Fixed points and the 'solution lemma'

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Schwarz lemma involving the boundary fixed point

Schwarz lemma involving the boundary fixed point

On the other hand, Schwarz lemma at the boundary is also an active topic in complex analysis, various interesting results have been obtained [–]. Before summarizing these results, it is necessary to give some elementary contents on the boundary fixed points []. Let D denote the unit disk in C , H( D , D ) denote the class of holomorphic self-mappings of D , N denote the set of all positive integers. The boundary point ξ ∈ ∂ D is called a fixed point of f ∈ H( D , D ) if

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FIXED POINTS FOR PAIRS OF

FIXED POINTS FOR PAIRS OF

Call for Papers Thinking about nonlinearity in engineering areas, up to the 70s, was focused on intentionally built nonlinear parts in order to improve the operational characteristics of a device or system. Keying, saturation, hysteretic phenomena, and dead zones were added to existing devices increasing their behavior diversity and precision. In this context, an intrinsic nonlinearity was treated just as a linear approximation, around equilibrium points.

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On characterizations of fixed points

On characterizations of fixed points

Abstract. We give some necessary and sufficient conditions for the existence of fixed points of a family of self mappings of a metric space and we establish an equivalent condi- tion for the existence of fixed points of a continuous compact mapping of a metric space. 2000 Mathematics Subject Classification. 54H25.

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Fixed Points and Mappings

Fixed Points and Mappings

In this paper we give some important types of mappings related to the fixed point concept. We begin with the basic definition of mappings. Then we define self maps and commutative maps. We discuss about the existence of the fixed points of such mappings with examples. The main part of this research article deals mainly with the common fixed points of a class of polynomial functions. The polynomials considered here are self compositions of a given polynomial of degree n. We prove that if a polynomial and its first composition with itself have an identical set of fixed points, then the polynomial and its n th composition with itself also have an identical set of
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FIXED POINTS AND COMMON FIXED POINTS FOR FUNDAMENTALLY NONEXPANSIVE MAPPINGS ON BANACH SPACES

FIXED POINTS AND COMMON FIXED POINTS FOR FUNDAMENTALLY NONEXPANSIVE MAPPINGS ON BANACH SPACES

MOHAMMAD MOOSAEI Abstract. In this paper, we present some fixed point theorems for fundamentally nonexpansive mappings in Banach spaces and give one common fixed point theorem for a commutative family of demiclosed fundamentally nonexpansive mappings on a nonempty weakly compact convex subset of a strictly convex Banach space with the Opial condition and a uniformly convex in every direction Banach space, respectively; moreover, we show that the common fixed points set of such a family of mappings is closed and convex.

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Vector-valued metrics, fixed points and coupled fixed points for nonlinear operators

Vector-valued metrics, fixed points and coupled fixed points for nonlinear operators

In the study of the fixed points for an operator, it is sometimes useful to consider a more general concept, namely coupled fixed points. The concept of coupled fixed point for nonlinear operators was introduced and studied by Opoitsev (see [–]) and then, in , by Guo and Lakshmikantham (see []) in connection with coupled quasisolutions of an initial value problem for ordinary differential equations. Later, a new research direction for the theory of coupled fixed points in ordered metric spaces was initiated by Gnana Bhaskar and Lakshmikantham in [] and by Lakshmikantham and Ćirić in []. Their approach is based on some contractive type conditions on the operator. For other results on coupled fixed point theory, see [–], etc.
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SPERNER S LEMMA AND BROUWER S FIXED POINT THEOREM

SPERNER S LEMMA AND BROUWER S FIXED POINT THEOREM

What we are intuitively doing with this labeling is picking a corner the point does not move closer to. We will eventually get a sequence of small 1-2-3 triangles converging to a point. If this point was not a fixed point, the continuity of f would suggest that as our triangles approach the point, all the corners would have the same labeling. This will be formalized as follows. First, we need to show that this labeling is in fact a Sperner labeling.

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Fixed points for cyclic R-contractions and solution of nonlinear Volterra integro-differential equations

Fixed points for cyclic R-contractions and solution of nonlinear Volterra integro-differential equations

In this paper, we introduce the notion of cyclic R-contraction mapping and then study the existence of fixed points for such mappings in the framework of metric spaces. Examples and application are presented to support the main result. Our result unify, complement, and generalize various comparable results in the existing literature.

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On common fixed points, periodic points, and recurrent points of continuous functions

On common fixed points, periodic points, and recurrent points of continuous functions

OF CONTINUOUS FUNCTIONS ALIASGHAR ALIKHANI-KOOPAEI Received 15 May 2002 and in revised form 27 November 2002 It is known that two commuting continuous functions on an interval need not have a common fixed point. However, it is not known if such two functions have a common periodic point. We had conjectured that two commuting continuous functions on an interval will typically have disjoint sets of periodic points. In this paper, we first prove that S is a nowhere dense subset of [0,1] if and only if {f ∈ C([0, 1]) : F m (f )∩S = ∅} is a nowhere dense subset of C([0,1]). We also give some results about the common fixed, periodic, and recurrent points of functions.
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Fixed Points and Coupled Fixed Points in Hausdorff Intuitionistic L Fuzzy Metric Spaces

Fixed Points and Coupled Fixed Points in Hausdorff Intuitionistic L Fuzzy Metric Spaces

Abstract: Fuzzy sets are sets whose elements have degrees of membership. Fuzzy sets are introduced by Lotfi.A.Zadeh [27] as an extension of the classical notion of sets. Intuitionistic fuzzy set can be utilized as a proper tool for representing hesitancy concerning both membership and non-membership of an element to a set. Atanassov [1] introduced and studied the concept of Intuitionistic fuzzy sets. The idea of Hausdorff fuzzy metric space introduced by Rodriguez-Lopez and Romaguera [16]. In this paper, a new concept of intuitionistic fuzzy fixed point theorems in Hausdorff intuitionistic L-fuzzy metric spaces is introduced and some properties and theorems about fixed points in Hausdorff intuitionistic L-fuzzy metric space are discussed.
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Fixed Points in Functional Inequalities

