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- Title
THE HYERS-ULAM STABILITY OF AN ADDITIVE AND QUADRATIC FUNCTIONAL EQUATION IN 2-BANACH SPACE.
- Authors
PATEL, B. M.; BOSMIA, M. I.; PATEL, N. D.
- Abstract
In 1940, the stability problem of functional equations was arose due to a question of Stanisaw Ulam concerning the stability of group homomorphisms. Significant work was done by Donald H. Hyers about HYERS-ULAM STABILITY and obtained a partial affirmative answer to the question of Ulam in the context of banach spaces in the case of additive mappings. In 1978, T. M. Rassias expanded Hyers's theorem for mappings between Banach spaces by considering an unbounded Cauchy difference subject to a continuity condition upon the mapping. After that, Many Researchers had studied about Hyers-Ulam stability of an additive quadratic type functional equations. In this research article, the Hyers-Ulam stability of an additive quadratic type functional equation was discussed and obtained the generalization of Hyers-Ulam stability of an additive quadratic type functional equation f(x + ay) + af(x - y) = f(x - ay) + af(x + y) for any integer a with a ≠ 1; 0; 1 in 2-Banach space.
- Subjects
FUNCTIONAL equations; ADDITIVE functions; BANACH spaces; FUNCTION spaces; QUADRATIC equations; RESEARCH personnel
- Publication
Electronic Journal of Mathematical Analysis & Applications, 2024, Vol 12, Issue 2, p1
- ISSN
3009-6731
- Publication type
Article
- DOI
10.21608/ejmaa.2024.284202.1178