On functional inequalities associated with Drygas functional equation

2014/05/21 by Manar Youssef, Youssef, Manar, Elhoucien Elqorachi +2
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Functional Equations Stability Results #math.FA

paper · pdf · doi:10.48550/arxiv.1405.7942

5 pages

arxiv created 2014/05/21 · openalex publication_date 2014/05/21 · arxiv updated 2014/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the paper, the equivalence of the functional inequality ‖2f(x)+f(y)+f(-y)-f(x-y)‖≤‖f(x+y)‖ (x,y∈G) and the Drygas functional equation f(x+y)+f(x-y)=2f(x)+f(y)+f(-y) (x,y∈G) is proved for functions f:G→ E where (G, +) is an abelian group, (E, <⋅, ⋅>) is an inner product space, and the norm is derived from the inner product in the usual way.

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