DSpace Collection: Volume 22 Number 1
http://hdl.handle.net/10525/523
Serdica Mathematical Journal Volume 22, Number 1, 1996The Collection's search engineSearch the Channelsearch
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A Note on Coercivity of Lower Semicontinuous Functions and Nonsmooth Critical Point Theory
http://hdl.handle.net/10525/600
Title: A Note on Coercivity of Lower Semicontinuous Functions and Nonsmooth Critical Point Theory<br/><br/>Authors: Corvellec, J.<br/><br/>Abstract: The first motivation for this note is to obtain a general versionof the following result: let E be a Banach space and f : E → R be a differentiablefunction, bounded below and satisfying the Palais-Smale condition; then, f is coercive,i.e., f(x) goes to infinity as ||x|| goes to infinity. In recent years, many variants andextensions of this result appeared, see [3], [5], [6], [9], [14], [18], [19] and the referencestherein.A general result of this type was given in [3, Theorem 5.1] for a lower semicontinuousfunction defined on a Banach space, through an approach based on an abstractnotion of subdifferential operator, and taking into account the “smoothness” of theBanach space. Here, we give (Theorem 1) an extension in a metric setting, based onthe notion of slope from [11] and coercivity is considered in a generalized sense, inspiredby [9]; our result allows to recover, for example, the coercivity result of [19], where aweakened version of the Palais-Smale condition is used. Our main tool (Proposition 1)is a consequence of Ekeland’s variational principle extending [12, Corollary 3.4], anddeals with a function f which is, in some sense, the “uniform” Γ-limit of a sequence offunctions.Generalizations of Cole's Systems
http://hdl.handle.net/10525/599
Title: Generalizations of Cole's Systems<br/><br/>Authors: Gizatullin, Marat<br/><br/>Abstract: There are four resolvable Steiner triple systems on fifteen elements.Some generalizations of these systems are presented here.Sharp Bounds on the Number of Resonances for Symmertic Systems II. Non-Compactly Supported Perturbations
http://hdl.handle.net/10525/598
Title: Sharp Bounds on the Number of Resonances for Symmertic Systems II. Non-Compactly Supported Perturbations<br/><br/>Authors: Vodev, G.<br/><br/>Abstract: We extend the results in [5] to non-compactly supported perturbationsfor a class of symmetric first order systems.Representable Banach Spaces and Uniformly Gateaux-Smooth Norms
http://hdl.handle.net/10525/597
Title: Representable Banach Spaces and Uniformly Gateaux-Smooth Norms<br/><br/>Authors: Frontisi, Julien<br/><br/>Abstract: It is proved that a representable non-separable Banach space doesnot admit uniformly Gâteaux-smooth norms. This is true in particular for C(K)spaces where K is a separable non-metrizable Rosenthal compact space.A Note on Preserved Smoothness
http://hdl.handle.net/10525/596
Title: A Note on Preserved Smoothness<br/><br/>Authors: Tang, Wee-Kee<br/><br/>Abstract: Let X be a Banach space equipped with norm || · ||. We say that || · || is Gâteauxdifferentiable at x if for every h ∈ SX(|| · ||),(∗) lim t→0 (||x + th|| − ||x||) / t exists.We say that the norm || · || is Gâteaux differentiable if || · || is Gâteaux differentiableat all x ∈ SX(|| · ||).<br/><br/>Description: * Supported by NSERC (Canada)Analytic Renormings of C(K) Spaces
http://hdl.handle.net/10525/595
Title: Analytic Renormings of C(K) Spaces<br/><br/>Authors: Hájek, Petr<br/><br/>Abstract: The aim of our present note is to show the strength of the existence of anequivalent analytic renorming of a Banach space, even compared to C∞-Fréchet smoothrenormings.It was Haydon who first showed in [8] that C(K) spaces for K countable admitan equivalent C∞-Fréchet smooth norm. Later, in [7] and [9] he introduced a largeclams of tree-like (uncountable) compacts K for which C(K) admits an equivalentC∞-Fréchet smooth norm.Recently, it was shown in [3] that C(K) spaces for K countable admit an equivalentanalytic norm. Our Theorem 1 shows that in the class of C(K) spaces this resultis the best possible.Equisummability Theorems for Laguerre Series
http://hdl.handle.net/10525/594
Title: Equisummability Theorems for Laguerre Series<br/><br/>Authors: Abd El-Aal El-Adad, El-Sayed<br/><br/>Abstract: Here we prove results about Riesz summability of classical Laguerre series,locally uniformly or on the Lebesgue set of the function f suchthat (∫(1 + x)^(mp) |f(x)|^p dx )^(1/p) < ∞, for some p and m satisfying 1 ≤ p ≤ ∞, −∞ < m < ∞.