Showing papers on "Fixed-point theorem published in 2012"
TL;DR: In this paper, the authors introduce a new concept of α - ψ -contractive type mappings and establish fixed point theorems for such mappings in complete metric spaces.
Abstract: In this paper, we introduce a new concept of α – ψ -contractive type mappings and establish fixed point theorems for such mappings in complete metric spaces. Starting from the Banach contraction principle, the presented theorems extend, generalize and improve many existing results in the literature. Moreover, some examples and applications to ordinary differential equations are given here to illustrate the usability of the obtained results.
981 citations
TL;DR: In this article, a new concept of contraction was introduced and a fixed point theorem which generalizes Banach contraction principle in a different way than in the known results from the literature was proved.
Abstract: In the article, we introduce a new concept of contraction and prove a fixed point theorem which generalizes Banach contraction principle in a different way than in the known results from the literature. The article includes an example which shows the validity of our results, additionally there is delivered numerical data which illustrates the provided example. MSC: 47H10; 54E50
874 citations
TL;DR: In this paper, fixed point theorems for cyclic contractive mappings are established for metric spaces endowed with a partial order and for a class of contractive mapping mappings.
Abstract: We establish fixed point theorems for a new class of contractive mappings. As consequences of our main results, we obtain fixed point theorems on metric spaces endowed with a partial order and fixed point theorems for cyclic contractive mappings. Various examples are presented to illustrate our obtained results.
328 citations
TL;DR: In this paper, a nonlinear Langevin equation involving two fractional orders α ∈ ( 0, 1 ] and β ∈( 1, 2 ] with three-point boundary conditions was studied and the contraction mapping principle was applied to prove the existence of solutions.
Abstract: This paper studies a nonlinear Langevin equation involving two fractional orders α ∈ ( 0 , 1 ] and β ∈ ( 1 , 2 ] with three-point boundary conditions. The contraction mapping principle and Krasnoselskii’s fixed point theorem are applied to prove the existence of solutions for the problem. The existence results for a three-point third-order nonlocal boundary value problem of nonlinear ordinary differential equations follow as a special case of our results. Some illustrative examples are also discussed.
253 citations
Journal Article•
TL;DR: In this paper, the authors introduce S-metric spaces and give some properties of these spaces and prove a fixed point theorem for a self-mapping on a complete Smetric space.
Abstract: In this paper, we introduce S-metric spaces and give some of their properties. Also we prove a fixed point theorem for a self-mapping on a complete S-metric space.
220 citations
TL;DR: In this article, the condition of contraction of the results of Azam et al. was extended and improved and applied to the unique common solution of system of Urysohn integral equation.
Abstract: Recently, Azam et al. introduced new spaces called the complex valued metric spaces and established the existence of fixed point theorems under the contraction condition. In this article, we extend and improve the condition of contraction of the results of Azam et al. and also apply the main result to the unique common solution of system of Urysohn integral equation. Mathematics Subject Classification (2000): 47H09; 47H10.
180 citations
TL;DR: In this paper, some new concepts in stability of fractional differential equations are offered from different perspectives, such as Hyers-Ulam stability, Rassias stability, and Ulam stability.
177 citations
TL;DR: The fixed point theorem combined with solutions operator theorems results show the existence of mild solutions for fractional differential equations with nonlocal conditions of order 1<@a<2.
Abstract: This paper is mainly concerned with the existence of mild solutions for fractional differential equations with nonlocal conditions of order 1<@a<2. The results are obtained by the fixed point theorem combined with solutions operator theorems.
164 citations
TL;DR: In this article, the authors discuss the concept of G-metric spaces and the fixed point existing results of contractive mappings defined on such spaces, and show that the most obtained fixed point theorems on these spaces can be deduced immediately from fixed point Theorem 1.
Abstract: We discuss the introduced concept of G-metric spaces and the fixed point existing results of contractive mappings defined on such spaces. In particular, we show that the most obtained fixed point theorems on such spaces can be deduced immediately from fixed point theorems on metric or quasi-metric spaces. MSC:47H10, 11J83.
163 citations
TL;DR: Coupled coincidence and common coupled fixed point theorems for (@j,@f)-weakly contractive mappings in ordered G-metric spaces are established.
