Abstract
In this paper, the authors achieve the generalized Ulam - Hyers stability of a Ramanujan Type Additive Functional Equation in Paranormed Spaces and Modular spaces via classical Hyers Method.
Highlights
The stability of a functional equation initiated from a question raised by Ulam: when is it true that the solution of an equation differing slightly from a given one must of necessity be close to the solution of the given equation?
The first answer to Ulams question was given by Hyers in [11]
A abundant number of papers on the stability problems have been extensively available as generalizing Ulams problem and Hyers theorem in various directions; see for instance [3, 10, 28, 29, 31], and the references given there
Summary
The stability of a functional equation initiated from a question raised by Ulam: when is it true that the solution of an equation differing slightly from a given one must of necessity be close to the solution of the given equation? (see [37] ). The stability of a functional equation initiated from a question raised by Ulam: when is it true that the solution of an equation differing slightly from a given one must of necessity be close to the solution of the given equation? The first answer (in the case of Cauchys functional equation in Banach spaces) to Ulams question was given by Hyers in [11]. Following his result, a abundant number of papers on the stability problems have been extensively available as generalizing Ulams problem and Hyers theorem in various directions; see for instance [3, 10, 28, 29, 31], and the references given there.
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