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The new investigation of the stability ofmixed type additive-quartic functionalequations in non-Archimedean spaces

Thanyacharoen Anurak, Sintunavarat Wutiphol

Demonstratio Mathematica

2020

Vol. 53, nr 1

174--192

In this article, we prove the generalized Hyers-Ulam stability for the following additive-quarticfunctional equation: f(x + 3y) + f(x - 3y) + f(x + 2y) + f(x - 2y) + 22f(x) + 24f(y) = 13[ f(x + y) + f(x - y)] + 12f(2y), where f maps from an additive group to a complete non-Archimedean normed space.

On locally Hilbert spaces

Gheondea A.

Opuscula Mathematica

2016

Vol. 36, no. 6

735--747

This is an investigation of some basic properties of strictly inductive limits of Hilbert spaces, called locally Hilbert spaces, with respect to their topological properties, the geometry of their subspaces, linear functionals and dual spaces.

Remarks on the Sobolev type spaces of multifunctions

Kasperski A.

Zeszyty Naukowe. Matematyka Stosowana / Politechnika Śląska

2015

z. 5

53--60

In this paper we introduce the spaces of multifunctions SX,pq and Xpq which correspond with the Sobolev space Wpq and the space of multifunctions Xmkc,φ,k,Y which correspond with the Orlicz-Sobolev space Wkφ. We study completeness of them. Also we give some theorems.

W artykule wprowadzamy przestrzenie multifunkcji SXpq and Xpq, które odpowiadają przestrzeni Soboleva Wpq, oraz przestrzeń multifunkcji Xmkc,φ,k,Y , która odpowiada przestrzeni Orlicza-Soboleva Wkφ. Badamy zupełność tych przestrzeni. Podajemy także pewne twierdzenia dotyczące tych przestrzeni.

Extreme points and support points of a class of analytic functions with missing coefficients

Xiong L., Tian L, Luo S., Liu X.

Demonstratio Mathematica

2013

Vol. 46, nr 3

525--532

Let Mn(a, b, c) denote a class of functions of the form (...) which are analytic in open unit disk (...) and satisfy the condition (...). In this paper, we obtain the extreme points and support points of the class Mn(a, b, c) of functions.

On the sign of L(f) and its "error term" when f is an n-convex function

Mercer A. McD., Mercer P. R.

Demonstratio Mathematica

2011

Vol. 44, nr 2

223-231

A method is presented for finding the sign and defect of a linear functional L when it operates on an n-convex function.