New Paths Opened by g ̅-Function in Pseudo-Analysis and Other Fields Through Several Applications

Abstract

The extension problem for the axiomatic concepts of pseudo-arithmetic operations {⊕ ̅,⊙ ̅,⊖ ̅,⊘ ̅} supported by g ̅-Functions are treated in the field of Pseudo-Analysis by many authors, opening new paths for development and investigation of their role as well as for the modifying and modified functions. The g ̅-Negation of the negation N is presented in this paper transformed by the g ̅-Function as a general or normed generator g ̅=g ̅_(a,r) in Pseudo-Analysis, where the role of the extended pseudo-arithmetic operations sistem {⊕ ̅_g ̅ ,⊙ ̅_g ̅ ,⊖ ̅_g ̅ (,⊘) ̅_g ̅ } is very specific and important for development of g ̅-Calculus. Furthermore, developing the theory of action of these special functions (g ̅,f_g ̅ ,t_g ̅ ,N_g ̅ ) by generalizations and modifications, we arrive at some connections of Generated Pseudo-Analysis with other fields such as Information Theory, Geometry, Trigonometry, Elementary Algebra and other areas of pure mathematics connected with combinatorial problems. In these fields, the paper addresses several composition of some real continuous parameterized functions with other special functions, above all showing the interesting forms of their generalization and transformation created by modification through g ̅-Transform. Some important formula and classical problems are generalized and transformed, leading us to new connections between different problems and fields.

Received: 05 May 2022 / Accepted: 14 June 2023 / Published: 23 July 2023