Search

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]

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]

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]

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 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]

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, 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, 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]

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 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]

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 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]

Abstract: In this paper, we extend the coupled fixed point theorems for mixed monotone operators obtained by Bhaskar and Lakshmikantham [T.G. Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. 65 (2006) 1379–1393] and Luong and Thuan [N.V. Luong and N.X. Thuan, Coupled fixed points in partially ordered metric spaces and application, Nonlinear Anal. 74 (2011) 983–992], by weakening the involved contractive condition. An example as well as an application to nonlinear Fredholm integral equations is also given in order to illustrate the effectiveness of our generalizations. [Copyright &y& Elsevier]

Abstract: Using the setting of cone metric space, a fixed point theorem is proved for two maps, and several corollaries are obtained. In these cases, the cone does not need to be normal. These results generalize several well known compatible recent and classical results in the literature. As an application, the existence of solution of an integral equation is presented. [Copyright &y& Elsevier]

We study the existence and uniqueness of periodic solutions and the stability of the zero solution of the nonlinear neutral differential equation d/dt x(t) = -a(t)x(t) + d/dt Q(t, x(t - g(t))) + G(t, x(t), x(t - g(t))). In the process we use integrating factors and convert the given neutral differential equation into an equivalent integral equation. Then we construct appropriate mappings and employ Krasnoselskii's fixed point theorem to show the existence of a periodic solution of this neutral differential equation. We also use the contraction mapping principle to show the existence of a unique periodic solution and the asymptotic stability of the zero solution provided that Q(0, 0) = G(t, 0, 0) = 0. [ABSTRACT FROM AUTHOR]

We use Krasnoselskii's fixed point theorem to show that the non-linear neutral differential equation with functional delay x'(t) = -a(t)x(t) + c(t)x'(t - g(t)) + q(t,x(t), x(t - g(t)) has a periodic solution. Also, by transforming the problem to an integral equation we are able, using the contraction mapping principle, to show that the periodic solution is unique. [ABSTRACT FROM AUTHOR]