about the zero solution for the following neutral nonlinear dynamic equations with unbounded delay χ▵ (t) = -a(t) χσ (t) + b(t)G(χ²(t),χ²(t - r(t))) + c(t)(χ²) ▵ (t - r(t), t ϵ(t))) +c(t) (χ²)▵ (t - r(t)), t ϵ T, and χ▵ (t) = -a(t) χσ (t) + b(t)G(χ²(t),χ²(t - r(t))) + c(t)(χ²) ▵ (t - r(t), t ϵ(t))) +c(t) (χ²)▵ (t - r(t)), t ϵ T, where ƒ▵ is the ▵-derivative on T and ƒ▵ is the ▵-derivative on (id - r) (T) . We provide interesting examples to illustrate our claims. [ABSTRACT FROM AUTHOR]

Abstract: We introduce a cyclic generalized -weakly contractive mappings for a map in a metric space and originate existence and uniqueness results of fixed points for such mappings. Examples are given to support the usability of our results. At the end of the results, an application to the study of existence and uniqueness of solutions for a class of nonlinear integral equations is presented. [Copyright &y& Elsevier]

In this paper, we introduce the concept of a τ -- φ-- concave--convex operator. Meanwhile by the properties of cone and monotone iterative technique, we prove some new existence and uniqueness theorems of fixed points for mixed monotone operators under more extensive conditions in ordered Banach spaces. Finally, we apple the results to a nonlinear Hammerstein integral equation. The results given in this work generalize and extend some known results (e.g., [Z. Q. Zhao, Existence and uniqueness of fixed points for some mixed monotone operators. Nonlinear Anal., 73 (2010) 1481-1490.]). [ABSTRACT FROM AUTHOR]

In this article, we give sufficient conditions for the existence of solutions for an integral equation of fractional order with multiple time delays in Banach spaces. Our main tool is a fixed point theorem of Mönch type associated with measures of noncompactness. Our results are illustrated by an example. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of a τ - ρ-concave-convex operator. Meanwhile by the properties of cone and monotone iterative technique, we prove some new existence and uniqueness theorems of fixed points for mixed monotone operators under more extensive conditions in ordered Banach spaces. Finally, we apple the results to a nonlinear Hammerstein integral equation. The results given in this work generalize and extend some known results (e.g., [Z. Q. Zhao, Existence and uniqueness of fixed points for some mixed monotone operators. Nonlinear Anal., 73 (2010)1481-1490.]). [ABSTRACT FROM AUTHOR]