[PDF] Top 20 Approximation of the Quadratic and Cubic Functional Equations in RN-spaces

... the quadratic functional equation (1) was proved by Skof for functions f : A → B, where A is normed space and B is a Banach space (see ...the functional equation ...the quadratic ... See full document

... x y + ≤ x + y for all x X ∈ . In this case, a quasi- ( β , p ) -Banach space is called a ( β , p ) -Banach space. For more details and related stability results on ( β , p ) -Banach spaces, we refer to [19] [20]. ... See full document

... S: Functional Equations and Inequalities in Several ...of Functional Equations in Several ...additive, quadratic, cubic ... See full document

... quasi-Banach spaces, where k is nonzero integer numbers with k ≠ ± ...the functional equation ...mixed functional equations has recently been obtained by Najati ...and quadratic ... 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

... normed spaces, and let f : X → Y be an arbitrarily given ...a quadratic, a cubic, a quadratic-additive, a cubic-additive, a cubic-quadratic, or a ... See full document

... Banach spaces. The notion of fuzzy stability of the functional equations was given in ...Jensen, cubic and quadratic functional equations were investigated in ... See full document

... a quadratic mapping, and an additive mapping, then we call f a quartic-cubic- quadratic-additive mapping and vice ...A functional equation is said to be a ... See full document

... of quadratic, cubic and quartic functional equations and its Hyers-Ulam-Rassias stability were discussed by various authors ([3], [7], [12], [21], [24], [27], [29], [32], [34], ...of ... See full document

... the cubic functional equation f2x y f2x − y 2fx y 2fx − y 12fx in fuzzy normed spaces was proved in earlier work; and the stability of the additive functional equations fx y fx fy, 2fx ... See full document

... The Hyers-Ulam-Rassias 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 14. Cholewa 15 noticed ... See full document

... additive functional equa- tion, the quadratic functional equation ...the cubic functional equation (.) and the quartic functional equation ...paranormed spaces by using ... See full document

... f (x + y) 6 f (x  y) + 4 f (3y) = 3 f (x + 2y) 3 f (x  2y) + 9 f (2y) (1.2) is said to be the cubic - quadratic type functional equation since ax 3 +bx 2 is its solution. Chang and Jung [12] ... See full document

... The concept of intuitionistic fuzzy normed spaces, initially has been introduced by Saadati and Park [16]. In [17], by modifying the separation condition and strength- ening some conditions in the definition of ... See full document

... Nonlinear functional differential equations occur in sev- eral problems of dynamic systems and have been studied in the literature for a long time via functional analytic meth- ...Similarly, ... See full document

... 12. Katsaras, AK: Fuzzy topological vector spaces II. Fuzzy Sets Syst. 12, 143-154 (1984) 13. Felbin, C: Finite-dimensional fuzzy normed linear space. Fuzzy Sets Syst. 48, 239-248 (1992) 14. Kramosil, I, Michálek, ... See full document

... of quadratic double centrali- zers and of quadratic multipliers on Banach algebras by fixed point ...of cubic double centralizers of Banach algebras which are strongly without order had been ... See full document

... The essential idea of the Dhage iteration principle may be described as “the monotonic convergence of the sequence of successive approxima- tions to the solutions of a nonlinear equation beginning with a lower or an ... See full document

... 3. Hyers, DH: On the stability of the linear functional equation. Proc. Natl. Acad. Sci. USA 27, 222-224 (1941) 4. Aoki, T: On the stability of the linear transformation in Banach spaces. J. Math. Soc. Jpn. ... See full document

... Keywords: Additive functional equations, Quadratic functional equations, Quartic functional equations, Mixed type functional equations, Ulam - Hyers stability, Ulam - Hyers - Rassias sta[r] ... See full document