Functional Aggregate Queries with Additive Inequalities
نویسندگان
چکیده
منابع مشابه
Generalized additive functional inequalities in Banach algebras
Using the Hyers-Ulam-Rassias stability method, weinvestigate isomorphisms in Banach algebras and derivations onBanach algebras associated with the following generalized additivefunctional inequalitybegin{eqnarray}|af(x)+bf(y)+cf(z)| le |f(alpha x+ beta y+gamma z)| .end{eqnarray}Moreover, we prove the Hyers-Ulam-Rassias stability of homomorphismsin Banach algebras and of derivations on Banach ...
متن کاملAdditive ρ-functional inequalities
In this paper, we solve the additive ρ-functional inequalities ‖f(x+ y)− f(x)− f(y)‖ ≤ ∥∥∥∥ρ(2f (x+ y 2 ) − f(x)− f(y) )∥∥∥∥ , (1) ∥∥∥∥2f (x+ y 2 ) − f(x)− f(y) ∥∥∥∥ ≤ ‖ρ (f(x+ y)− f(x)− f(y))‖ , (2) where ρ is a fixed non-Archimedean number with |ρ| < 1 or ρ is a fixed complex number with |ρ| < 1. Using the direct method, we prove the Hyers-Ulam stability of the additive ρ-functional inequalit...
متن کاملFunctional Inequalities Associated with Additive Mappings
The functional inequality ‖f x 2f y 2f z ‖ ≤ ‖2f x/2 y z ‖ φ x, y, z x, y, z ∈ G is investigated, where G is a group divisible by 2, f : G→ X and φ : G3 → 0,∞ are mappings, and X is a Banach space. The main result of the paper states that the assumptions above together with 1 φ 2x,−x, 0 0 φ 0, x,−x x ∈ G and 2 limn→∞ 1/2 φ 2 1x, 2y, 2z 0, or limn→∞2φ x/2n−1, y/2, z/2 0 x, y, z ∈ G , imply that ...
متن کاملgeneralized additive functional inequalities in banach algebras
using the hyers-ulam-rassias stability method, weinvestigate isomorphisms in banach algebras and derivations onbanach algebras associated with the following generalized additivefunctional inequalitybegin{eqnarray}|af(x)+bf(y)+cf(z)| le |f(alpha x+ beta y+gamma z)| .end{eqnarray}moreover, we prove the hyers-ulam-rassias stability of homomorphismsin banach algebras and of derivations on banach ...
متن کاملStability of Functional Inequalities with Cauchy-Jensen Additive Mappings
In 1940, Ulam [1] gave a talk before the Mathematics Club of the University of Wisconsin in which he discussed a number of unsolved problems. Among these was the following question concerning the stability of homomorphisms. We are given a group G and a metric group G′ with metric ρ(·,·). Given > 0, does there exist a δ > 0 such that if f :G→G′ satisfies ρ( f (xy), f (x) f (y)) < δ for all x, y ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: ACM Transactions on Database Systems
سال: 2020
ISSN: 0362-5915,1557-4644
DOI: 10.1145/3426865