Showing papers on "Fixed-point theorem published in 2014"
Book•
14 Mar 2014
TL;DR: The FIXED POINT Theory of MULTIVALUED MAPPINGS (FPTTH) as mentioned in this paper is a fixed point theory of multiview mapping. But it is not suitable for multivaluided mapping.
Abstract: BACKGROUND IN TOPOLOGY.- MULTIVALUED MAPPINGS.- APPROXIMATION METHODS IN FIXED POINT THEORY OF MULTIVALUED MAPPINGS.- HOMOLOGICAL METHODS IN FIXED POINT THEORY OF MULTIVALUED MAPPINGS.- CONSEQUENCES AND APPLICATIONS.- FIXED POINT THEORY APPROACH TO DIFFERENTIAL INCLUSIONS.- RECENT RESULTS.
596 citations
Book•
14 Mar 2014
TL;DR: In this paper, the authors introduce the concept of triangular norms in topological vector spaces and apply it to random normed spaces, where the Hicks' contraction principle is applied for single-valued mappings and the GBPIiGBP-contraction principle for multi-valued mapping.
Abstract: Introduction 1 Triangular norms 2 Probabilistic metric spaces 3 Probabilistic GBPIiGBP-contraction principles for single-valued mappings 4 Probabilistic GBPIiGBP-contraction principles for multi-valued mappings 5 Hicks' contraction principle 6 Fixed point theorems in topological vector spaces and applications to random normed spaces Bibliography Index
461 citations
TL;DR: In this paper, the authors extend the result of Wardowski by applying some weaker conditions on the self map of a complete metric space and on the mapping F, concerning the contractions defined by Wardowski.
Abstract: In this paper, we extend the result of Wardowski (Fixed Point Theory Appl. 2012:94, 2012) by applying some weaker conditions on the self map of a complete metric space and on the mapping F, concerning the contractions defined by Wardowski. With these weaker conditions, we prove a fixed point result for F-Suzuki contractions which generalizes the result of Wardowski.
MSC:74H10, 54H25.
210 citations
TL;DR: In this article, the notion of F-weak contraction was introduced and a fixed point theorem for F -weak contractions was proved. But this result is not a proper extension of some results known in the literature.
Abstract: Abstract In this paper, we introduce the notion of an F-weak contraction and prove a fixed point theorem for F-weak contractions. Examples are given to show that our result is a proper extension of some results known in the literature
160 citations
TL;DR: In this paper, the concept of partial b-metric spaces is introduced as a generalization of partial metric and b-measure spaces, and an analog to Banach contraction principle, as well as a Kannan type fixed point result is proved in such spaces.
Abstract: The purpose of this paper is to introduce the concept of partial b-metric spaces as a generalization of partial metric and b-metric spaces. An analog to Banach contraction principle, as well as a Kannan type fixed point result is proved in such spaces. Some examples are given which illustrate the results.
148 citations
TL;DR: In this article, the authors generalize the results obtained in Cho et al. (2013) and give other conditions to prove the existence and uniqueness of a fixed point of α-Geraghty contraction type maps in the context of complete metric spaces.
Abstract: We generalize the results obtained in Cho et al. (Fixed Point Theory Appl. 2013:329, 2013) and give other conditions to prove the existence and uniqueness of a fixed point of α-Geraghty contraction type maps in the context of a complete metric space.
140 citations
TL;DR: It is established that the uniqueness of positive solution for a fractional model of turbulent flow in a porous medium is established by using the fixed point theorem of the mixed monotone operator.
135 citations
TL;DR: In this article, a fixed point theorem for self-mappings on complete metric spaces or complete ordered metric spaces has been proved and an example is given to illustrate the usability of the obtained results.
Abstract: Recently, Wardowski introduced a new concept of contraction and proved a fixed
point theorem which generalizes Banach contraction principle. Following this
direction of research, in this paper, we will present some fixed point
results of Hardy-Rogers-type for self-mappings on complete metric spaces or
complete ordered metric spaces. Moreover, an example is given to illustrate
the usability of the obtained results.
130 citations
TL;DR: In this article, a thorough study of fixed point theory and the asymptotic behaviour of Picard iterates of these mappings in different classes of geodesic spaces, such as (uniformly convex) W -hyperbolic spaces, Busemann spaces and CAT(0) spaces, is presented.
