Abstract
Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of an additive functional equation, a quadratic functional equation, a cubic functional equation and a quartic functional equation in paranormed spaces. Furthermore, we prove the Hyers-Ulam stability of functional inequalities in paranormed spaces by using the fixed point method and the direct method. MSC: Primary 35A17; 47H10; 39B52; 39B72
Highlights
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
We prove the Hyers-Ulam stability of the Cauchy additive functional equation, the quadratic functional equation ( . ), the cubic functional equation ( . ) and the quartic functional equation ( . ) in paranormed spaces by using the fixed point method and the direct method
2 Hyers-Ulam stability of the Cauchy additive functional equation Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the Cauchy additive functional equation in paranormed spaces
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.
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