FUNCTIONAL-EQUATIONS
A general theorem on the stability of a class of functional equations including monomial equations
... We combine Lemmas . and . in the following theorem to formulate the main theo- rem which is easily applicable. We here notice that conditions () and () are satisfied in usual cases provided we apply the direct ...
12
Stability of quadratic functional equations in tempered distributions
... was proved by Skof []. Thereafter, many authors studied the stability problems of (.) in various settings (see [, , , ]). Usually, quadratic functional equations are used to characterize the inner ...
11
Quadratic functional equations of Pexider type
... of Functional Equations and Inequalities, Prace Naukowe Uniwersytetu Slaskiego w Katowicach [Scientific Publications of the Uni- versity of Silesia], ...
9
A remark on k th order linear functional equations with constant coefficients
... Abel functional equations are associated to a linear homogeneous functional equation with constant ...Abel functional equation, and linear homogeneous functional equa- tion in S with ...
8
On the Stability of Functional Equations in Random Normed Spaces
... 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] established the ...
10
Approximately cubic functional equations and cubic multipliers
... In 1941, Hyers [2] gave a first affirmative answer to the question of Ulam for Banach spaces. Later, Rassias in [3] provided a remarkable generalization of the Hyers’ result by allowing the Cauchy difference to be ...
8
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, ...
14
Superstability of generalized cauchy functional equations
... During the last decades, Hyers-Ulam stability of various functional equations has been extensively studied by a number of authors (see [3-5,8-10]). Especially, Forti [11] proved the Hyers-Ulam stability of ...
7
Nonlinear Fuzzy stability of cubic functional equations
... We established the Hyers-Ulam-Rassias stability of the cubic functional equations (1.1), (1.2), and (1.3) in various fuzzy spaces. In Section 4, we proved the stability of func- tional equations ...
19
Generalized orthogonal stability of some functional equations
... As mentioned before, we will consider functional equations defined only for orthog- onal vectors and we will start with the Cauchy functional equation. A mapping f from an inner product space (X, ( · ...
23
A new approach for studying fuzzy functional equations
... of functional equations with its wide range of appli- cations is an interesting subject that dates back to the work of ...these equations is deterministic and can be obtained using numerical or ...
9
Fuzzy Stability of Quadratic Functional Equations
... The stability problem of functional equations is originated from a question of Ulam 11 concerning the stability of group homomorphisms. Hyers 12 gave a first affirmative partial answer to the question of Ulam ...
16
Functional equations and inequalities in matrix paranormed spaces
... quadratic functional equation is said to be a quadratic ...quadratic functional equation was proved by Skof [] for mappings f : X → Y, where X is a normed space and Y is a Banach ...quadratic ...
13
Functional equations in paranormed spaces
... quadratic functional equation is said to be a quadratic ...quadratic functional equation was proved by Skof [] for mappings f : X → Y , where X is a normed space and Y is a Banach ...quadratic ...
14
Functional equations and inequalities in paranormed spaces
... of functional equations for the proof of new fixed point theorems with ...several functional equations have been extensively investigated by a number of authors (see ...
23
Identification problems for systems of nonlinear evolution equations and functional equations
... of functional equations by using the given data and then we obtain the solution by the method of Kuczma (Functional Equations in a Single Variable, ...
8
Multiquartic functional equations
... single functional equation and vice ...multiquartic functional equations by applying the fixed point method, which was used for the first time by Baker in ...
10
On Cauchy type functional equations
... i=1 g i (x)h i (y), x, y ∈ G, where the functions f, {g i }, {h i }: G → C to be determined are bounded and continuous functions on G. We show how the solutions of these equations are closely related to the ...
13
The method of averaging and functional differential equations with delay
... One can also precise the long time behaviour of a solution of (2.1) provided that more is known about the solution of (2.2). To give estimate for all time, we assume that the solution of (2.2) tends toward an ...
15
The First Order Functional Differential Equation
... The functional differential equation ...differential equations and some special cases of these functional differential equations with ≡ 1 have been studied in the literature on closed and ...
10