Abstract: Firmly nonexpansive mappings play an important role in metric fixed point theory and optimization due to their correspondence with maximal monotone operators. In this paper we do a thorough study of fixed point theory and the asymptotic behaviour of Picard iterates of these mappings in different classes of geodesic spaces, such as (uniformly convex) W -hyperbolic spaces, Busemann spaces and CAT(0) spaces. Furthermore, we apply methods of proof mining to obtain effective rates of asymptotic regularity for the Picard iterations. MSC: Primary: 47H09, 47H10, 53C22; Secondary: 03F10, 47H05, 90C25, 52A41.
127 citations
TL;DR: An extension of Darbo's fixed point theorem associated with measures of noncompactness is given, and some results on the existence of coupled fixed points for a class of condensing operators in Banach spaces are presented.
125 citations
TL;DR: A uniform framework to derive a formula of solutions for impulsive fractional Cauchy problem involving generalization of classical Caputo derivative with the lower bound at zero is constructed and a new concept of generalized Ulam–Hyers–Rassias stability is introduced.
TL;DR: This paper investigates a general class of neural networks with a fractional-order derivative by using the contraction mapping principle, Krasnoselskii fixed point theorem and the inequality technique to ensure the existence and uniqueness of the nontrivial solution.
TL;DR: In this article, a concept of -algebra-valued metric spaces and fixed point theorems for self-maps with contractive or expansive conditions on such spaces are introduced.
Abstract: Based on the concept and properties of -algebras, the paper introduces a concept of -algebra-valued metric spaces and gives some fixed point theorems for self-maps with contractive or expansive conditions on such spaces. As applications, existence and uniqueness results for a type of integral equation and operator equation are given.
MSC:47H10, 46L07.
TL;DR: An existence result of optimal multi-control pairs governed by the presented system is proved and a new kind of Sobolev type appears in terms of two linear operators.
TL;DR: In this article, the generalized Lipschitz mappings on cone metric spaces over Banach algebras without the assumption of normality were studied and the main results improve and generalize the corresponding results in the recent paper by Liu and Xu.
Abstract: In this paper, we first present some elementary results concerning cone metric spaces over Banach algebras. Next, by using these results and the related ones about c-sequence on cone metric spaces we obtain some new fixed point theorems for the generalized Lipschitz mappings on cone metric spaces over Banach algebras without the assumption of normality. As a consequence, our main results improve and generalize the corresponding results in the recent paper by Liu and Xu (Fixed Point Theory Appl. 2013:320, 2013).
TL;DR: In this article, the authors introduced the concepts of complete metric space and continuous function and established fixed point results for modified rational contraction mappings in complete metric spaces, and derived some Suzuki type fixed point theorems for -graphic-rational contractions.
Abstract: The aim of this paper is to introduce new concepts of --complete metric space and --continuous function and establish fixed point results for modified ---rational contraction mappings in --complete metric spaces. As an application, we derive some Suzuki type fixed point theorems and new fixed point theorems for -graphic-rational contractions. Moreover, some examples and an application to integral equations are given here to illustrate the usability of the obtained results.
TL;DR: By using fixed point theorems of concave operators in partial ordering Banach spaces, the existence and uniqueness of positive solutions to a class of four-point boundary value problem of Caputo fractional differential equations for any given parameter are established.
TL;DR: The approximate controllability of fractional evolution equations involving Caputo fractional derivative under the assumption that the corresponding linear system is approximately controllable is discussed.
TL;DR: In this article, the authors introduce generalized contractive mappings in the setting of generalized metric spaces and, based on the very recent paper (Kirk and Shahzad in Fixed Point Theory Appl. 2013:129, 2013), they omit the Hausdorff hypothesis to prove some fixed point results involving such mappings.
Abstract: In this paper, we introduce some generalized -contractive mappings in the setting of generalized metric spaces and, based on the very recent paper (Kirk and Shahzad in Fixed Point Theory Appl. 2013:129, 2013), we omit the Hausdorff hypothesis to prove some fixed point results involving such mappings. Some consequences on existing fixed point theorems are also derived. MSC:46T99, 47H10, 54H25.
TL;DR: A nonlocal control condition and the notion of approximate controllability for fractional order quasilinear control inclusions are introduced and an appropriate set of sufficient conditions for the considered system to be approximately controllable are given.
TL;DR: The fixed point method has been applied for the first time, in proving the stability results for functional equations, by Baker (1991); he used a variant of Banach's fixed point theorem to obtain the stability of a functional equation in a single variable as discussed by the authors.
Abstract: The fixed point method has been applied for the first time, in proving the stability results for functional equations, by Baker (1991); he used a variant of Banach's fixed point theorem to obtain the stability of a functional equation in a single variable. However, most authors follow the approaches involving 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 stability of functional equations, motivated by a problem raised by Ulam in 1940.
