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We obtain the Hyers-Ulam stability and modified Hyers-Ulam stability for the equations of the form g(x+p)=φ(x)g(x) in the following settings: |g(x+p)−φ(x)g(x)|≤δ, |g(x+p)−φ(x)g(x)|≤ϕ(x), |(g(x+p)/φ(x)g(x))−1|≤ψ(x). As a consequence we obtain the stability theorems for the gamma functional equation.

In this paper, we find solutions and investigate the superstability bounded by function for the sine functional equation (S) from the approximate inequality of the Pexider type functional equation: f (x+y/2)²-g(x-y/2)2 = h(x)k(y). Furthermore, the results are extended to Banach algebras. As a consequence, we obtain the superstability for the exponential functional equations, the hyperbolic functional equations, and the jointed Pexider Lobacevski equation. [ABSTRACT FROM AUTHOR]

In this paper, we make 2-Banach version of hyperstability results for the Jensen equation. Indeed, by using Brzdek's fixed point theorem [15], we present some hyperstability results for the Jensen equation in 2-Banach spaces [ABSTRACT FROM AUTHOR]

Using the fixed point approach, we prove some results on hyperstability of the following quadratic functional equation f(x + y + z) + f(x y) + f(x z) + f(y z) = 3[f(x) + f(y) + f(z)]; in the class of functions from an abelian group into a Banach space. [ABSTRACT FROM AUTHOR]

In this paper, we obtain the superstability of the functional equation f (pr, qs) + f (ps, qr) = θ(pq, rs)f (p, q)f (r, s) for all p, q, r, s ∈ G, where G is an Abelian group, f a functional on G2, and θ a cocycle on G². This functional equation is a generalized form of the functional equation f (pr, qs) + f (ps, qr) = f (p, q)f (r, s), which arises in the characterization of symmetrically compositive sum-form distance measures, and as products of some multiplicative functions. In reduction, they can be represented as exponential functional equations. Also we investigate the superstability with following functional equations: f (pr, qs) + f (ps, qr) = θ(pq, rs)f (p, q)g(r, s), f (pr, qs) + f (ps, qr) = θ(pq, rs)g(p, q)f (r, s), f (pr, qs) + f (ps, qr) = θ(pq, rs)g(p, q)g(r, s), f (pr, qs) + f (ps, qr) = θ(pq, rs)g(p, q)h(r, s). [ABSTRACT FROM AUTHOR]

Using fixed point method, we prove the stability of generalized derivations on non-Archimedean Banach algebras associated to the Jensen functional equation [ABSTRACT FROM AUTHOR]

The aim of this paper is to investigate the superstability of the Lobacevski equation f(x+y/2)² = f(x)f(y),which is bounded by the unknown functions φ(x) or φ(y). The obtained result is a generalization of P. Găvruta's result in 1994. [ABSTRACT FROM AUTHOR]

The present work continues the study of the stability of the functional equations of the type f(pr, qs) + f(ps, qr) = f(p, q) f(r, s) namely (i) f(pr, qs)+f(ps, qr) = g(p, q) g(r, s), and (ii) f(pr, qs)+f(ps, qr) = g(p, q) h(r, s) for all p, q, r, s ∈ G, where G is an abelian group. These functional equations arise in the characterization of symmetrically compositive sumform distance measures. [ABSTRACT FROM AUTHOR]

We will investigate the superstability of the sine functional equation from the following Pexidertype functional equation f(x+y)+g(x-y) = λ∙h(x)k(y) (λ : constant),which can be considered the mixed functional equation of the sine and cosine functions, the mixed functional equation of the hyperbolic sine and hyperbolic cosine functions, and the exponential-type functional equations. [ABSTRACT FROM AUTHOR]

We will investigate the superstability of the (hyperbolic) trigonometric functional equation from the following functional equations: f(x + y) ± g(x - y) = λf(x)g(y) and f(x + y) ± g(x - y) = λg(x)f(y), which can be considered the mixed functional equations of the sine function and cosine function, the hyperbolic sine function and hyperbolic cosine function, and the exponential functions, respectively. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study the stability problem of the generalized sine functional equations as follows: . Namely, we have generalized the Hyers-Ulam stability of the (pexiderized) sine functional equation. [ABSTRACT FROM AUTHOR]

We will investigate the superstability of the (hyperbolic) trigonometric functional equation from the following functional equations: f(x+y) ± g(x-y) = γf(x)g(y), f(x+y) ± g(x-y) = γg(x)f(y), f(x+y) ± g(x-y) = γf(x)f(y), f(x+y) ± g(x-y) = γg(x)g(y), which can be considered the mixed functional equations of the sine function and cosine function, of the hyperbolic sine function and hyperbolic cosine function, and of the exponential functions, respectively. [ABSTRACT FROM AUTHOR]