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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]

The objective of this research is to present new fixed point theorems for two separate families of fuzzy-dominated mappings. These mappings must satisfy a unique locally contraction in a complete b-multiplicative metric space. Also, we have obtained novel results for families of fuzzy-dominated mappings on a closed ball that meet the requirements of a generalized locally contraction. This research introduces new and challenging fixed-point problems for families of ordered fuzzy-dominated mappings in ordered complete b-multiplicative metric spaces. Moreover, we demonstrate a new concept for families of fuzzy graph-dominated mappings on a closed ball in these spaces. Additionally, we present novel findings for graphic contraction endowed with graphic structure. These findings are groundbreaking and provide a strong foundation for future research in this field. To demonstrate the uniqueness of our novel findings, we provide evidence of their applicability in obtaining the common solution of integral and fractional differential equations. Our findings have resulted in modifications to several contemporary and classical results in the research literature. This provides further evidence of the originality and impact of our work. [ABSTRACT FROM AUTHOR]

The focus of this study is to establish the existence and uniqueness of solutions for differential and integral equations within specific metric spaces. Our investigation begins by introducing the concept of the so-called cone Eb-metric space and presenting crucial findings in this particular space. We have presented fixed point results for specific contractions, particularly in the context of non-solid cones that possess semi-interior points. Not only do the results enhance specific previous fixed points outcomes, but they also encompass and extend previous findings documented in the literature. Furthermore, we apply our findings in the cone Eb-metric space to various examples and applications. The ultimate outcome is the rigorous validation of the existence and uniqueness of solutions for certain differential and integral equations.

In a recent paper, Khojasteh et al. presented a new collection of simulation functions, said Z-contraction. This form of contraction generalizes the Banach contraction and makes different types of nonlinear contractions. In this article, we discuss a pair of nonlinear operators that applies to a nonlinear contraction including a simulation function in a partially ordered metric space. For this pair of operators with and without continuity, we derive some results about the coincidence and unique common fixed point. In the following, many known and dependent consequences in fixed point theory in a partially ordered metric space are deduced. As well, we furnish two interesting examples to explain our main consequences, so that one of them does not apply to the principle of Banach contraction. Finally, we use our consequences to create a solution for a particular type of nonlinear integral equation. [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 manuscript, a novel general family of contraction, called hybrid-interpolative Reich- Istrățescu-type (G-α-µ)-contraction is introduced and some fixed point results in generalised metric space that are not deducible from their akin in metric spaces are obtained. The preeminence of this class of contraction is that its contractive inequality can be extended in a variety of manners, depending on the given parameters. Consequently, a number of corollaries that reduce our result to other wellknown results in the literature are highlighted and analysed. Substantial examples are constructed to validate the assumptions of our obtained theorems and to show their distinction from corresponding results. Additionally, one of our obtained corollaries is applied to set up unprecedented existence conditions for solution of a family of integral equations. [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]

The aim of this paper is to improve some fixed point results given by I.A. Rus in (On a fixed point theorem of Maia, Studia Univ. Babes¸-Bolyai Math., 22(1977), 40-42), (Basic problem for Maia's theorem, Sem. on Fixed Point Theory, Preprint 3(1981), Babes¸-Bolyai Univ. Cluj- Napoca, 112-115) and (Data dependence of the fixed points in a set with two metrics, Fixed Point Theory, 8(2007), no. 1, 115-123), by applying, instead of contraction principle, some variants of Maia's fixed point theorem. 2010 Mathematics Subject Classification: 47H10, 47H09, 34K05, 34K12, 45D05, 45G10, [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]

In this paper by taking into account three trends, prevalent in metric fixed point theory, namely, use of control functions instead of contraction constants, consideration of relational structure in the metric space and fixed point studies of discontinuous functions, we formulate and solve a new problem in relational metric fixed point theory. Our result extends the well known result of Kannan. The theorems are illustrated with examples. Further the problem is shown to have Hyers-Ulam-Rassias stability property. We make an application of our main result to a problem of a nonlinear integral 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 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]

In this paper, we introduce a new class of algebras satisfying certain conditions which has been named power algebras and we prove some fixed point theorems for a new class of contractions. We give new conditions for the existence and uniqueness of fixed points for this new class of mappings which are not a contraction in the usual algebra. Also, we introduce a new iterative algorithm for fixed-point problems in a Banach algebra. This results improve and extend the corresponding conclusions of the Ishikawa algorithm under weaker conditions and lead to stronger results. In conclusion, we give an application to nonlinear integral equations. [ABSTRACT FROM AUTHOR]

We first introduce a novel notion named C*-algebra-valued bv(s)-metric spaces. Then, we give proofs of the Banach contraction principle, the expansion mapping theorem, and Jungck's theorem in C*-algebra-valued bv(s)-metric spaces. As an application of our results, we establish a result for an integral equation in a C*-algebra-valued bv(s)-metric space. Finally, a numerical method is presented to solve the proposed integral equation, and the convergence of this method is also studied. Moreover, a numerical example is given to show applicability and accuracy of the numerical method and guarantee the theoretical results. [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 aim of this work is to establish results in fixed point theory for a pair of fuzzy dominated mappings which forms a rational fuzzy dominated V-contraction in modular-like metric spaces. Some results via a partial order and using the graph concept are also developed. We apply our results to ensure the existence of a solution of nonlinear Volterra-type integral equations. [ABSTRACT FROM AUTHOR]

