WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 22, 2023
General Formulas in the Table of $$\bar{g}$$-Derivatives for $$\bar{g}$$ -Functions
Authors: ,
Abstract: The consistent system of pseudo-arithmetical operations and its generator $$\bar{g}$$ are applied to $$\bar{g}$$-functions that are derived as solutions of some functional equations. Some interesting classes of $$\bar{g}$$-functions are built and the $$\bar{g}$$-calculus for real functions marks a new development over the years. But, $$\bar{g}$$-derivative opens a new perspective highlighting the fundamental properties of these $$\bar{g}$$-transform functions. Based on the fundamental properties of these $$\bar{g}$$-functions, we have further outlined our study in verifying other properties for pseudo-linearity, pseudo-nonlinearity and generalization of the table of $$\bar{g}$$-derivative for these transformed functions, with some pseudo-derivative identities as Pseudo-Basic Properties/Pseudo-General Rules. The table of $$\bar{g}$$-derivative for the $$\bar{g}$$-functions is built as a first attempt and equipped with the Pseudo-Linearity, the Constant Pseudo-Term, the Pseudo-Product, the Pseudo-Quotient and the Pseudo-Chain Rule as $$\bar{g}$$-formulas grouped into eight cases. Further, it will be completed for different cases, as more modified functions take part in pseudo-nonlinear combinations, Elementary Transcendental Functions or $$\bar{g}$$-table for $$\bar{g}$$-integrals of $$\bar{g}$$-functions etc., showing once again the importance of generated Pseudo-Analysis with the broad field of its applications as a generalization of Classical Analysis.
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Keywords: Pseudo-arithmetical operations, generator, $$\bar{g}$$-transform, $$\bar{g}$$-functions, $$\bar{g}$$-derivative, table of $$\bar{g}$$-derivative, functional equations
Pages: 1012-1024
DOI: 10.37394/23206.2023.22.110