Asian Journal of Mathematics and Computer Research

GENERALIZED HYERS - ULAM STABILITY OF A TWO VARIABLE QUARTIC FUNCTIONAL EQUATION

K. RAVI *

Department of Mathematics, Sacred Heart College, Tirupattur - 635 601, Tamil Nadu, India.

A. EDWIN RAJ

Department of Mathematics, MVJ College of Engineering, Channasandra, Bangalore-560067, Karnataka, India

*Author to whom correspondence should be addressed.

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Abstract

In this paper, we study solutions of the 2-variable quartic functional equation g(2x + y, 2u + v) + g(2x − y, 2u − v) = 4g(x +y, u + v) + 4g(x − y, u − v) + 24g(x, u) − 6g(y, v) which has the quartic form of f(x, y) = ax⁴ + bx³y + cx²y² + dxy³ + ey⁴ as a solution. Also the generalized Hyers-Ulam stability of this equation is investigated.

Keywords: 2-variable quartic functional equation;, Ulam-Hyers stability;, Hyers-Ulam-Rassias stability.

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