[PDF] Top 20 Quadratic Quartic Functional Equations in RN Spaces
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Quadratic Quartic Functional Equations in RN Spaces
... for all x ∈ E. Moreover, if ftx is continuous in t ∈ R for each fixed x ∈ E, then T is R-linear. In 1978, Rassias 3 provided a generalization of Hyers’ theorem which allows the Cauchy difference to be unbounded. In 1991, ... See full document
14
Random Stability of an Additive Quadratic Quartic Functional Equation
... additive-quadratic-quartic functional equation f x 2y f x − 2y 2f x y 2f − x − y 2fx − y 2f y − x − 4f−x − 2fx f2y f−2y − 4fy − 4f−y in complete random normed ... See full document
18
On stability of functional equations related to quadratic mappings in fuzzy Banach spaces
... a quadratic functional equation. Quadratic functional equations were used to characterize inner product ...the quadratic equation is said to be a quadratic ...the ... See full document
12
Intuitionistic fuzzy stability of a quadratic and quartic functional equation
... f (2x + y) + f(2x − y) = 4f (x + y) + 4f (x − y) + 24f (x) − 6f(y). (1.2) In fact, they proved that a function f between two real vector spaces X and Y is a solution of (1.2) if and only if there exists a unique ... See full document
25
Stability of Mixed Type Cubic and Quartic Functional Equations in Random Normed Spaces
... In the sequel we adopt the usual terminology, notations, and conventions of the theory of random normed spaces, as in 19–21. Throughout this paper, Δ is the space of distribution functions that is, the space of ... See full document
9
Functional equations and inequalities in paranormed spaces
... additive functional equa- tion, the quadratic functional equation ...cubic functional equation (.) and the quartic functional equation ...paranormed spaces by using the ... See full document
23
Refined stability of additive and quadratic functional equations in modular spaces
... of functional equations originated with Ulam [], who raised the stability problem of group ...Cauchy functional equation in Banach ...of functional equations may be called Hyers-Ulam ... See full document
13
Approximate Quartic and Quadratic Mappings in Quasi Banach Spaces
... the functional equation ...of functional equation 1.7 when f is a function between vector spaces, and then we prove the generalized Hyers-Ulam stability of ... See full document
19
Solution and stability of system of quartic functional equations
... In 1941, D. H. Hyers [9] gave an affirmative answer to the question of S.M. Ulam for Banach spaces. In 1950, T. Aoki [2] was the second author to treat this problem for additive mappings. In 1978, Th.M. Rassias ... See full document
18
Quadratic $rho$-functional inequalities in $beta$-homogeneous normed spaces
... the quadratic ρ-functional inequalities ...Banach spaces and prove the Hyers-Ulam stability of quadratic ρ-functional equations associated with the quadratic ... See full document
6
Functional equations in paranormed spaces
... a quadratic functional ...the quadratic functional equation is said to be a quadratic ...the quadratic functional equation was proved by Skof [] for mappings f : X → Y , ... See full document
14
Stability of quadratic functional equations in tempered distributions
... the spaces of generalized functions such as S of tempered distributions and F of Fourier hyperfunc- ...the spaces S and F ...the spaces of generalized functions as ... See full document
11
Stability of quadratic functional equations in generalized functions
... the spaces of generalized functions such as S of tempered distributions, F of Fourier hyper- functions and D of ...the spaces of generalized functions as ... See full document
15
The Hyers Ulam Rassias stability of the quartic functional equation in fuzzy β normed spaces
... In the next year, Hyers [] gave a positive answer to the above question for additive groups under the assumption that the groups are Banach spaces. In , Rassias [] ex- tended the theorem of Hyers by ... See full document
14
Quadratic functional equations of Pexider type
... the functional equation ...vector spaces. Theorem 5.1. Assume that X and Y are vector spaces over fields of characteristic different from 2, ... See full document
9
Fuzzy Stability of Quadratic Functional Equations
... This paper is organized as follows. In Section 2, we prove the generalized Hyers-Ulam stability of the quadratic functional equation 1.1 in fuzzy Banach spaces. In Section 3, we prove the generalized ... See full document
16
Approximate solution of generalized inhomogeneous radical quadratic functional equations in 2 Banach spaces
... 2-Banach spaces and showed its applications to the Ulam stability of some single-variable equations and the most important functional equation in several variables, namely, the Cauchy ...n-normed ... See full document
13
Quadratic $alpha$-functional equations
... The functional equation f (x + y) = f (x) + f(y) is called the Cauchy equation. In particular, every solution of the Cauchy equation is said to be an additive mapping. Hyers [19] gave a first affirmative partial ... See full document
9
On the Stability of a Generalized Quadratic and Quartic Type Functional Equation in Quasi Banach Spaces
... The generalized Hyers-Ulam stability problem for the quadratic functional equation 1.3 was proved by Skof for mappings f : A → B, where A is a normed space and B is a Banach space see 8. Cholewa 9 noticed ... See full document
26
A Fixed Point Approach to the Stability of an Additive-Quadratic-Cubic-Quartic Functional Equation
... a quadratic functional ...the quadratic functional equation is said to be a quadratic ...the quadratic functional equation was proved by Skof 6 for mappings f : X → Y , ... See full document
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