Author:
M. Arunkumar ,E. Sathya ,S. Ramamoorthi
Abstract
In this paper, we introduce and investigate the general solution and generalized Ulam- Hyers stability of a additive functional equation$$f\left(\frac{\sum_{k=1}^N x_k}{N}\right)=\frac{1}{N} \sum_{k=1}^N f\left(x_k\right)$$originating from $N$ observations of an arithmetic mean in Banach spaces using various substitutions in two different approaches with $N \geq 2$.
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