[PDF] Top 20 Additive Functional Inequalities in Banach Modules

... in Banach A-modules associated with the functional inequality ...complex Banach algebras and prove the generalized Hyers-Ulam stability of homomorphisms in complex Banach ... See full document

... functional equations. The paper of Rassias 4 had great influence on the development of a generalization of the Hyers-Ulam stability concept. This new concept is known as Hyers-Ulam- Rassias stability of ... See full document

... The Hyers-Ulam stability for the case of r = 1 was excluded in Corollary 3.2. In fact, the functional Equation (1.2) is not stable for r = 1 in (3.13) as we shall see in the fol- lowing example, which is a ... See full document

... of functional equations originated from a question of Ulam 12 concerning the stability of group ...for Banach spaces. Hyers’ theorem was generalized by Aoki 14 for additive mappings and by ... See full document

... of functional equa- tion (b) and functional inequality (c) has been presented in ...of functional inequalities and the stability of functional equations in quasi-Banach spaces ... See full document

... Before stating the main results, let us fix the rest of our notation. We assume, unless stated otherwise, throughout this section that A is a unital Banach ∗-algebra. Also if X is a semi- inner product A-module ... See full document

... for all x ∈ X. The inequality ( ∗ ) has provided a lot of influence in the development of what is known as generalized Hyers–Ulam stability of functional equations. Beginning around the year 1980, the topic of ... See full document

... Throughout this paper, let A be a unital C ∗ -algebra with unitary group UA, unit e, and norm | · |. Assume that X is a left A-module and Y is a left Banach A-module. An additive mapping T : X → Y is called ... See full document

... of functional equations originated from a question of Ulam 1 concerning the stability of group ...be Banach spaces. Hyers’ theorem was generalized by Aoki 3 for additive mappings and by ... See full document

... The further part of the proof is similar to the proof of Theorem .. Now we prove the superstability of the Jensen functional equation in -Banach spaces. Theorem . Let θ ∈ [, ∞ ), p, q, r, t ∈ (, ∞ ) ... See full document

... The rest of the proof is similar to the proof of Theorem .. Corollary . Let p, θ and K be positive real numbers with p >  and K > . Let f : X → Y be a mapping satisfying (.). Then there exists a unique ... See full document

... The stability problem of functional equations originated from a question of Ulam [38] concerning the stability of group homomorphisms. Hyers [9] gave a first affir- mative partial answer to the question of Ulam ... See full document

... quadratic functional equation. The stability problems of several functional equations have been extensively investigated by a number of authors and there are many interesting results concerning this problem ... See full document

... for functional equations is related to a question of Ulams[24] concerning the stability of group homomorphism’s was affirmatively answered for Banach spaces by Hyers[9,10] for linear mappings and by ... See full document

... The study of stability of functional equations is important problem in nonlinear sciences and application in solving integral equation via VIM 27–29 PDE and ODE 30– 34. Let X be a set A function d : X × X → 0, ∞ ... See full document

... f (2x + y) + f (2x − y) = 4[ f (x + y) + f (x − y)] + 24 f (x) − 6 f (y) (1.5) and discussed its general solution. In fact Lee et al. [17] proved that a function f between vector spaces X and Y is a solution of (1.5) if ... See full document

... Definition 1.8. Let X be set of positive real numbers. A function H : X ×X → R be such that H(x, y) = x+y 2xy is called harmonic mean function if it satisfies the functional equation (1.12). The functional ... See full document

... for all x ∈ E. Moreover if ftx is continuous in t ∈ R for each fixed x ∈ E, then T is linear. In 1978, Rassias 3 provided a generalization of Hyers’ Theorem which allows the Cauchy difference to be unbounded. In 1991, ... See full document

... which is mixed of a quadratic and an additive functional equations. In this paper, we establish the generalized Hyers-Ulam-Rassias stability for 1.6 on the punctured domain V \ {0} and obtain its general ... See full document

... the functional equation 1.7. In the sequel, we investigate the general solution of functional equation 1.7 when f is a function between vector spaces, and then we prove the generalized Hyers-Ulam stability ... See full document