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Items from 1 to 20 out of 23 results

article

On the stability of a generalization of Jensen functional equation

M. Almahalebi

Acta Mathematica Hungarica > 2018 > 154 > 1 > 187-198

Using the fixed point method, we investigate the stability of a generalization of Jensen functional equation $$ \sum_{k=0}^{n-1} f(x+ b_{k}y)=nf(x),$$ ∑ k = 0 n - 1 f ( x + b k y ) = n f ( x ) , where $${n \in \mathbb{N}_{2}}$$ n ∈ N 2 , $${b_{k}=\exp(\frac{2i\pi k}{n})}$$ b k = exp ( 2 i π k n ) for $${0\leq k \leq n-1}$$ 0 ≤ k ≤ n -...

article

Generalized hyperstability of the Jensen functional equation in ultrametric spaces

Muaadh Almahalebi

The Journal of Analysis > 2018 > 26 > 1 > 1-8

The aim of this paper is to investigate the generalized hyperstability for the Jensen functional equation in ultrametric Banach spaces using the fixed point method derived from Bahyrycz and Piszczek (Acta Math Hungar 142:353–365, 2014), Brzdȩk (Acta Math Hungar 141:58–67, 2013), and (Fixed Point Theory Appl 2013:285, 2013). The obtained results generalize the existing ones in Alamahalebi and Chahbi...

article

Hyperstability of the Jensen functional equation in ultrametric spaces

Muaadh Almahalebi, Abdellatif Chahbi

Aequationes mathematicae > 2017 > 91 > 4 > 647-661

In this paper, we present hyperstability results of Jensen functional equations in ultrametric Banach spaces.

article

Hyperstability of an n-dimensional Jensen type functional equation

Iz-iddine EL-Fassi

Afrika Matematika > 2016 > 27 > 7-8 > 1377-1389

In this paper, we will investigate some hyperstability results of an n-dimensional Jensen type functional equation $$\begin{aligned} \sum _{i=1}^{n} p_{i} f(x_{i})=f\left( \sum _{i=1}^{n} p_{i} x_{i}\right) , \end{aligned}$$ ∑ i = 1 n p i f ( x i ) = f ∑ i = 1 n p i x i , where $$n>1$$ n > 1 is an integer, and $$p_{1},\ldots ,p_{n}$$ p...

article

Operatorial approach to the non-Archimedean stability of a Pexider K-quadratic functional equation

A.B. Chahbi, A. Charifi, B. Bouikhalene, S. Kabbaj

Arab Journal of Mathematical Sciences > 2015 > 21 > 1 > 67-83

We use the operatorial approach to obtain, in non-Archimedean spaces, the Hyers–Ulam stability of the Pexider K-quadratic functional equation∑k∈Kf(x+k·y)=κg(x)+κh(y),x,y∈E,where f,g,h:E→F are applications and K is a finite subgroup of the group of automorphisms of E and κ is its order.

article

Stability of functional equations in ( n , β ) $(n,\beta)$ -normed spaces

Xiuzhong Yang, Lidan Chang, Guofen Liu, Guannan Shen

Journal of Inequalities and Applications > 2015 > 2015 > 1 > 1-18

In this paper, we first introduce the notions of ( n , β ) $(n,\beta)$ -normed space and non-Archimedean ( n , β ) $(n,\beta)$ -normed space, then we study the Hyers-Ulam stability of the Cauchy functional equation and the Jensen functional equation in non-Archimedean ( n , β ) $(n,\beta)$ -normed spaces and that of the pexiderized Cauchy functional equation in ( n ,...

article

General solution and generalized Hyers-Ulam stability of a two-variable Jensen functional equation

Asadollah Aghajani, Faezeh Zahedi

Mathematical Sciences > 2013 > 7 > 1 > 1-4

In this paper, we obtain the general solution of the following two-variable Jensen functional equation: and investigate the generalized Hyers-Ulam stability. MSC(2010) 39B52; 39B72

article

Intuitionistic fuzzy stability of a Jensen functional equation via fixed point technique

S.A. Mohiuddine, M. Cancan, H. Şevli

Mathematical and Computer Modelling > 2011 > 54 > 9-10 > 2403-2409

The object of this paper is to determine Hyers–Ulam–Rassias stability concerning the Jensen functional equation in intuitionistic fuzzy normed space (IFNS) by using the fixed point method. Further, we establish stability of the Cauchy functional equation in IFNS.

article

On the stability of the equation stemming from Lagrange MVT

Tomasz Szostok, Szymon Wąsowicz

Applied Mathematics Letters > 2011 > 24 > 4 > 541-544

The stability behaviour of the functional equation F(y)−F(x)=(y−x)f((x+y)/2) is studied. It is proved that this equation is superstable i.e. if f,F satisfy |F(y)−F(x)(y−x)f((x+y)/2)|≤ε then f satisfies this equation (with some F). In order to obtain this result the equation hΔh2f(x)=0 is considered and it is proved that also this equation is superstable.

