© Hindawi Publishing Corp. A RENORMING OF 2, RARE BUT WITH THE FIXED-POINT PROPERTY (original) (raw)
Related papers
On fixed points of fundamentally nonexpansive mappings in Banach spaces
2016
We first obtain some properties of a fundamentally nonexpansive self-mapping on a nonempty subset of a Banach space and next show that if the Banach space is having the Opial condition, then the fixed points set of such a mapping with the convex range is nonempty. In particular, we establish that if the Banach space is uniformly convex, and the range of such a mapping is bounded, closed and convex, then its the fixed points set is nonempty, closed and convex.
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.
Fixed point theorems for -nonexpansive mappings
Applied Mathematics Letters, 2010
compact convex subsets of a Banach space X which is uniformly convex in every direction. Furthermore, if {T i } i∈I is any compatible family of strongly nonexpansive self-mappings on such a C and the graphs of T i , i ∈ I, have a nonempty intersection, then T i , i ∈ I, have a common fixed point in C.
Fixed Points and Common Fixed Points for Fundamentally Nonexpansive Mappings on Banach Spaces
2015
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.
Fixed point property and approximation of a class of nonexpansive mappings
Fixed Point Theory and Applications, 2014
We introduce the concept of ψ-firmly nonexpansive mapping, which includes a firmly nonexpansive mapping as a special case in a uniformly convex Banach space. It is shown that every bounded closed convex subset of a reflexive Banach space has the fixed point property for ψ-firmly nonexpansive mappings, an important subclass of nonexpansive mappings. Furthermore, Picard iteration of this class of mappings weakly converges to a fixed point. MSC: 47H06; 47J05; 47J25; 47H10; 47H17
Fixed-Point Theorems for Multivalued Non-Expansive Mappings Without Uniform Convexity
Abstract and Applied …, 2003
Let X be a Banach space whose characteristic of noncompact convexity is less than 1 and satisfies the nonstrict Opial condition. Let C be a bounded closed convex subset of X, KC(C) the family of all compact convex subsets of C, and T a nonexpansive mapping from C into KC(C). We prove that T has a fixed point. The nonstrict Opial condition can be removed if, in addition, T is a 1-χcontractive mapping.
Fixed point theory and nonexpansive mappings
Arabian Journal of Mathematics, 2012
Recall that a Banach space X has the weak fixed point property if for any nonempty weakly compact subset C of X and any nonexpansive mapping T : C→C, T has at least one fixed point. In this article, we present three recent results using the ultraproduct technique. We also provide some open problems in this area.
Common fixed-point results in uniformly convex Banach spaces
Fixed Point Theory and Applications, 2012
We introduce a condition on mappings, namely condition (K). In a uniformly convex Banach space, the condition is weaker than quasi-nonexpansiveness and weaker than asymptotic nonexpansiveness. We also present the existence theorem of common fixed points for a commuting pair consisting of a mapping satisfying condition (K) and a multivalued mapping satisfying conditions (E) and (C λ ) for some λ ∈ (0, 1).