TL;DR: In this paper, a new fixed point theorem in the setting of Branciari metric spaces is established, which is an extension of the recent fixed-point theorem established in Jleli and Samet (J. Inequal. 2014:38, 2014).
Abstract: We establish a new fixed point theorem in the setting of Branciari metric spaces. The obtained result is an extension of the recent fixed point theorem established in Jleli and Samet (J. Inequal. Appl. 2014:38, 2014).
TL;DR: This work investigates the existence of solutions for a nonlinear fractional q-difference integral equation (q-variant of the Langevin equation) with two different fractional orders and nonlocal four-point boundary conditions.
Abstract: We investigate the existence of solutions for a nonlinear fractional q-difference integral equation (q-variant of the Langevin equation) with two different fractional orders and nonlocal four-point boundary conditions. Our results are based on some classical fixed point theorems. An illustrative example is also presented.
TL;DR: In this paper, the p-metric space is extended to an M-measure space and generalized contractions for getting fixed points and common fixed points for mappings are presented.
Abstract: In this paper, we extend the p-metric space to an M-metric space, and we shall show that the definition we give is a real generalization of the p-metric by presenting some examples. In the sequel we prove some of the main theorems by generalized contractions for getting fixed points and common fixed points for mappings.
TL;DR: In this article, the authors prove the existence and uniqueness of mild solutions to Sobolev type fractional nonlocal dynamic equations in Banach spaces, in terms of a Riemann-Liouville fractional derivative.
Abstract: We prove existence and uniqueness of mild solutions to Sobolev type fractional nonlocal dynamic equations in Banach spaces. The Sobolev nonlocal condition is considered in terms of a Riemann-Liouville fractional derivative. A Lagrange optimal control problem is considered, and existence of a multi-integral solution obtained. Main tools include fractional calculus, semigroup theory, fractional power of operators, a singular version of Gronwall's inequality, and Leray-Schauder fixed point theorem. An example illustrating the theory is given.
TL;DR: In this article, the authors introduced an alpha-GF contraction with respect to a general family of functions and established Wardowski type fixed point results for GF-contractions in metric and ordered metric spaces.
Abstract: Recently, Wardowski [Fixed Point Theory Appl. 2012:94, 2012] introduced and studied a new contraction called F-contraction to prove a fixed point result as a generalization of the Banach contraction principle. Abbas et al. [2] further generalized the concept of F-contraction and proved certain fixed and common fixed point results. In this paper, we introduce an $\alpha$-GF-contraction with respect to a general family of functions $G$ and establish Wardowski type fixed point results in metric and ordered metric spaces. As an application of our results we deduce Suzuki type fixed point results for GF-contractions. We also derive certain fixed and periodic point results for orbitally continuous generalized F-contractions. Moreover, we discuss some illustrative examples to highlight the realized improvements.
TL;DR: In this article, the existence of a class of fractional initial value problems (FIVP) with fixed-point theorems and lower and upper solution methods was proved.
Abstract: In this paper, by using fixed-point theorems, and lower and upper solution method, the existence for a class of fractional initial value problem (FIVP) D αu(t )= f (t, u(t)) ,t ∈ (0 ,h ), t 2−α u(t) |t=0= b1 ,D α−1 0+ u(t) |t=0= b2,
TL;DR: In this paper, the theory of fractional hybrid differential equations with linear and nonlinear perturbations involving the Caputo fractional derivative of order was developed, and the existence of mild solutions for two types of hybrid equations was proved.
Abstract: We develop the theory of fractional hybrid differential equations with linear and nonlinear perturbations involving the Caputo fractional derivative of order . Using some fixed point theorems we prove the existence of mild solutions for two types of hybrid equations. Examples are given to illustrate the obtained results.
TL;DR: The results of this paper are completely new even when the time scale T = R or Z and show that the delays in the leakage term do harm to the existence and global exponential stability of almost automorphic solutions.
TL;DR: The results presented in this paper substantially generalize and extend several comparable results in the existing literature and some examples are given to support the usability of the results.
Abstract: The aim of this paper is to introduce a new class of contractive mappings such as fuzzy α-ψ-contractive mappings and to present some fixed point theorems for such mappings in complete fuzzy metric space in the sense of Kramosil and Michalek. The results presented in this paper substantially generalize and extend several comparable results in the existing literature. Also, some examples are given to support the usability of our results.