Tensor norms on ordered normed spaces, polarization constants, and exchangeable distributions

In this paper, we extend normed spaces to quasi-normed spacesÂ and prove the generalized Hyers-Ulam stability of a nonic functional equation:$$\aligned&f(x+5y) - 9f(x+4y) + 36f(x+3y) - 84f(x+2y) + 126f(x+y) - 126f(x)\\&\qquad + 84f(x-y)-36f(x-2y)+9f(x-3y)-f(x-4y) = 9 ! f(y),\endaligned$$where $9 ! = 362880$ in quasi-normed spaces.

Download Full-text

Solutions and Stability of Generalized Mixed Type QCA-Functional Equations in Random Normed Spaces

Annals of the Alexandru Ioan Cuza University - Mathematics ◽

10.2478/v10157-012-0047-2 ◽

2013 ◽

Vol 59 (2) ◽

pp. 299-320

Author(s):

M. Eshaghi Gordji ◽

Y.J. Cho ◽

H. Khodaei ◽

M. Ghanifard

Keyword(s):

Functional Equation ◽

General Solution ◽

Functional Equations ◽

Mixed Type ◽

Additive Functional ◽

Normed Spaces ◽

Additive Functional Equation ◽

Probabilistic Normed Spaces ◽

Random Normed Spaces ◽

Generalized Stability

Abstract In this paper, we investigate the general solution and the generalized stability for the quartic, cubic and additive functional equation (briefly, QCA-functional equation) for any k∈ℤ-{0,±1} in Menger probabilistic normed spaces.

Download Full-text

ON LACUNARY STATISTICAL CONVERGENCE AND SOME PROPERTIES IN FUZZY N-NORMED SPACES

i-manager’s Journal on Mathematics ◽

10.26634/jmat.7.3.14868 ◽

2018 ◽

Vol 7 (3) ◽

pp. 1

Author(s):

RECAİ TÜRKMEN MUHAMMED ◽

Keyword(s):

Statistical Convergence ◽

Normed Spaces ◽

Lacunary Statistical Convergence

Download Full-text

Hyers-Ulam stability of quadratic forms in 2-normed spaces

Demonstratio Mathematica ◽

10.1515/dema-2019-0038 ◽

2019 ◽

Vol 52 (1) ◽

pp. 496-502

Author(s):

Won-Gil Park ◽

Jae-Hyeong Bae

Keyword(s):

Banach Spaces ◽

Quadratic Forms ◽

Functional Equations ◽

Ulam Stability ◽

Normed Spaces

AbstractIn this paper, we obtain Hyers-Ulam stability of the functional equationsf (x + y, z + w) + f (x − y, z − w) = 2f (x, z) + 2f (y, w),f (x + y, z − w) + f (x − y, z + w) = 2f (x, z) + 2f (y, w)andf (x + y, z − w) + f (x − y, z + w) = 2f (x, z) − 2f (y, w)in 2-Banach spaces. The quadratic forms ax2 + bxy + cy2, ax2 + by2 and axy are solutions of the above functional equations, respectively.

Download Full-text