What is it about?
In this work, the existence of the fixed points of the mappings is independent of their smoothness, of the single-value or multi-value using a new geometrical approach is studied. Here, the fixed-point theorems are proved, which generalize the fixed-point theorems of Brouwer and Schauder, and also Kakutani, in some sense. This approach is based on the idea of the Poincare article [1] and the geometry of the image of mappings. It is independent of the topological properties of spaces, which allows for studying mappings acting in vector spaces. We studied the solvability of the nonlinear equations and inclusions by applying the obtained general results. Here some auxiliary results are obtained, also
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Why is it important?
In this work, the existence of the fixed points of the mappings is independent of their smoothness, of the single-value or multi-value using a new geometrical approach is studied.
Perspectives
To study various nonlinear problems, which contain nonsmooth mappings that arose in the areas of mathematical physics, math economy, math biology, etc.
Dr. Sci., Professor Kamal N. Soltanov
Institute of Mathematics and Mechanics National Academy of Sciences of Azerbaijan
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This page is a summary of: Generalized fixed-point theorems. Applications, TRANSACTIONS ISSUE MATHEMATICS, January 2023, Trade Unions Republican Commiittee of Azerbaijan Water Economy Workers,
DOI: 10.30546/2617-7900.43.1.2023.112.
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