[Turkmath:5529] (no subject)

[Allaberen Ashyralyev]

Dear Colleagues!

You are cordially invited to the Weekly Online Seminar “Analysis and
Applied Mathematics” on

Date: Tuesday, April 5, 2022

Time: 14.00-15.00 (Istanbul) = 13.00-14.00 (Ghent) = 17.00-18.00 (Almaty)

Zoom link:
https://us02web.zoom.us/j/6678270445?pwd=SFNmQUIvT0tRaH-lDaVYrN3l5bzJVQT09,
Conference ID: 667 827 0445, Access code: 1

Speaker: Prof. Dr. Eberhard Malkowsky

Department of Mathematics, State University of Novi Pazar, Serbia

Title: Some measures of noncompactness and their applica-tions

Abstract: Measures of noncompactness are very useful tools in functional
analysis, for in-stance in metric fixed point theory and the theory of
operator equations in Banach spaces. They are also used in the studies of
functional equations, ordinary and partial differential equations,
fractional partial differential equations, integral and
integro-differential equa-tions, optimal control theory, and in the
characterizations of compact operators between Ba-nach spaces. We present
an axiomatic introduction to measures of noncompactness on bounded subsets
of complete metric spaces [6, 4, 5, 3], and also the alternative axiomatic
approaches by Banaś and Goebel [2] and by Akhmerov et al. [1] for measures
of noncompact-ness in Banach spaces. As examples, we consider the
Kuratowski, Hausdorff and separation measures of noncompactness and their
most important properties. The Kuratowski measure of noncompactness is used
in Darbo’s fixed point theorem. Furthermore we study the notion of measures
of noncompactness of operators between Banach spaces and some of their
prop-erties. Finally we give a few applications to the characterization of
compact linear operators between certain BK spaces and to some results
concerning the solvability of integral equa-tions.
References:
[1] R.R. Akhmerov, M.I. Kamenskii, A.S. Potapov, A.E. Rodkina, and B.N.
Sadovskii. Measures of Noncompactness and Condensing Operators. Birkhäuser
Verlag, Basel, 1992.
[2] J. Banaś and K. Goebel. Measures of Noncompactness in Banach Spaces,
volume 60 of Lecture Notes in Pure and Applied Mathematics. Marcel Dekker
Inc., New York and Basel, 1980.
[3] B. de Malafosse, E. Malkowsky, and V. Rakočević. Operators Between
Sequence Spaces and Applications. Springer, 2021.
[4] E. Malkowsky and V. Rakočević. An introduction into the theory of
sequence spaces and measures of noncompactness, volume 9(17) of Zbornik
radova, Matematčki in-stitut SANU, pages 143–234. Mathematical Institute of
SANU, Belgrade, 2000.
[5] E. Malkowsky and V. Rakočević. Advanced Functional Analysis. Taylor and
Francis, 6000 Broken Sound Parkway NW, Suite 300, Boca Raton, FL 33487,
USA, 2019.
[6] J.M. Ayerbe Toledano, T. Dominguez Benavides, and G. Lopez Acedo.
Measures of Noncompactness in Metric Fixed Point Theory, volume 99 of
Operator Theory Ad-vances and Applications. Birkhäuser Verlag, Basel,
Boston, Berlin, 1997.

Abstracts and forthcoming talks can be found on our webpage

https://sites.google.com/view/aam-seminars

Kind regards,

*Prof. Dr. Allaberen Ashyralyev *
*Department of Mathematics, Bahcesehir University, 34353, Istanbul, Turkey*
*  and **Near East University, Lefkoşa(Nicosia), Mersin 10 Turkey*
*Peoples' Friendship University of Russia (RUDN University),** Ul Miklukho
Maklaya 6, Moscow 117198, Russian Federation *
*Institute of Mathematics and Mathematical Modelling, 050010, Almaty,
Kazakhstan*
*e-mail: allaberen.ashyralyev at eng.bau.edu.tr
<allaberen.ashyralyev at neu.edu.tr> and **aallaberen at gmail.com
<aallaberen at gmail.com> *
 http://akademik.bahcesehir.edu.tr/web/allaberenashyralyev

https://sites.google.com/view/aam-seminars
https://content.sciendo.com/view/journals/ejaam/ejaam-overview.xml
*icaam-online.org <http://icaam-online.org>*

*https://www.genealogy.math.ndsu.nodak.edu/id.php?id=95872&fChrono=1
<https://www.genealogy.math.ndsu.nodak.edu/id.php?id=95872&fChrono=1>*
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