Институт математики и математического моделирования

“Analysis and Applied Mathematics” Еженедельный онлайн семинар 23

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Date: Tuesday, February 6, 2024
Time: 12.00-13.00 (Istanbul) = 10.00-11.00 (Ghent) = 15.00-16.00 (Almaty)
Zoom link: https://us02web.zoom.us/j/6678270445?pwd=SFNmQUIvT0tRaH-lDaVYrN3l5bzJVQT09,

Conference ID: 667 827 0445, Access code: 1

Speaker:
Prof. Dr. Mohammad Mursaleen
China Medical University, Taichung, Taiwan

Title: On Some Applications of Measures of Noncompactness
Abstract: In this talk, we discuss the classical measures of noncompactness and in partic-ular Hausdorff measure of noncompactness. We discuss their applications in various prob-lems of analysis such as differential equations, integral equations and characterization of compact matrix operators between sequence spaces. The most effective way in the charac-terization of compact operators between the Banach spaces is applying the Hausdorff measure of noncompactness. In this talk, we present some identities or estimates for the operator norms and the Hausdorff measures of noncompactness of certain operators given by infinite matrices that map an arbitrary BK-space into classicla sequence spaces. Many linear compact operators may be represented as matrix operators in sequence spaces or in-tegral operators in function spaces [2]. Recently the measures of noncompactness are ap-plied in solving infinite system of differential equations [5], [4] and integral equations in sequence spaces [1, 3].

References:
[1] R. Arab, M. Mursaleen and S.M.H. Rizvi, Positive solution of a quadratic integral equation using generalization of Darbo’s fixed point theorem, Numer. Funct. Anal. Optim., 40(10) (2019), 1150–1168.
[2] J. Banas and M. Mursaleen, Sequence Spaces and Measures of Noncompactness with Applications to Differential and Integral Equations, Springer, 2014.
[3] B. Hazarika, R. Arab and M. Mursaleen, Applications of measure of noncompactness and operator type contraction for existence of solution of functional integral equa-tions, Complex Anal. Oper. Theory, DOI: 10.1007/s11785-019-00933-y.

Kazakh Mathematical Journal

“Analysis and Applied Mathematics” Еженедельный онлайн семинар 23

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