Abstract: In this paper, we establish coupled coincidence and common coupled fixed point theorems for (@j,@f)-weakly contractive mappings in ordered G-metric spaces. Presented theorems extend, generalize and improve many existing results in the literature. An example is given.
159 citations
TL;DR: Some common fixed pointTheorems satisfying certain rational expressions are proved in complex valued metric spaces which generalize fixed point theorems due to Azam et al., Imdad et al. and others.
Abstract: Some common fixed point theorems satisfying certain rational expressions are proved in complex valued metric spaces which generalize fixed point theorems due to Azam et al., Imdad et al. and others. Some related results are also derived besides furnishing illustrative examples to highlight the realized improvements.
TL;DR: Coupled fixed point theorems for mixed monotone mappings satisfying nonlinear contraction involving two altering distance functions in ordered partial metric spaces are established.
TL;DR: In this article, the existence of boundary value solutions for fractional hybrid differential equations was proved under mixed Lipschitz and Caratheodory conditions under a fixed point theorem in Banach algebra due to Dhage.
TL;DR: In this article, the authors obtained two fixed point theorems for complete partial metric space that, by one hand, clarify and improve some results that have been recently published in Topology and its Applications, and, on the other hand, generalize in several directions the celebrated Boyd and Wong fixed point theorem, respectively.
TL;DR: In this article, the authors presented some iterative scheme results for G -contractive and G -none-expansive mappings on graphs, by using main idea of their work and the idea of combining fixed point theory and graph theory.
TL;DR: In this article, the authors present applications of different fixed point theorems to the theory of the Hyers-Ulam stability of functional equations and compare them to Radu's approach and make use of a theorem of Diaz and Margolis.
Abstract: The fixed point method, which is the second most popular technique of proving the Hyers-Ulam stability of functional equations, was used for the first time in 1991 by J.A. Baker who applied a variant of Banach's fixed point theorem to obtain the stability of a functional equation in a single variable. However, most authors follow Radu's approach and make use of a theorem of Diaz and Margolis. The main aim of this survey is to present applications of different fixed point theorems to the theory of the Hyers-Ulam stability of functional equations.
TL;DR: Three tripled coincidence point theorems are established for a pair of mappings F : X × X ×X → X and g : X → X satisfying a nonlinear contractive condition ordered metric spaces.
TL;DR: In this paper, a discrete fractional three-point boundary value problem (BVP) was studied, and it was shown that the range of admissible boundary conditions depends upon the order of the difference equation.
Abstract: In this paper, we analyse a ν-th order, , discrete fractional three-point boundary value problem (BVP). We show that Green's function associated to this problem satisfies certain conditions. We demonstrate that the range of admissible boundary conditions depends upon the order ν of the difference equation, and we give explicit formulae for this dependence. By using both the Brouwer fixed point theorem and the Krasnosel'skiĭ fixed point theorem, we then show that a solution to this problem exists. Our results extend recent results on discrete fractional BVPs (FBVPs), and they also provide an initial set of results on the theory of multipoint FBVPs on the time scale of integers.
TL;DR: In this paper, the coupled fixed point theorems for mixed monotone operators F : X × X → X obtained by Bhaskar and Lakshmikantham are extended by weakening the involved contractive condition.
Abstract: In this paper, we extend the coupled fixed point theorems for mixed monotone operators F : X × X → X 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.
Journal Article•
TL;DR: In this article, a fixed point theorem with help of self mapping which satisfying contractive type of condition in Banach space was established with self-mapping and self-ordering.
Abstract: In this paper, we established fixed point theorem with help of self mapping which satisfying contractive type of condition in Banach space.
TL;DR: In this article, the existence and multiplicity of positive solutions for boundary value problem of fractional differential equation with p-Laplacian operator with standard Riemann-Liouville derivatives were investigated.
Abstract: In this article, the author investigates the existence and multiplicity of positive solutions for boundary value problem of fractional differential equation with p-Laplacian operator where and are the standard Riemann-Liouville derivatives with 1 < α ≤ 2, 0 < β ≤ 1, 0 < γ ≤ 1, 0 ≤ α - γ - 1, the constant σ is a positive number and p-Laplacian operator is defined as φ
p
(s) = |s|p-2s, p > 1. By means of the fixed point theorem on cones, some existence and multiplicity results of positive solutions are obtained. 2010 Mathematical Subject Classification: 34A08; 34B18.
