|
|
|
AUTHOR(S): Dhurata Valera
|
|
TITLE |
 PDF |
|
ABSTRACT This paper focuses on πΜ β πππππ’ππ’π for modified gΜ -functions as ππΜ β ππ’πππ‘πππ and relations through some interesting pseudo-functional equations as their solutions and also expression by some parameterized nonlinear continuous functions π‘πΜ . The main problem we are dealing with in this research paper is generalizing the relations formulated by RybaΜrikβs theorem for pseudo-functional equations and complementing it with some other treated cases expressed by some parameterized nonlinear continuous functions. We have proven in detail all the cases of RybaΜrikβs theorem. Still, in this paper, we will generalize them and some exceptional cases related to the conditions that satisfy the set of parameters or functions (β, π, π, β, πΜ ) that participate in the relevant pseudo-nonlinear relations of the generalized theorem from parameterized nonlinear continuous functions. Furthermore, some exceptional cases for each relation are presented as main results that will connect this generalization theorem with RybaΜrikβs theorem and lead us to new results. We have built a system of important pseudo-nonlinear relations for representation the ππΜ β πππππ’ππ’π , π‘πΜ β πππππ’ππ’π by the parameterized nonlinear continuous functions π‘πΜ . Also, we are again in cases of classical analysis for the particular case of generator πΜ as πΜ β πππππ‘ππ‘π¦. |
|
KEYWORDS Pseudo-Arithmetic Operation, Generator, πΜ β πππππ’ππ’π , πΜ β ππ’πππ‘ππππ , πΜ β π‘ππππ ππππ,Pseudo-Arithmetic Operation, Generator, πΜ β πππππ’ππ’π , πΜ β ππ’πππ‘ππππ , πΜ β π‘ππππ ππππ,Modified Function, Pseudo-Functional Equation, Pseudo-Nonlinear Problem Generalized Theorem,Parameterized Nonlinear Continuous Function |
|
|
|
Cite this paper Dhurata Valera. (2024) Treatment of the Nonlinear Problems Through the Generalization of a Theorem from Parameterized Nonlinear Continuous Functions. International Journal of Mathematical and Computational Methods, 9, 16-28 |
|
|
