Search

We consider the functional equation f(ax+y)+f(ax-y)-a(a+1)f(x)-a(a-1)f(-x)-[f(y)+f(-y)]+k[f(x+y)+f(x-y)-2f(x)-f(y)-f(-y)]=0 for a fixed rational number a with a≠1,-1,0 and a fixed real number k. We study the solution of the equation between linear spaces and prove the generalized Hyers-Ulam stability for it when the target space is a fuzzy normed space.

We investigate the following typical form of a certain class of quadratic functional equations: . Furthermore, we provide a systematic program to prove the generalized Hyers-Ulam stability for the class of functional equations via the stability for the typical form.

In this paper, we consider the generalized Hyers-Ulam stability for the following cubic functional equation f (x + 2y) - 3f (x + y) + 3f (x) - f (x - y) - 6f (y) + Gf (x, y) = 0. with an extra term Gf which is a functional operator of f. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the orthogonally Euler-Lagrange type cubic functional equation f(ax + by) + f(ax - by) - ab²[f(x + y) + f(x - y)] - 2a(a² - b²)f(x) + c[f(x + 2y) - 3f(x + y) + 3f(x) - f(x - y) - 6f(y)] = 0; x?y for fixed non-zero rational numbers a; b and a fixed non-zero real number c with a² ≠ b² and a ≠ ±1 and prove the generalized Hyers-Ulam stability for it by using the fixed point method, [ABSTRACT FROM AUTHOR]

In this paper, we prove the generalized Hyers-Ulam stability for the following functional inequality p(f(x+y)+f(x-y)-2f(x)-2f(y))≥ p(k[f(ax+by)+f(ax-by)-2a²f(x)-2b²f(y)]) in modular spaces without Δ-conditions. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the functional inequality N(f(2x + y) + f(2x - y) - 6f(x) - 2f(-x) - f(y) - f(-y); t) ≥ N(f(x + y) + f(x - y) - 2f(x) - f(y) - f(-y); kt) for some fixed real number k and prove the generalized Hyers-Ulam stability for it in fuzzy Banach spaces. [ABSTRACT FROM AUTHOR]

In this paper, we prove the generalized Hyers-Ulam stability for the following cubic functional equation with involution f(2x + y) + f(2x + σ(y)) - 2f(x + y) - 2f(x + σ(y)) - 12f(x) = 0 in modular spaces by using a fixed point theorem. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the functional inequality N(f(x + 2y) - 3f(x + y) + 3f(x) - f(x - y) - 6f(y), t) ∁ N(f(2x + y) + f(2x - y) - 2f(x + y) - 2f(x - y) - 12f(x); kt) for some fixed nonzero real number k and prove the generalized Hyers-Ulam stability for it in fuzzy Banach spaces by fixed point methods. [ABSTRACT FROM AUTHOR]

In this paper, we prove the generalized Hyers-Ulam stability of the following additive-quadratic p-functional inequalities N(f(x+y) + f(x-y) - 2f(x) - f(y) - f(-y), -p[4f(x+y/2) + 4f(x-y/2) - 3f(x) + f(-x) - f(-y)],t) ≥ t/t+ɸ(x,y), (p≠1, 1/2) and n(4f(x+y/2)+4f(x-y) -2f(x)-f(y)-f(y) - f(-y)], t) ≥ t/t+ɸ(x,y), (p ≠ 0,1,2) in fuzzy Banach spaces. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the following typical form of a class of cubic functional equations: f (x + 2y) - 3f (x + y) + 3f (x) - f (x - y) - 6f (y) + k[f (mx + y) + f (mx - y)- m[f (x + y) + f (x - y)] - 2(m3 -m)f (x)] = 0 for some rational number m and some real number k. Furthermore, we provide a systematic program to prove the generalized Hyers-Ulam stability for the class of functional equations via the stability for the typical form in fuzzy normed spaces. [ABSTRACT FROM AUTHOR]

In this paper, we consider the following functional equation af(x + y) + bf(x - y) + cf(y - x) = (a + b)f(x) + cf(-x) + (a + c)f(y) + bf(-y) for a xed real numbers a; b; c with a = b + c and a ≠0. We study the fuzzy version of the generalized Hyers-Ulam stability for it in the sense of Mirmostafaee and Moslehian. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a fixed point theorem for a mapping without the condition of bounded orbit in a modular space, whose induced modular is lower semi-continunous. Using this fixed point theorem, we prove the generalized Hyers-Ulam stability for an additive-cubic functional equation in modular spaces without Δ2-conditions and the convexity. [ABSTRACT FROM AUTHOR]

In this paper, we consider the generalized Hyers-Ulam stability for the following quadratic functional equation.... Here Gf is a functional operator of f . We consider some sufficient conditions on Gf which can be applied easily for the generalized Hyers-Ulam stability, and illustrate some new functional equations by using them. [ABSTRACT FROM AUTHOR]

We introduce a viewpoint to analyze functional inequalities for the generalized version of Hyers-Ulam stability problems. Especially, this article focuses the following generalized version of Cauchy functional inequality containing an general extra term Gf. ||f(x + y) - f(x) - f(y) - Gf(x,y)|| ≤ φ (x,y) We investigate the functional operator properties of Gf. And by virtue of this observation, we provide a method to produce lots of interesting additive functional equations as applications. [ABSTRACT FROM AUTHOR]