Fixed point theorems for local strong pseudo-contractions (original) (raw)
Related papers
2012
A Banach space X is said to satisfy property (D) if there exists α ∈ [0,1) such that for any nonempty weakly compact convex subset E of X, any sequence {xn }⊂ E which is regular relative to E, and any sequence {yn }⊂ A(E,{xn}) which is regular relative to E, we have r(E,{yn}) ≤ αr (E,{xn}). A this property is the mild modification of the (DL)-condition. Let X be a Banach space satisfying property (D) and let E be a weakly compact convex subset of X .I fT : E → E is a mapping satisfying condition (E) and (Cλ) for some λ ∈ (0,1). We study the existence of a fixed point for this mapping.
Acta Mathematica Sinica, English Series, 2001
In this paper, we first prove the following best approximation theorems: Let E be a Hausdorff locally convex space and W be a wedge in E. Let D be an open subset of E with QED such that the closure D of D is convex. Suppose that f: B,-t CK(W) is a continuous condensing mapping. Then there exists e0 E B, such that dPD (f(eo), e,) = d,, (f(eo), D,), where pow denotes the Minkowskii function of 0; in E. Moreove:, if d,,, (/(e,,), 6,) > 0, then es E aD,. As a direct consequence, we improve and general&e the main results of Fan, Lin, and Sehgal and Singh. Next, we show several best approximation theorems and fixed point theorems for multivalued k-set-contractive mapping defined on the closed balls and annulus in cones of Banach spaces which generalize the recent results of Lin and Sehgal and Singh.
On Presic Type Extension of Banach Contraction Principle
m-hikari.com
Let (X, d) be a metric space, k a positive integer, T : X k −→ X, f : X −→ X be mappings. In this paper we have investigated under what conditions the mappings f and T will have a common fixed point. Our results extends and generalises the results of [3], [4], [5] and [6].
Fixed points and their approximation in Banach spaces for certain commuting mappings
Glasgow Mathematical Journal, 1982
1. Let X be a Banach space. Then a self-mapping A of X is said to be nonexpansive provided that ‖AX − Ay‖≤‖X − y‖ holds for all x, y ∈ X. The class of nonexpansive mappings includes contraction mappings and is properly contained in the class of all continuous mappings. Keeping in view the fixed point theorems known for contraction mappings (e.g. Banach Contraction Principle) and also for continuous mappings (e.g. those of Brouwer, Schauderand Tychonoff), it seems desirable to obtain fixed point theorems for nonexpansive mappings defined on subsets with conditions weaker than compactness and convexity. Hypotheses of compactness was relaxed byBrowder [2] and Kirk [9] whereas Dotson [3] was able to relax both convexity and compactness by using the notion of so-called star-shaped subsets of a Banach space. On the other hand, Goebel and Zlotkiewicz [5] observed that the same result of Browder [2] canbe extended to mappings with nonexpansive iterates. In [6], Goebel-Kirk-Shimi obtainedfix...
Fixed point theorems for nonself Kannan type contractions in Banach spaces endowed with a graph
Carpathian Journal of Mathematics, 2016
Let K be a non-empty closed subset of a Banach space X endowed with a graph G. The main result of this paper is a fixed point theorem for nonself Kannan G-contractions T : K → X that satisfy Rothe's boundary condition, i.e., T maps ∂K (the boundary of K) into K. Our new results are extensions of recent fixed point theorems for self mappings on metric spaces endowed with a partial order and also of various fixed point theorems for self and nonself mappings on Banach spaces or convex metric spaces.
Fixed Point of Pseudo Contractive Mapping in a Banach Space
2020
Let X be a Banach space, B a closed ball centred at origin in X, f : B → X a pseudo contractive mapping i.e. (α−1)‖x− y‖ ≤ ‖(αI−f)(x)− (αI−f)(y)‖ for all x and y in B and α > 1. Here we shown that Mapping f satisfies the property that f(x) = −f(−x) ∀ x in ∂B called antipodal boundary condition assures existence of fixed point of f in B provided that ball B has a fixed point property with respect to non expansive self mapping. Also included some fixed point theorems which involve the Leray-Schauder condition.
APPROXIMATION OF FIXED POINTS OF ASYMPTOTICALLY PSEUDOCONTRACTIVE MAPPINGS IN BANACH SPACES
Let T be an asymptotically pseudocontractive self-mapping of a nonempty closed convex subset D of a reflexive Banach space X with a Gâteaux differentiable norm. We deal with the problem of strong convergence of almost fixed points xn = µnT n xn + (1 − µn)u to fixed point of T . Next, this result is applied to deal with the strong convergence of explicit iteration process
On the approximation of fixed points for locally pseudo-contractive mappings
Proceedings of the American Mathematical Society, 1995
Let X and its dual X* be uniformly convex Banach spaces, D an open and bounded subset of X, Ta continuous and pseudo-contractive mapping defined on cl(D) and taking values in X. If T satisfies the following condition: there exists z £ D such that \\z-Tz\\ < \\x-Tx\\ for all x on the boundary of D , then the trajectory t-* zt £ D, t G [0, 1), defined by Z(= tT(z,) + (1-t)z is continuous and converges strongly to a fixed point of T as t-> 1- .