article

Local stability of the Pexiderized Cauchy and Jensen's equations in fuzzy spaces

Abbas Najati, Jung Im Kang, Yeol Je Cho

Journal of Inequalities and Applications > 2011 > 2011 > 1 > 1-8

Lex X be a normed space and Y be a Banach fuzzy space. Let D = {(x, y) ∈ X × X : ||x|| + ||y|| ≥ d} where d > 0. We prove that the Pexiderized Jensen functional equation is stable in the fuzzy norm for functions defined on D and taking values in Y. We consider also the Pexiderized Cauchy functional equation. 2000 Mathematics Subject Classification: 39B22; 39B82; 46S10.

article

Stability of homomorphisms for a 3D Cauchy–Jensen type functional equation on C∗-ternary algebras

Abbas Najati, Asghar Ranjbari

Journal of Mathematical Analysis and Applications > 2008 > 341 > 1 > 62-79

In this paper, we investigate homomorphisms between C∗-ternary algebras, and derivations on C∗-ternary algebras associated with the following Cauchy–Jensen type additive functional equation:f(x+y2+z)+f(x+z2+y)+f(y+z2+x)=2(f(x)+f(y)+f(z)).

article

Fuzzy stability of the Jensen functional equation

A.K. Mirmostafaee, M. Mirzavaziri, M.S. Moslehian

Fuzzy Sets and Systems > 2008 > 159 > 6 > 730-738

We establish a generalized Hyers–Ulam–Rassias stability theorem in the fuzzy sense. In particular, we introduce the notion of fuzzy approximate Jensen mapping and prove that if a fuzzy approximate Jensen mapping is continuous at a point, then we can approximate it by an everywhere continuous Jensen mapping. As a fuzzy version of a theorem of Schwaiger, we also show that if every fuzzy approximate...

article

Hyers–Ulam–Rassias stability of homomorphisms in quasi-Banach algebras

Choonkil Park

Bulletin des sciences mathematiques > 2008 > 132 > 2 > 87-96

In this paper, we prove the Hyers–Ulam–Rassias stability of homomorphisms in quasi-Banach algebras. This is applied to investigate isomorphisms between quasi-Banach algebras.

article

Isomorphisms Between Quasi-Banach Algebras*

Choonkil Park

Chinese Annals of Mathematics, Series B > 2007 > 28 > 3 > 353-362

In this paper, the author proves the Hyers–Ulam–Rassias stability of homo-morphisms in quasi-Banach algebras. This is used to investigate isomorphisms between quasi-Banach algebras.

article

The stability of d'Alembert and Jensen type functional equations

Gwang Hui Kim

Journal of Mathematical Analysis and Applications > 2007 > 325 > 1 > 237-248

The aim of this paper is to study the stability problem of the d'Alembert type and Jensen type functional equations:f(x+y)+f(x+σy)=2g(x)f(y),f(x+y)+f(x+σy)=2f(x)g(y),f(x+y)+f(x+σy)=2f(x).

article

Stability of a quadratic Jensen type functional equation in the spaces of generalized functions

Young-Su Lee, Soon-Yeong Chung

Journal of Mathematical Analysis and Applications > 2006 > 324 > 2 > 1395-1406

Making use of the fundamental solution of the heat equation we find the solution and prove the stability theorem of the quadratic Jensen type functional equation9f(x+y+z3)+f(x)+f(y)+f(z)=4[f(x+y2)+f(y+z2)+f(z+x2)] in the spaces of Schwartz tempered distributions and Fourier hyperfunctions.

article

On mappings preserving equilateral triangles in normed spaces

Justyna Sikorska, Tomasz Szostok

Journal of Geometry > 2006 > 85 > 1-2 > 149-156

. Let (X,||·||) and (Y,||·||) be normed linear spaces, dim X, dim Y ≥ 2. We say that f: X → Y preserves equilateral triangles if for all triples of points x, y, z ∈X with ||x − y|| = ||y − z|| = ||x − z|| we have $$||f (x) -f (y)||=||f (y)-f (z)||=||f (x)- f (z)||.$$ We prove that if X and Y are at least three-dimensional and f : X → Y is surjective and preserves equilateral triangles, then...

article

A Generalized Cubic Functional Equation

P. K. Sahoo

Acta Mathematica Sinica, English Series > 2005 > 21 > 5 > 1159-1166

In this paper, we determine the general solution of the functional equation f ₁(2x + y) + f ₂(2x − y) = f ₃(x + y) + f ₄(x − y) + f ₅(x) without assuming any regularity condition on the unknown functions f ₁, f ₂, f ₃, f ₄, f ₅ : ℝ → ℝ. The general solution of this equation is obtained by finding the general solution of the functional equations f(2x + y) + f(2x − y) = g(x + y) + g(x − y) + h(x) and...

