Title of article :
A Generalized Mixed Quadratic-Quartic Functional Equation
Author/Authors :
XU, TIAN ZHOU Beijing Institute of Technology - School of Mathematics, China , XU, TIAN ZHOU University of Kentucky - College of Engineering - Department of Electrical and Computer Engineering, USA , RASSIAS, JOHN MICHAEL National and Kapodistrian University of Athens - Section of Mathematics and Informatics, Pedagogical Department E E, Greece , RASSIAS, JOHN MICHAEL University of Kentucky - College of Engineering - Department of Electrical and Computer Engineering, USA , XU, WAN XIN University of Electronic Science and Technology of China - School of Communication and Information Engineering, China , XU, WAN XIN University of Kentucky - College of Engineering - Department of Electrical and Computer Engineering, USA
Abstract :
In this paper, we determine the general solution of the functional equation f(kx+y)+f(kx−y)=g(x+y)+g (x−y)+h(x)+ĥ(y) for fixed integers k with k≠0,±1 without assuming any regularity condition on the unknown functions f,g,h,ĥ. The method used for solving these functional equations is elementary but exploits an important result due to Hosszú. The solution of this functional equation can also be determined in certain type of groups using two important results due to Székelyhidi. The results improve and extend some recent results.
Keywords :
Quadratic function , quartic function , difference operator , Frechet functional equation , mixed quadratic , quartic functional equation
Journal title :
Bulletin of the Malaysian Mathematical Sciences Society
Journal title :
Bulletin of the Malaysian Mathematical Sciences Society
