General solution and generalized Ulam - Hyers stability of a additive functional equation originating from N observations of an arithmetic mean in Banach spaces using various substitutions in two different approaches

M. Arunkumar; E. Sathya; S. Ramamoorthi

doi:10.26637/mjm501/002

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 $N \geq 2$.

Keywords:

Arithmetic mean, additive functional equation, Generalized Hyers-Ulam stability, fixed point

Mathematics Subject Classification:

39B52, 32B72, 32B82

Authors Imprint References Funding Related Articles Downloads

M. Arunkumar Department of Mathematics, Government Arts College, Tiruvannamalai - 606 603, Tamil Nadu, India.
E. Sathya Department of Mathematics, Government Arts College, Tiruvannamalai - 606 603, Tamil Nadu, India.
S. Ramamoorthi Department of Mathematics, Arunai Engineering College, Tiruvannamalai - 606 604, Tamil Nadu, India.

Pages: 4-18
Date Published: 01-01-2017
Vol. 5 No. 01 (2017): Malaya Journal of Matematik (MJM)

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