[PDF] Top 20 On the Stability of a General Mixed Additive Cubic Functional Equation in Random Normed Spaces

... the equation is stable see 1. The first stability problem concerning group homomorphisms was raised by Ulam 2 in 1940 and affirmatively solved by Hyers ... See full document

... Hyers-Ulam stability of the Cauchy-Jensen additive functional inequality In this section, we prove the Hyers-Ulam stability of Cauchy-Jensen additive functional inequality ... See full document

... the functional equation (1.2), which is called a cubic functional equation and every solution of the cubic functional equation is said to be a cubic ... See full document

... of stability for functional equation arises when we replace the functional equation by an inequality which acts as a perturbation of the ...Banach spaces. Let f : E → E be a ... See full document

... If inf{t > 0 : Ft > a} ≤ inf{t > 0 : Gt > a}, in general we cannot conclude that Ft ≥ Gt. For example, let Ft 3/4, Gt t/t 1 and a 1/2. We know that inf{t > 0 : 3/4 > 1/2} 0 ≤ inf{t > 0 : t/t 1 ... See full document

... In the sequel we adopt the usual terminology, notations and conventions of the theory of random normed spaces, as in 37–41. Throughout this paper, Δ is the space of all probability distribution ... See full document

... mentioned stability involving a product of powers of norms is called Ulam- Gavruta-Rassias stability by various authors see ...of mixed type functional equations and their Ulam-Hyers ... See full document

... of random normed spaces RN-spaces is important as a generalization of deterministic result of linear normed spaces and also in the study of random operator ...Hyers-Ulam ... See full document

... the cubic functional equations, since the function f(x) = cx 3 is their solu- ...the cubic functional equations is said to be a cubic ...The stability problem for the ... See full document

... quadratic functional equation because the quadratic function f (x) = ax 2 is a solu- tion of the functional equation ...quadratic functional equation was used to characterize ... See full document

... this equation is called a quadratic functional ...vector spaces is quadratic if and only if there exits a unique symmetric bi-additive mapping B such that f(x) = B(x, x) for all x (see ... See full document

... Hyers-Ulam stability problem for the quadratic functional equa- tion was proved by Skof [] for mappings f : X → Y , where X is a normed space and Y is a Banach ...Hyers-Ulam stability of the ... See full document

... operator spaces and Banach lattices. Motivations for the study of multi-normed spaces and many examples are given in ...the stability problems in mul- ti-Banach spaces are studied by ... See full document

... some stability results for the functional equation of cubic in random 2-normed spaces which seems to be a quite new and interesting ...conditional cubic mapping in ... See full document

... Fuzzy Normed Spaces, International Mathematical Forum, 4, 2009, ...the stability of the linear functional equation, ...Rassias, Stability of functional equations in ... See full document

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

... of stability problems for a functional equation is related to a question of Ulam [], concerning the stability of group homomorphisms, affirma- tively answered for Banach spaces by Hyers ... See full document

... Under what condition is there a homomorphism near an approximately homomorphism between a group and a metric group? This is called the stability problem of functional equations which was first raised by S. ... See full document

... In recent years, the fuzzy theory has emerged as the most active area of research in many branches of mathematics and engineering. This new theory was introduced by Zadeh [1], in 1965 and since then a large number of ... See full document

... the general pertinent Euler-Lagrange quadratic ...to functional equations via the pioneering in- troduction of the Euler-Lagrange-Rassias quadratic weighted means and fundamental mean equations ( [15], ... See full document