Fixed Points in Functional Inequalities

2 the sequence {J n x} converges to a fixed point y ∗ of J; 3 y ∗ is the unique fixed point of J in the set Y {y ∈ X | dJ n 0 x, y < ∞}; 4 dy, y ∗ ≤ 1/1 − Ldy, Jy for all y ∈ Y . In 1996, Isac and Th. M. Rassias 23 were the first to provide applications of stability theory of functional equations for the proof of new fixed point theorems with applications. By using fixed point methods, the stability problems of several functional equations have been extensively investigated by a number of authors see 24–28.

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Fixed points in uniform spaces

Fixed points in uniform spaces

We improve Angelov’s fixed point theorems of -contractions and j-nonexpansive maps in uniform spaces and investigate their fixed point sets using the concept of virtual stability. Some interesting examples and an application to the solution of a certain integral equation in locally convex spaces are also given.

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FIXED POINTS ON T0-QPMS

FIXED POINTS ON T0-QPMS

All the results we prove assumed a kind of continuity for the map T involved. This condition is meant to guarantee that we can pass the limit under the function and keep it. In [4], we will present more general fixed points results which do require any type of continuity.

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Quasi Contraction and Fixed Points

Quasi Contraction and Fixed Points

—————————————————————————————————— Abstract In this note, we establish and improve some results on fixed point theory in topological vector spaces. As a generalization of contraction maps, the concept of quasi contraction multivalued maps on a topological vector space will be defined. Further, it is shown that a quasi contraction and closed multivalued map on a topological vector space has a unique fixed point if it is bounded value.

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Existence and Data Dependence of Fixed Points and Strict Fixed Points for Contractive-Type Multivalued Operators

Existence and Data Dependence of Fixed Points and Strict Fixed Points for Contractive-Type Multivalued Operators

[15] I. A. Rus, A. Petrus¸el, and A. Sˆınt˘am˘arian, “Data dependence of the fixed point set of some multivalued weakly Picard operators,” Nonlinear Analysis, vol. 52, no. 8, pp. 1947–1959, 2003. Cristian Chifu: Department of Business, Faculty of Business, Babes¸-Bolyai University Cluj-Napoca, Horea 7, 400174 Cluj-Napoca, Romania

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New iterative methods for a common solution of fixed points for pseudo-contractive mappings and variational inequalities

New iterative methods for a common solution of fixed points for pseudo-contractive mappings and variational inequalities

In this paper, we introduce three iterative methods for finding a common element of the set of fixed points for a continuous pseudo-contractive mapping and the solution set of a variational inequality problem governed by continuous monotone mappings. Strong convergence theorems for the proposed iterative methods are proved. Our results improve and extend some recent results in the literature.

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A new iterative method for a common solution of fixed points for pseudo-contractive mappings and variational inequalities

A new iterative method for a common solution of fixed points for pseudo-contractive mappings and variational inequalities

In this article, we introduce a new iterative scheme for finding a common element of the set of fixed points for a continuous pseudo-contractive mapping and the solution set of a variational inequality problem governed by continuous monotone mappings. Strong convergence for the proposed iterative scheme is proved. Our results improve and extend some recent results in the literature.

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LEMMA 2. Let Fbe an affine transformation ofR2 , and let xyzw be points such that the

LEMMA 2. Let Fbe an affine transformation ofR2 , and let xyzw be points such that the

a and b are minimal and maximal points of the interval X = [a, b] it follows that x 6= a, b, which means that a and b are extreme points of X . EXAMPLE 1. If a, b, c are noncollinear points and X is the solid triangular region consisting of all convex combinations of these vectors, then the extreme points of X are a, b, and c. — First of all, this set is convex because Lemma 3 implies that a convex combination of convex combinations is again a convex combination. To prove the assertion about extreme points, note that if t a + u b + v c is a convex combination in which at least two coefficients are positive, then an argument like the inductive step of Lemma 3 implies that this convex combination is between two others, and therefore the only possible extreme points are the original vectors. Furthermore, if p = t x + (1 − t) y where x and y are convex combinations and 0 < t < 1, then one can check directly that at least two barycentric coordinates of p must be positive (this is a bit messy but totally elementary). Therefore a point that is not an extreme point cannot be one of a, b, c and hence these must be the extreme points of X .
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On the Set of Fixed Points and Periodic Points of Continuously Differentiable Functions

On the Set of Fixed Points and Periodic Points of Continuously Differentiable Functions

In recent years, researchers have studied the size of different sets related to the dynamics of self-maps of an interval. In this note we investigate the sets of fixed points and periodic points of continuously differentiable functions and show that typically such functions have a finite set of fixed points and a countable set of periodic points. 1. Introduction and Notation

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Fixed points and coincidence points for multimaps with not necessarily bounded images

Fixed points and coincidence points for multimaps with not necessarily bounded images

Many authors have been using the Hausdorff metric to obtain fixed point and coincidence point theorems for multimaps on a metric space. In most cases, the metric nature of the Hausdorff metric is not used and the existence part of theorems can be proved without using the concept of Hausdorff metric under much less stringent conditions on maps. The aim of this paper is to illustrate this and to obtain fixed point and coincidence point theorems for multimaps with not necessarily bounded images. Incidentally we obtain improvements over the results of Chang [3], Daffer et al. [6], Jachymski [9], Mizoguchi and Takahashi [12], and We¸grzyk [17] on the famous conjecture of Reich on multimaps (Conjecture 3.12).
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