2018
3
2
8
125
Different type of fixed point theorem for multivalued mappings
2
2
In this paper by using the measure of noncompactness concept, we present new fixed point theorems for multivalued maps. In further we introduce a new class of mappings which are general than MeirKeeler mappings. Finally, we use these results to investigate the existence of weak solutions to an Evolution differential inclusion with lack of compactness.
1

326
336


Nour El Houda
Bouzara
Algeria
bzr.nour@gmail.com


Vatan
Karakaya
Turkey
vkkaya@yahoo.com
fixed point
Measure of noncompactness
Evolution inclusions
Singular Riesz measures on symmetric cones
2
2
A fondamental theorem due to Gindikin says that the generalized power $Delta_{s}(theta^{1})$ defined on a symmetric cone is the Laplace transform of a positive measure $R_{s}$ if and only if $s$ is in a given subset $Xi$ of $Bbb{R}^{r}$, where $r$ is the rank of the cone. When $s$ is in a well defined part of $Xi$, the measure $R_{s}$ is absolutely continuous with respect to Lebesgue measure and has a known expression. For the other elements $s$ of $Xi$, the measure $R_{s}$ is concentrated on the boundary of the cone and it has never been explicitly determined. The aim of the present paper is to give an explicit description of the measure $R_{s}$ for all $s$ in $Xi$. The work is motivated by the importance of these measures in probability theory and in statistics since they represent a generalization of the class of measures generating the famous Wishart probability distributions.
1

337
350


Abdelhamid
Hassairi
Sfax university
Sfax university
Tunisia
abdelhamid.hassairi@fss.rnu.tn


Sallouha
Lajmi
Sfax University
Sfax University
Tunisia
sallouha.lajmi@enis.tn
Jordan algebra
symmetric cone
generalized power
Laplace transform
Riesz measure
Cover topologies, subspaces, and quotients for some spaces of vectorvalued functions
2
2
Let $X$ be a completely regular Hausdorff space, and let $mathcal{D}$ be a cover of $X$ by $C_{b}$embedded sets. Let $pi :mathcal{E}$ $rightarrow X$ be a bundle of Banach spaces (algebras), and let $Gamma(pi)$ be the section space of the bundle $pi .$ Denote by $Gamma _{b}(pi,mathcal{D})$ the subspace of $Gamma (pi )$ consisting of sections which are bounded on each $Din mathcal{D}$. We construct a bundle $rho ^{prime }:mathcal{F}^{prime}rightarrow beta X$ such that $Gamma _{b}(pi ,mathcal{D}) $ is topologically and algebraically isomorphic to $Gamma(rho^prime)$, and use this to study the subspaces (ideals) and quotients resulting from endowing $Gamma _{b}(pi,mathcal{D})$ with the cover topology determined by $mathcal{D}$.
1

351
364


Terje
Hoim
Wilkes Honors College
Florida Atlantic University
Jupiter, FL 33458
Wilkes Honors College
Florida Atlantic University
USA
thoim@fau.edu


David
Robbins
Trinity College
Hartford, CT 06106
Trinity College
Hartford, CT 06106
USA
david.robbins@trincoll.edu
cover topology
bundle of Banach spaces
bundle of Banach algebras
Integral representations and asymptotic behaviour of a MittagLeffler type function of two variables
2
2
Integral representations play a prominent role in the analysis of entire functions. The representations of generalized MittagLeffler type functions and their asymptotics have been (and still are) investigated by plenty of authors in various conditions and cases.The present paper explores the integral representations of a special function extending to two variables the twoparametric MittagLeffler type function. Integral representations of this functions within different variation ranges of its arguments for certain values of the parameters are thus obtained. Asymptotic expansion formulas and asymptotic properties of this function are also established for large values of the variables. This yields corresponding theorems providing integral representations as well as expansion formulas.
1

365
373


Christian
Lavault
LIPN, CNRS UMR 7030, Universite Paris 13, Sorbonne Paris Cite,
F93430 Villetaneuse, France.
LIPN, CNRS UMR 7030, Universite Paris 13,
France
lavault@lipn.univparis13.fr
Generalized twoparametric MittagLeffler type functions of two variables
Integral representations
Special functions
Hankel's integral contour
Asymptotic expansion formulas
Operator algebras associated to modules over an integral domain
2
2
We use the Fock semicrossed product to define an operator algebra associated to a module over an integral domain. We consider the $C^*$envelope of the semicrossed product, and then consider properties of these algebras as models for studying general semicrossed products.
1

374
387


Benton
Duncan
Department of Mathematics, North Dakota State University, Fargo, North Dakota, USA
Department of Mathematics, North Dakota State
USA
benton.duncan@ndsu.edu
semicrossed product
integral domain
module
On the truncated twodimensional moment problem
2
2
We study the truncated twodimensional moment problem (with rectangular data) to find a nonnegative measure $mu(delta)$, $deltainmathfrak{B}(mathbb{R}^2)$, such that $int_{mathbb{R}^2} x_1^m x_2^n dmu = s_{m,n}$, $0leq mleq M,quad 0leq nleq N$, where ${ s_{m,n} }_{0leq mleq M, 0leq nleq N}$ is a prescribed sequence of real numbers; $M,Ninmathbb{Z}_+$. For the cases $M=N=1$ and $M=1, N=2$ explicit numerical necessary and sufficient conditions for the solvability of the moment problem are given. In the cases $M=N=2$; $M=2, N=3$; $M=3, N=2$; $M=3, N=3$ some explicit numerical sufficient conditions for the solvability are obtained. In all the cases some solutions (not necessarily atomic) of the moment problem can be constructed.
1

