[PDF] Top 20 Fixed point property and approximation of a class of nonexpansive mappings

... On the other hand, using the Picard iterative method, the well-known Banach Contrac- tion Principle is obtained: Let (E, d) be a complete metric space and T : E → E is a con- traction (i.e. d(Tx, Ty) ≤ kd(x, y), ∀ x, y ∈ ... See full document

... new class of self-maps which satisfy the (E.A.) property with respect to some q ∈ M, where M is q-starshaped subset of a convex metric space and establish some common fixed point results for this ... See full document

... Remark . Our results extend and unify most of the results that have been proved for this important class of nonlinear mappings. In particular, Theorem . improves Theo- rem . of Yang et al. [] and of ... See full document

... unique fixed point of T , but it fails to approxi- mate fixed point for nonexpansive mappings, even when the existence of a fixed point of T is ...a fixed ... See full document

... the class of SKC-mappings, which is a generalization of the class of Suzuki-generalized nonexpansive mappings, and we prove the strong and -convergence theorems of the S-iteration ... See full document

... Nonexpansive mappings are Lipschitzian with Lipschitz constant equal to . The class of nonexpansive mappings enjoys the fixed point property and even the approximate fixed ... See full document

... The purpose of this paper is to study sufficient and necessary conditions for finite- step iterative sequences with mean errors for a finite family of asymptotically quasi- nonexpansive-type mappings in ... See full document

... only if it is reflexive (see [4]). This result is a partial answer to a longtime open major question in metric fixed-point theory: does every reflexive Banach space have FPP? (See [22].) A particular case of this ... See full document

... common fixed points of nonexpansive mappings, the set of solutions of an equilibrium problem, and the solution set of the classical variational inequality problem for a monotone L-Lipschitz ... See full document

... the class of quasi-nonexpansive mappings, that is, the set of common fixed points of a countable family of quasi-nonexpansive mappings is identical to the ... See full document

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

... Let E be a reflexive Banach space with a uniformly Gˆateaux differentiable norm. Suppose that every weakly compact convex subset of E has the fixed point property for nonexpansive ... See full document

... The class of hemirelatively nonexpansive mappings is more general than the class of relatively nonexpansive mappings which requires the restriction: FT FT ...hemirelatively ... See full document

... pansive mappings (or ...convex approximation property of a space, proved that contractions satisfy an inequality analogue to the Zarantonello inequality (see []) and then studied the asymptotic ... See full document

... of fixed point sets of nonexpansive mappings,” in Inherently Parallel Algorithms in Feasibility and Optimization and Their Applications, ... See full document

... The purpose of this paper is to extend Theorem . to countably many numbers of single-valued nonexpansive mappings on strictly convex Banach spaces, thereby the re- sult in Theorem . is covered. The ... See full document

... Fixed point theory for multivalued mappings has many useful applications in Applied Sciences, in particular, in game theory and mathematical ...known fixed point results for ... See full document

... new class of generalized nonexpansive mappings which is wider than the class of mappings satisfying (C) ...fixed point results for these mappings are obtained ...fixed ... See full document

... the fixed points set of T ...is nonexpansive if kT (x)− T (y)k 6 kx − yk for all x, y ∈ ...the fixed point property (or weak fixed point property) if for every ... See full document

... this property (around the early sixties of last century) that it depends strongly on ¨nice¨ geometrical properties of the ...metric fixed point theory is: Does every reflexive Banach space have ... See full document