Скачать или смотреть GIAN : 2024 - DAY 4 - Mathematics - Recent Trends in Metrical Fixed Point Theory and Applications.

GIAN :2024 - Mathematics - Recent Trends in Metrical Fixed Point Theory and Applications 25-29th Nov 2024.

Overview
Fixed Point Theory, in general, and Metrical Fixed Point Theory, in particular, offers one of the most powerful tools of nonlinear functional analysis. By means of a metrical fixed point theorem one can establish the existence and uniqueness of solutions of differential and integral equations and many other nonlinear problems that can be formulated as a fixed point problem (e.g., problems in control theory, convex optimization, differential inclusions, and economics).
The fundamental theorem in metrical fixed point theory is the contraction mapping principle due to Banach, which has laid the foundation of metric fixed point theory for contraction mappings on a complete metric space.

Objectives:
The primary objectives of this course are as follows:

1. Cover the basic fundamentals of Metrical Fixed Point Theory.
2. Expose some important fixed point theorems in Metrical Fixed Point Theory.
3. Indicate some basic applications of Metrical Fixed Point Theory in nonlinear analysis.
4. To foster the knowledge for evaluating and implementing the wide range of emerging
and newly adopted methodologies and technologies in the field of Nonlinear Functional
Analysis and in particular Metric Fixed Point Theory and Applications.
5. Fixed Point Theorems related to Cyclic Contraction Mappings, Schauder Fixed Point
Theorem and some related fixed point theorems involving Multi - Valued Mappings.
Some Applications of the theorems mentioned above.
6. Browder - Gohde - Kirk Fixed Point Theorem of nonexpansive mappings and some
related open problems in fixed point theorems related to nonexpansive mappings. Best Proximity Point Theorems and their Applications to Game Theory.
7. Expose students to current technologies and issues that are specific To Fixed Point Theory and Applications by using MATLAB (if time permits).
8. Learn the basics of Python programming, including the use of mathematical libraries also few apps for graph sketching to enhance concept comprehension.

The Faculty (Foreign Expert)

Vasile BERINDE is Professor of Mathematics at Technical University of Cluj-Napoca, Baia Mare Campus, Romania, where he has been teaching since 1990. He earned B.S. and M.S. degrees in Computer Science and Ph.D. in Mathematics from the "Babes-Bolyai" University of Cluj-Napoca.