in the present paper, the concepts of module (uniform) approximate amenability and contractibility of banach algebras that are modules over another banach algebra, are introduced. the general theory is developed and some hereditary properties are given. in analogy with the banach algebraic approximate amenability, it is shown that module approximate amenability and contractibility are the same ...

Let X be a uniformly convex Banach space and S {T s : 0 ≤ s < ∞} be a nonexpansive semigroup such that F S ⋂s>0 F T s / ∅. Consider the iterative method that generates the sequence {xn} by the algorithm xn 1 αnf xn βnxn 1 − αn − βn 1/sn ∫sn 0 T s xnds, n ≥ 0, where {αn}, {βn}, and {sn} are three sequences satisfying certain conditions, f : C → C is a contraction mapping. Strong convergence of t...

A sequence (Mk) of closed subsets of Rn converges normally to M ⊂ Rn if (sc) M = lim supMk = lim inf Mk in the sense of Painlevé–Kuratowski and (nc) lim sup G(NMk ) ⊂ G(NM ), where G(NM ) (resp., G(NMk )) denotes the graph of NM (resp., NMk ), Clarke’s normal cone to M (resp., Mk). This paper studies the normal convergence of subsets of Rn and mainly shows two results. The first result states t...

Consider the linear space n of polynomials of degree n or less over the complex field. The abscissa mapping on n is the mapping that takes a polynomial to the maximum real part of its roots. This mapping plays a key role in the study of stability properties for linear systems. Burke and Overton have shown that the abscissa mapping is everywhere subdifferentially regular in the sense of Clarke o...

* Correspondence: manuel. [email protected] Instituto de Investigacion y Desarrollo de Procesos, Universidad del Pais Vasco, Campus of Leioa (Bizkaia), Aptdo. 644-Bilbao, 48080Bilbao, Spain Full list of author information is available at the end of the article Abstract This article discusses a more general contractive condition for a class of extended (p ≥ 2) -cyclic self-mappings on the union of ...

Lipschitzian and kernel aggregation operators with respect to the natural T indistinguishability operator ET and their powers are studied. A t-norm T is proved to be ET -lipschitzian, and is interpreted as a fuzzy point and a fuzzy map as well. Given an archimedean t-norm T with additive generator t, the quasi-arithmetic mean generated by t is proved to be the more stable aggregation operator w...

Keywords: Set-valued mapping Chebyshev center Uniformly convex Locally uniformly convex Chebyshev fixed point a b s t r a c t The existence of a continuous Chebyshev selection for a Hausdorff continuous set-valued mapping is studied in a Banach space with some uniform convexity. As applications, some existence results of Chebyshev fixed point for condensing set-valued mappings are given, and th...

In a previous work the authors proved under a complex assumption on the set-valued mapping, the existence of Lipschitz solutions for second order convex sweeping processes in p-uniformly smooth and q-uniformly convex Banach spaces. In the present work we prove the same result, under a condition on the distance function to the images of the set-valued mapping. Our assumption is much simpler than...

We prove that a Lipschitz (or uniformly continuous) mapping f : X → Y can be approximated by smooth Lipschitz (resp. uniformly continuous) mapping, if X is a separable Banach space admitting a smooth Lipschitz bump and either X or Y is a C(K) space (resp. super-reflexive space). As a corollary we obtain also smooth approximation of C1-smooth mappings together with their first derivatives.