[PDF] Top 20 Approximating fixed points of nonexpansive type mappings

... In a uniformly convex Banach space, the convergence of Ishikawa iterates to a unique fixed point is proved for nonexpansive type mappings under certain conditions.. 2000 Mathematics Subje[r] ... See full document

... for nonexpansive single valued mappings in CAT ...multivalued nonexpansive map- pings in CAT(0) ...valued mappings, called conditions (E ) and (C λ ), which are weaker than nonexpansiveness ... See full document

... Let C be a closed convex subset of a Banach space E. A mapping T on C is called a non- expansive mapping if Tx − T y ≤ x − y for all x , y ∈ C . We denote by F ( T ) the set of fixed points of T. Kirk [17] ... See full document

... quasi-nonexpansive mappings to a common fixed point of the mappings defined on a nonempty closed convex subset of a uniformly convex Banach ... See full document

... Motivated and inspired by Xu [36], Kimura and Nakajo [16], we introduce a new hybrid projection algorithm for finding a common element of the solutions set of a generalized mixed equilibrium problem and the fixed ... See full document

... In 2000, Noor [16] introduced a three-step iterative scheme and studied the approximate solu- tions of variational inclusion in Hilbert spaces. Suantai [19] defined a new three-step iterations which is an extension of ... See full document

... for sequences of fuzzy mappings which generalize the results in In this paper we define g-nonexpansive and g-nonexpansive type fuzzy mappings and show that a sequence of fuzzy mappings w[r] ... See full document

... all fixed points of ...asymptotic fixed point of T (see Reich [23]) if there exists a sequence { z n } in C converging weakly to z and lim n z n − Tz n = ... See full document

... fixed points of monotone nonexpansive mappings defined in Banach spaces endowed with a ...contraction mappings defined in metric spaces endowed with a ... See full document

... It is our purpose in this paper to extend the above results from a Hilbert spaces to arbitrary Banach spaces and from nonexpansive mappings to the more general asymptotically nonexpan- sive mappings. ... See full document

... of mappings has a fixed point, which is a point of discontinuity for all the ...study fixed points of discontinuous mappings in various ...common fixed point theorem in an ... See full document

... the fixed point property, if for each nonexpansive mapping T : E −→ E on a nonempty bounded closed convex subset E of X has a fixed ...the fixed point ... See full document

... Theorem 2.2: Let C be a non empty , closed , convex and bounded subset of a banach space X. If f: CC satisfies the inequalities (2.2) and (2.3) with a>0,b>0 then f has a unique fixed point. Proof: Let x = 𝑥 ... See full document

... nonexpansive mappings include properly the class of nonexpansive mappings in locally convex spaces, prove a theorem on the existence of fixed points, and the convergence of the sequence [r] ... See full document

... A family of commuting nonexpansive self-mappings, one of which is weakly contractive, are stud- ied. Some convergence theorems are established for the iterations of types Krasnoselski-Mann, Kirk, and ... See full document

... Lemma . Let C be a nonempty subset of a CAT() space X. Let T : C → X be an α- nonexpansive mapping for some α <  such that F(T) = ∅. Then T is quasi-nonexpansive. Lemma . Let C be a nonempty closed ... See full document

... Remark 2.8. Theorem 3 in 3 and Theorem 1 in 7 and 8 are special cases of Corollary 2.7. Corollary 2.9. Let X be a nonempty closed subset of a Banach space E, · and let T : X, · → E, · be quasi-nonexpansive. Assume ... See full document

... fixed points set F(T ) in D will be said to satisfy condition A [2, 4] if there is a nondecreasing function f : [0,∞) → [0,∞) with f (0) = 0, f (r ) > 0 for r ∈ (0,∞), such that x − Sx ≥ f (d(x,F(T ))) for all x ... See full document

... called nonexpansive. The nonexansive mappings have been studied by Kirk and Goebel [6] for fixed ...generalized nonexpansive mappings characterized by the ... See full document

... 1. [[3], Proposition 2.4] Let K be a convex subset of X which is complete in the induced metric. Then for every x Î X, there exists a unique point P(x) Î K such that d(x, P(x)) = inf{d(x, y): y Î K}. Moreover, the map x ... See full document