Introduction/purpose: The aim of the paper is to establish some coupled fixed point results in C*-algebra-valued b-metric spaces. Moreover, the obtained results are used to define the sufficient conditions for the existence of the solutions of some classes of integral equations. Methods: The method of coupled fixed points gives the sufficient conditions for the existence of the solution of some classes of integral equations. Results: New results were obtained on coupled fixed points in C * -algebra-valued b-metric space. Conclusion: The obtained results represent a contribution in the fixed point theory and open new possibilities of application in the theory of differential and integral equations. [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 prove the existence of solutions for the following fractional boundary value problem c D α u (t) = f (t , u (t)) , α ∈ (n , n + 1) , 0 ≤ t < + ∞ , u (0) = 0 , u ′ ′ (0) = 0 , ... , u (n) (0) = 0 , lim t → + ∞ c D α − 1 u (t) = β u (ξ). The considerations of this paper are based on the concept of a new family of measures of noncompactness in the space of functions C n , γ (R +) satisfying the Hölder condition and a fixed point theorem of Darbo type. We also provide an illustrative example in support of our existence theorems. Finally, to credibility, we apply successive approximation and homotopy perturbation method to find solution of the above problem with high accuracy. [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]

The efficiency of a process, especially a long memory seasonal autoregressive fractional integral moving average (SARFIMA) process, has commonly been measured through the quality control chart. In this paper, a generalized long memory SARFIMA process of the exponentially weighted moving average (EWMA) control chart is carried out and shown. Also, analytical and numerical average run length (ARL) were designed to measure the efficiency of the EWMA control. Existence and uniqueness by the fixed point theory are proven for the analytical ARL. Error and convergence of numerical integration equations are also given for the numerical ARL. The findings indicated that the analytical ARL was evaluated more quickly and accurately than the numerical ARL. As a result, the analytical ARL is an alternative for measuring the efficiency of an EWMA control chart over a long memory SARFIMA process. [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]

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]

In this paper, we prove the existence of solutions for a boundary value problem involving both left Riemann-Liouville and right Caputo-type fractional derivatives. For this, we convert the posed problem to a sum of two integral operators, then we apply Krasnoselskii's fixed point theorem to conclude the existence of nontrivial solutions. [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]

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 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]

In this paper, we study the existence of periodic and nonnegative periodic solutions of the nonlinear neutral differential equation x' (f) = —a (t) h(x(t — τ (t))) + c (t) x' (t— τ (t)) + G (t, x (t) , x (t — τ (t))). We invert this equation to construct a sum of a compact map and a large contraction which is suitable for applying the modification of Krasnoselskii’s theorem. The Carathéodory condition is used for the function G. [ABSTRACT FROM AUTHOR]

In this paper, we will consider coupled fixed point problems in b-metric spaces for single-valued operators satisfying a symmetric contraction condition. On one hand, existence and uniqueness of the solution and, on the other hand, data dependence, well-posedness, Ulam-Hyers stability, limit shadowing property of the coupled fixed point problem are discussed. The approach is based on the application of a Ran-Reurings type fixed point theorem for an appropriate operator on the Cartesian product space. Some applications to a system of integral equations and to a periodic boundary value problems are also given. [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 paper, we investigate the common approximate fixed points of monotone nonexpansive semigroups of nonlinear mappings $\{T(t)\}_{t \geq0}$, i.e., a family such that $T(0)x=x$, $T(s+t)x=T(s)\circ T(t)x $, where the domain is a Banach space. In particular we prove that under suitable conditions, the common approximate fixed points are the same as the common approximate fixed points set of two mappings from the family. Then we give an algorithm of how to construct an approximate fixed point sequence of the semigroup in the case of a uniformly convex Banach space. [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 study the existence of periodic and positive periodic solutions of the nonlinear neutral integro-differential equation x'(t) = - ∫t-τ(t)t a(t,s)x(s)ds + d/dt Q(t,x(t-τ(t))) + G(t,x(t), x(t-τ(t))). We invert this equation to obtain an integral equation. By using Krasnoselski's fixed point Theorem we obtain the existence of periodic solution and by contraction mapping principle we obtain the uniqueness, an example is included to show the feasibility of our results. The positive solutions are studied. [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]

In this paper we prove convergence theorems for pointwise Henstock-Kurzweil integrable functions from a compact real interval to the space L(H) of bounded linear operators of a separable complex Hilbert space H, ordered by the cone of positive operators. Using the so obtained theorems and fixed point theorems in partially ordered sets we prove fixed point theorems in spaces of L(H)-valued functions, and apply them to prove existence and comparison results for extremal solutions of discontinuous functional integral equations containing pointwise Henstock-Kurzweil integrable operator-valued functions. [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 use fixed point techniques to obtain asymptotic stability results of the zero solution of a nonlinear neutral differential equation with variable delays. This investigation uses new conditions which allow the coefficient functions to change sign and do not require the boundedness of delays. An asymptotic stability theorem with a necessary and sufficient condition is proved. The obtained results improve and extend those due to Burton, Zhang, Raffoul, Jin and Luo, Ardjouni and Djoudi, and Djoudi and Khemis. Two examples are also given to illustrate this work. [ABSTRACT FROM AUTHOR]

A fixed point theorem in ordered spaces and a recently proved monotone convergence theorem are applied to derive existence and comparison results for solutions of a functional integral equation of Volterra type and a functional impulsive Cauchy problem in an ordered Banach space. A novel feature is that equations contain locally Henstock-Kurzweil integrable functions. [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]

In this paper we use the contraction mapping theorem to obtain asymptotic stability results of a nonlinear neutral differential equation with variable delays. An asymptotic stability theorem with a necessary and sufficient condition is proved, which improves and generalizes some previous results due to T. A. Burton [6], B. Zhang [20], Y. M. Dib, M. R. Maroun, Y. N. Raffoul [14]. Two examples are also given to illustrate our work. [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]