Abstract
Abstract In this paper, we prove the Hyers-Ulam stability of the Cauchy additive functional inequality, the Cauchy additive functional equation and the quadratic functional equation in matrix paranormed spaces. MSC:47L25, 39B82, 39B72, 46L07, 39B52, 39B62.
Highlights
1 Introduction and preliminaries The concept of statistical convergence for sequences of real numbers was introduced by Fast [ ] and Steinhaus [ ] independently, and since several generalizations and applications of this notion have been investigated by various authors
A Hyers-Ulam stability problem for the quadratic functional equation was proved by Skof [ ] for mappings f : X → Y, where X is a normed space and Y is a Banach space
In Section, we prove the Hyers-Ulam stability of Cauchy additive functional inequality
Summary
Introduction and preliminariesThe concept of statistical convergence for sequences of real numbers was introduced by Fast [ ] and Steinhaus [ ] independently, and since several generalizations and applications of this notion have been investigated by various authors (see [ – ]). A Hyers-Ulam stability problem for the quadratic functional equation was proved by Skof [ ] for mappings f : X → Y , where X is a normed space and Y is a Banach space. Czerwik [ ] proved the Hyers-Ulam stability of the quadratic functional equation. Gilányi [ ] and Fechner [ ] proved the Hyers-Ulam stability of functional inequality
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