Displaying similar documents to “Ball intersection model for Fejér zones of convex closed sets”

Existence and approximation results for SKC mappings in Busemann spaces

Safeer Hussain Khan, Mujahid Abbas, Talat Nazir (2017)

Waves, Wavelets and Fractals

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In this paper, we first discuss some properties of SKC mappings in the context of Busemann spaces and obtain a demiclosedness principle.We then prove the existence and approximation results for SKC mappings in a uniformly convex Busemann space. At the end, we give a numerical example in support of our main result. This example also shows that our iterative process is faster than some well-known iterative processes even for SKC mappings. Our results are certainly more general than many...

Convergence theorems by hybrid projection methods for Lipschitz-continuous monotone mappings and a countable family of nonexpansive mappings

Somyot Plubtieng, Poom Kumam (2011)

Banach Center Publications

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In this paper, we introduce two iterative schemes for finding a common element of the set of a common fixed points of a countable family of nonexpansive mappings and the set of solutions of the variational inequality problem for a monotone, Lipschitz-continuous mapping in a Hilbert space by using the hybrid projection methods in the mathematical programming. Then we prove strong convergence theorems by the hybrid projection methods for a monotone, Lipschitz-continuous mapping and a countable...

Delta-convex mappings between Banach spaces and applications

L. L. Veselý, L. Zajíček

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We investigate delta-convex mappings between normed linear spaces. They provide a generalization of functions which are representable as a difference of two convex functions (labelled as 5-convex or d.c. functions) and are considered in many articles. We show that delta-convex mappings have many good differentiability properties of convex functions and the class of them is very stable. For example, the class of locally delta-convex mappings is closed under superpositions and (in some...

Stability of the Iteration Method for non Expansive Mappings

Lemaire, B. (1996)

Serdica Mathematical Journal

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The general iteration method for nonexpansive mappings on a Banach space is considered. Under some assumption of fast enough convergence on the sequence of (“almost” nonexpansive) perturbed iteration mappings, if the basic method is τ−convergent for a suitable topology τ weaker than the norm topology, then the perturbed method is also τ−convergent. Application is presented to the gradient-prox method for monotone inclusions in Hilbert spaces.

Proximal normal structure and relatively nonexpansive mappings

A. Anthony Eldred, W. A. Kirk, P. Veeramani (2005)

Studia Mathematica

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The notion of proximal normal structure is introduced and used to study mappings that are "relatively nonexpansive" in the sense that they are defined on the union of two subsets A and B of a Banach space X and satisfy ∥ Tx-Ty∥ ≤ ∥ x-y∥ for all x ∈ A, y ∈ B. It is shown that if A and B are weakly compact and convex, and if the pair (A,B) has proximal normal structure, then a relatively nonexpansive mapping T: A ∪ B → A ∪ B satisfying (i) T(A) ⊆ B and T(B) ⊆ A, has a proximal point in...