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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]

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]

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]

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 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]

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 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 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 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, 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 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 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]

The purpose of this paper is to present some fixed point theorems for weak α-admissible mappings type in the setting of b-metric spaces. The results greatly optimize and improve some fixed point results in the existing literature. Moreover, we highlight our assertions by utilizing an example. In addition, we use our results to obtain the existence of solution for a class of nonlinear integral equations. [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]

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]

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]

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]

The purpose of this paper is to prove some new common fixed point and coincidence point theorems for a pair of intuitionistic fuzzy mappings on a complete metric linear space in association with the Hausdorff metric as well as d1 metric on the family of intuitionistic fuzzy sets (IFS). Moreover, as an application, in function space C [a; b], an existence of coincidence theorem for a family of nonlinear integral equations has been established. Some illustrative examples which demonstrate the validity of the hypothesis and novelty of our main results are presented. [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]

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]

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 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]

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 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 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]

We present a coincidence theorem for a pair of fuzzy mappings satisfying a Jungck type contractive condition which generalizes Heilpern's fuzzy contraction theorem. Moreover, we deduce coincidence points of a pair of multivalued mappings which is an improvement/generalization of Nadler's fixed point theorem and several of its successive generalizations. As applications, we obtain an existence theorem of solution for a class of nonlinear integral equations by utilizing completeness property of function space (C [a,b], $\mathbb{R}$). [ABSTRACT FROM AUTHOR]