388
399


Sergey
Zagorodnyuk
V. N. Karazin Kharkiv National University
School of Mathematics and Computer Sciences
Department of Higher Mathematics and Informatics
Svobody Square 4, 61022, Kharkiv, Ukraine
V. N. Karazin Kharkiv National University
School
Ukraine
sergey.m.zagorodnyuk@gmail.com
moment problem
Hankel matrix
nonlinear inequalities
Compactness of a class of radial operators on weighted Bergman spaces
2
2
In this paper, we study some connection between the compactness of radial operators and the boundary behavior of the corresponding Berezin transform on weighted Bergman spaces. More precisely, we prove that, under some mild condition, the vanishing of the Berezin transform on the unit circle is equivalent to the compactness of a class of radial operators on weighted Bergman spaces. Moreover, we also study the radial essential commutant of the Toeplitz operator $T_z$.
1

400
410


Yucheng
Li
Hebei Normal University
Hebei Normal University
China
liyucheng@hebtu.edu.cn


Maofa
Wang
Wuhan University
Wuhan University
China
whuwmf@163.com


Wenhua
Lan
China
lanwenhua2006@126.com
Weighted Bergman space
radial operator
Berezin transform
compact operator
essential commutant
Extensions of theory of regular and weak regular splittings to singular matrices
2
2
Matrix splittings are useful in finding a solution of linear systems of equations, iteratively. In this note, we present some more convergence and comparison results for recently introduced matrix splittings called indexproper regular and indexproper weak regular splittings. We then apply to theory of double indexproper splittings.
1

411
422


Litismita
Jena
School of Basic Sciences, Indian Institute of Technology Bhubaneswar,
Bhubaneswar  751 013, Odisha, India
School of Basic Sciences, Indian Institute
India
litumath@gmail.com
Drazin inverse
group inverse
nonnegativity
indexproper splittings
convergence theorem
comparison theorem
On linear maps preserving certain pseudospectrum and condition spectrum subsets
2
2
We define two new types of spectrum, called the $varepsilon$left (or right) pseudospectrum and the $varepsilon$left (or right) condition spectrum, of an element $a$ in a complex unital Banach algebra $A$. We prove some basic properties among them the property that the $varepsilon$left (or right) condition spectrum is a particular case of Ransford spectrum. We study also the linear preserver problem for our defined functions and we establish the following: (1) Let $A$ and $B$ be complex unital Banach algebras and $varepsilon>0$. Let $phi : Alongrightarrow B $ be an $varepsilon$left (or right) pseudospectrum preserving onto linear map. Then $phi$ preserves certain standart spectral functions.(2) Let $A$ and $B$ be complex unital Banach algebras and $0< varepsilon<1$. Let $phi : Alongrightarrow B $ be unital linear map. Then(a) If $phi $ is $varepsilon$almost multiplicative map, then $sigma^{l}(phi(a))subseteq sigma^{l}_varepsilon(a)$ and $sigma^{r}(phi(a))subseteq sigma^{r}_varepsilon(a)$, for all $a in A$.(b) If $phi$ is an $varepsilon$left (or right) condition spectrum preserving, then (i) if $A$ is semisimple, then $phi$ is injective; (ii) if B is spectrally normed, then $phi$ is continuous.
1

423
432


Sayda
Ragoubi
Department of Mathematic, Univercity of Monastir, Preparatory Institute for Engineering Studies of Monastir, Tunisia
Department of Mathematic, Univercity of Monastir,
Tunisia
ragoubis@yahoo.fr
Linear preserver
condition spectrum
pseudospectrum
Certain geometric structures of $Lambda$sequence spaces
2
2
The $Lambda$sequence spaces $Lambda_p$ for $1< pleqinfty$ and their generalized forms $Lambda_{hat{p}}$ for $1<hat{p}<infty$, $hat{p}=(p_n)$, $nin mathbb{N}_0$ are introduced. The James constants and strong $n$th James constants of $Lambda_p$ for $1<pleqinfty$ are determined. It is proved that the generalized $Lambda$sequence space $Lambda_{hat{p}}$ is a closed subspace of the Nakano sequence space $l_{hat{p}}(mathbb{R}^{n+1})$ of finite dimensional Euclidean space $mathbb{R}^{n+1}$, $nin mathbb{N}_0$. Hence it follows that sequence spaces $Lambda_p$ and $Lambda_{hat{p}}$ possess the uniform Opial property, $(beta)$property of Rolewicz, and weak uniform normal structure. Moreover, it is established that $Lambda_{hat{p}}$ possesses the coordinate wise uniform KadecKlee property. Further, necessary and sufficient condition for element $xin S(Lambda_{hat{p}})$ to be an extreme point of $B(Lambda_{hat{p}})$ are derived. Finally, estimation of von NeumannJordan and James constants of two dimensional $Lambda$sequence space $Lambda_2^{(2)}$ are carried out. Upper bound for the Hausdorff matrix operator norm on the nonabsolute type $Lambda$sequence spaces is also obtained.
1

433
450


Atanu
Manna
Indian Institute of Carpet Technology, Chauri road, Bhadohi221401, Uttar Pradesh, India.
Indian Institute of Carpet Technology, Chauri
India
atanuiitkgp86@gmail.com
Cesaro sequence space
Nakano sequence space
James constant
von NeumannJordan constant
Extreme point
KadecKlee property
Hausdorff method