Journal Article•
TL;DR: In this paper, the existence of positive solu- tions for nonlinear fractional dierential equations whose nonlinearity contains the first-order derivative was studied, where the derivative is defined as the product of the first order derivative and the derivative of the second order derivative, D 0+u (t) + f(t,u(t),u 0 (t)) = 0.
Abstract: In this article, we are concerned with the existence of positive solu- tions for nonlinear fractional dierential equation whose nonlinearity contains the first-order derivative, D 0+u(t) + f(t,u(t),u 0 (t)) = 0, t 2 (0,1), n 1 < n,
TL;DR: In this paper, the authors studied coupled coincidence and coupled common fixed point theorems in ordered generalized metric spaces for nonlinear contraction condition related to a pair of altering distance functions.
Abstract: In this article, we study coupled coincidence and coupled common fixed point theorems in ordered generalized metric spaces for nonlinear contraction condition related to a pair of altering distance functions. Our results generalize and modify several comparable results in the literature. 2000 MSC: 54H25; 47H10; 54E50.
TL;DR: In this paper, several characterizations of MT -functions are first given in this paper, and then they are applied to establish some existence theorems for coincidence point and fixed point in complete metric spaces.
TL;DR: In this article, the existence of positive solutions to the singular fractional boundary value problem was investigated and the results were based on combining regularization and sequential techniques with a fixed point theorem on cones.
Abstract: We investigate the existence of positive solutions to the singular fractional boundary value problem: , u′(0) = 0, u(1) = 0, where 1 < α < 2, 0 < μ < 1, f is a Lq-Caratheodory function, , and f(t, x, y, z) may be singular at the value 0 of its space variables x, y, z. Here stands for the Caputo fractional derivative. The results are based on combining regularization and sequential techniques with a fixed point theorem on cones.
TL;DR: In this article, the authors present some new fixed point theorems for mixed monotone operators with perturbation by using the properties of cones and a fixed point theorem for mixed mixtures.
Abstract: The purpose of this paper is to present some new fixed point theorems for mixed monotone operators with perturbation by using the properties of cones and a fixed point theorem for mixed monotone operators. As applications, we utilize the results obtained in this paper to study the existence and uniqueness of positive solutions for nonlinear fractional differential equation boundary value problems.
TL;DR: The proof of Theorem 6 in the letter “Fixed point theory for cyclic weak ϕ -contraction” is correct.
TL;DR: In this paper, Sintunavarat and Kumam proved fixed point theorems for mappings satisfying certain point-dependent contractive conditions, which were later confirmed by Rouzkard and Imdad.
Abstract: Owning the concept of complex valued metric spaces introduced by Azam et al., we prove several fixed point theorems for mappings satisfying certain point-dependent contractive conditions. The main results announced by Sintunavarat and Kumam (J. Inequal. Appl. 2012:84, 2012), Rouzkard and Imdad (Comput. Math. Appl., 2012, doi:10.1016/j.camwa.2012.02.063), and Dass and Gupta (Indian J. Pure Appl. Math. 6(12):1455-1458, 1975) are deduced from our results under weaker assumptions.
TL;DR: This work proves the approximate controllability of control systems governed by a class of partial neutral functional differential systems of fractional order with state-dependent delay in an abstract space using the Krasnoselskii–Schaefer type fixed point theorem.
Abstract: We prove the approximate controllability of control systems governed by a class of partial neutral functional differential systems of fractional order with state-dependent delay in an abstract space. Sufficient conditions for approximate controllability of the control systems are established provided the approximate controllability of the corresponding linear control systems. The results are obtained by using the Krasnoselskii–Schaefer type fixed point theorem with the fractional power of operators. An example is provided to illustrate the main results.
TL;DR: In this article, the existence of random periodic solutions for SPDEs on a bounded domain with a smooth boundary was studied and the authors identified them as the solutions of coupled forward-backward infinite horizon stochastic integral equations on L 2 (D ) in general cases.