ON THE ULAM-GAVRUTA-RASSIAS STABILITY OF THE EULER-LAGRANGE TYPE FUNCTIONAL EQUATION

Author (s) : P. Sridhar, A. Anandhu, R.Kirthika, V.Rajeshwari

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Abstract :
In this current research work, the main focus is on investigating the Hyers-Ulam stability of a novel n-dimensional Euler-Lagrange type quadratic functional equation in Orthogonally space. The study aims to explore the behavior of the functional equation and determine its stability properties under certain conditions. The Hyers-Ulam stability is a significant concept in mathematical analysis, concerned with the sensitivity of functional equations to perturbations. By establishing the stability of the proposed Euler-Lagrange type quadratic functional equation, the researchers aim to demonstrate the robustness of the equation's solutions in response to small variations in the input.Moreover, the study also delves into Ulam-Gavruta-Rassias Stability, which is another aspect of stability analysis in functional equations, known for its wide applicability in various mathematical contexts.Throughout the research, the Euler-Lagrange Functional Equation and Quadratic Mapping play crucial roles, providing the mathematical framework and tools for addressing the problem effectively. The findings of this research work have potential implications in diverse fields, including optimization, physics, and engineering, where functional equations and stability analyses play vital roles in understanding complex systems and phenomena.

Keywords : Hyers-Ulam Stability, Ulam-Gavruta-Rassias Stability, EulerLagrange Functional Equation, Quadratic Mapping.

Conference Date : 13/11/2020

Pages : 34

Paper ID : 20034