STABILITY OF DIMENSIONAL QUADRATIC FUNCTIONAL EQUATION IN METRIC SPACES

Author (s) : P. Muthukumar, C. Nandhini, C.Karunaivelan, V.Jothilaxmi

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Abstract :
The purpose of this current work, we introduced the finite dimensional quadratic functional equation of the form In this research, the primary objective is to introduce and study a finite dimensional quadratic functional equation of the form "f(x) = Σ[i=1 to n] Σ[j=1 to n] a_ij f(x_i) f(x_j) + b_i f(x_i) + c," where m is a positive integer and n is greater than three. The investigation focuses on understanding the Hyers-Ulam stabilities of this quadratic functional equation in Metric spaces. To achieve this, two different techniques are employed, allowing for a comprehensive analysis of the stability properties of the equation's solutions. The findings from this study provide valuable insights into the behavior and robustness of the solutions to the given quadratic functional equation under perturbations and variations in Metric spaces, contributing to the field of functional analysis. The research aims to explore the stability properties of the introduced finite dimensional quadratic functional equation in Metric spaces. By employing two distinct techniques, the study delves into understanding the behavior of solutions and their resilience under perturbations. The findings offer significant contributions to the field of functional analysis, shedding light on the stability aspects of this particular quadratic functional equation, particularly in Metric spaces.

Keywords : Fixed point and Hyers-Ulam stabilities.

Conference Date : 13/11/2020

Pages : 36

Paper ID : 20036