Functional equation originating from sum of higher powers of arithmetic progression using difference operator is stable in Banach space

M. Arunkumara,* and G. Britto Antony Xavierb

Functional equation originating from sum of higher powers of arithmetic progression using difference operator is stable in Banach space

Authors :

M. Arunkumar^a,*and G. Britto Antony Xavier^b

Author Address :

^aDepartment of Mathematics, Government Arts College, Tiruvannamalai - 606 603, Tamil Nadu, India.
^bDepartment of Mathematics, Sacred Heart College, Tirupattur - 635 601, Tamil Nadu, India.

*Corresponding author.

Abstract :

In this paper, the authors has proved the solution of a new type of functional equation
egin{align*}
f left(sum_{j =1}^k ~j^p~x_j ight) = sum_{j =1}^k left(j^p~ f(x_j) ight), qquad k,p geq 1
end{align*}
which is originating from sum of higher powers of an arithmetic progression. Its generalized Ulam - Hyers stability in Banach space using direct and fixed point methods are investigated. An application of this functional equation is also studied.

Keywords :

Additive functional equations, stirling numbers, polynomial factorial, difference operator, generalized Ulam - Hyers stability, fixed point.

DOI :

Article Info :

Received : April 04, 2013; Accepted : November 25, 2013.