article

A Generalized Cubic Functional Equation

P. Sahoo

Acta Mathematica Sinica, English Series > 2005 > 21 > 5 > 1159-1166

In this paper, we determine the general solution of the functional equation f1(2x + y) + f2(2x − y) = f3(x + y) + f4(x − y) + f5(x) without assuming any regularity condition on the unknown functions f1, f2, f3, f4, f5 : ℝ → ℝ. The general solution of this equation is obtained by finding the general solution of the functional equations f(2x + y) + f(2x − y) = g(x + y) + g(x − y) + h(x) and f(2x + y)...

article

The Stability of Jensen’s Equation on Amenable Locally Compact Groups

Dilian Yang

Results in Mathematics > 2004 > 46 > 3-4 > 381-388

The stability of Jensen’s equation on amenable locally compact groups is proved in this note.

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Keywords

JENSEN FUNCTIONAL EQUATION (23)
STABILITY (6)
HYERS–ULAM–RASSIAS STABILITY (5)
CAUCHY FUNCTIONAL EQUATION (4)
HYPERSTABILITY (4)
DIFFERENCE OPERATOR (3)
39B22 (2)
ADDITIVE FUNCTION (2)
CUBIC FUNCTIONAL EQUATION (2)
FIXED POINT METHOD (2)
FRÉCHET FUNCTIONAL EQUATION (2)
GENERALIZED HYERS-ULAM STABILITY (2)
HOMOMORPHISM IN QUASI-BANACH ALGEBRA (2)
P-BANACH ALGEBRA (2)
PEXIDERIZED CAUCHY FUNCTIONAL EQUATION (2)
QUADRATIC FUNCTIONAL EQUATION (2)
ULTRAMETRIC SPACE (2)
N–ADDITIVE FUNCTION (1)
P-BANACH ALGEBRA (1)
( N , Β ) $(N,\BETA)$ -NORMED SPACES (1)
39B72 (1)
46B03 (1)
47J (1)
ADDITIVE MAPPING (1)
AMENABLE LOCALLY COMPACT GROUP (1)
BANACH SPACE (1)
COMPLETENESS (1)
CONTINUITY (1)
COSINE FUNCTION (1)
D'ALEMBERT FUNCTIONAL EQUATION (1)
FIXED POINT (1)
FIXED POINT THEOREM (1)
FUNCTIONAL EQUATION (1)
FUZZY NORMED SPACE (1)
GAUSS TRANSFORM (1)
GENERAL SOLUTION (1)
GENERALIZED FUNCTION (1)
GROUP AUTOMORPHISMS (1)
HEAT KERNEL (1)
HOMOMORPHISM (1)
HYERS-ULAM-RASSIAS STABILITY (1)
HYERS–ULAM STABILITY (1)
INTUITIONISTIC FUZZY NORMED SPACE (1)
ISOMETRY (1)
K-QUADRATIC FUNCTIONAL EQUATION (1)
LAGRANGE MEAN VALUE THEOREM (1)
NON-ARCHIMEDEAN ( N , Β ) $(N,\BETA)$ -NORMED SPACE (1)
NON-ARCHIMEDEAN HYERS–ULAM STABILITY (1)
NON-ARCHIMEDEAN SPACE (1)
N–ADDITIVE FUNCTION (1)
PEXIDER EQUATION (1)
PEXIDER FUNCTIONAL EQUATION (1)
QUASI-BANACH ALGEBRA (1)
SIMILARITY TRANSFORMATION (1)
STABILITY. (1)
SUPERSTABILITY (1)
T-CONORM (1)
T-NORM (1)
Α-APPROXIMATELY JENSEN TYPE MAPPING (1)
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On the stability of a generalization of Jensen functional equation

Generalized hyperstability of the Jensen functional equation in ultrametric spaces

Hyperstability of the Jensen functional equation in ultrametric spaces

Hyperstability of an n-dimensional Jensen type functional equation

Operatorial approach to the non-Archimedean stability of a Pexider K-quadratic functional equation

Stability of functional equations in ( n , β ) $(n,\beta)$ -normed spaces

General solution and generalized Hyers-Ulam stability of a two-variable Jensen functional equation

Intuitionistic fuzzy stability of a Jensen functional equation via fixed point technique

On the stability of the equation stemming from Lagrange MVT

Local stability of the Pexiderized Cauchy and Jensen's equations in fuzzy spaces

Stability of homomorphisms for a 3D Cauchy–Jensen type functional equation on C∗-ternary algebras

Fuzzy stability of the Jensen functional equation

Hyers–Ulam–Rassias stability of homomorphisms in quasi-Banach algebras

Isomorphisms Between Quasi-Banach Algebras*

The stability of d'Alembert and Jensen type functional equations

Stability of a quadratic Jensen type functional equation in the spaces of generalized functions

On mappings preserving equilateral triangles in normed spaces

A Generalized Cubic Functional Equation

A Generalized Cubic Functional Equation

The Stability of Jensen’s Equation on Amenable Locally Compact Groups

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