A Fixed Point Approach to the Stability of Quintic and Sextic Functional Equations in Quasi-β-Normed Spaces. (5th January 2011)

• Record Type: Journal Article
• Authors: Xu, Tian Zhou; Rassias, John Michael; Rassias, Matina John; Xu, Wan Xin
• Other Names: Gupta Vijay Academic Editor.
• Is Part Of: Journal of inequalities and applications. Volume 2010(2010)
• Publication Date: 2011-01-05
• Subjects: Inequalities (Mathematics) -- Periodicals; 512.97
• DOI: 10.1155/2010/423231
• Languages: English
• ISSNs: 1029-242X

Abstract

Abstract : We achieve the general solution of the quintic functional equationf ( x + 3 y ) - 5 f ( x + 2 y ) + 10 f ( x + y ) - 10 f ( x ) + 5 f ( x - y ) - f ( x - 2 y ) = 120 f ( y ) and the sextic functional equationf ( x + 3 y ) - 6 f ( x + 2 y ) + 15 f ( x + y ) - 20 f ( x ) + 15 f ( x - y ) - 6 f ( x - 2 y ) + f ( x - 3 y ) = 720 f ( y ) . Moreover, we prove the stability of the quintic and sextic functional equations in quasi-β -normed spaces via fixed point method.