Functional equation originating from sum of higher powers of arithmetic progression using difference operator is stable in Banach space: direct and fixed point methods
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DOI:
https://doi.org/10.26637/mjm201/007Abstract
In this paper, the authors has proved the solution of a new type of functional equation
$$
f\left(\sum_{j=1}^k j^p x_j\right)=\sum_{j=1}^k\left(j^p f\left(x_j\right)\right), \quad k, p \geq 1
$$
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 operatorMathematics Subject Classification:
39B52, 39B72, 39B82- Pages: 49-60
- Date Published: 01-01-2014
- Vol. 2 No. 01 (2014): Malaya Journal of Matematik (MJM)
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