Kragujevac Journal of Mathematics
University of Kragujevac - Faculty of Science

Fixed Point Theorems and Continuity Characterization for Linear Maps in Colombeau Algebras

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Authors: A. TAQBIBT, M. CHAIB AND S. MELLIANI

DOI: 10.46793/KgJMat2604.579T

Abstract:

In this article, we present a novel characterization of the continuity of linear maps within Colombeau algebras. Additionally, we introduce an alternative representation for the contraction of these maps. Moreover, we put forth a new concept of fixed-point theorems in Colombeau algebra, extending classical fixed-point theorems, including those of Banach, Chatterjea, and Kannan. To underscore the practical relevance of our findings, we offer various examples and applications.

Keywords:

Fixed point, generalized function, Colombeau algebra, conctraction mapping, ultra pseudo-seminorm.

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