Stability of Functional Equations in Matrix Random Normed Spaces: A Fixed Point Approach

In this paper, we prove the Hyers–Ulam stability of the Cauchy additive functional equation and the quadratic functional equation in matrix random normed spaces by using fixed point method.     

On a problem of Schwaiger in random normed spaces

We consider a problem of Schwaiger in the setting of random normed spaces to obtain a characterization for the completeness of these spaces by means of the stability of the Cauchy additive functional equation.     

Generalized Ulam-Hyers stability of random homomorphisms in random normed algebras associated with the Cauchy functional equation

Using the fixed point method, we prove the generalized Ulam-Hyers stability of random homomorphisms in random normed algebras associated with the Cauchy functional equation.     

An AQCQ-Functional Equation in Matrix Normed Spaces

In this paper, we prove the Hyers–Ulam stability of an additive–quadratic–cubic–quartic functional equation in matrix normed spaces.     

Functional inequalities in non-Archimedean normed spaces

In this paper, we introduce an additive functional inequality and a quadratic functional inequality in normed spaces, and prove the Hyers–Ulam stability of the functional inequalities in Banach spaces. Furthermore, we introduce an additive functional inequality and a quadratic functional inequality in non-Archimedean normed spaces, and prove the Hyers–Ulam stability of the functional inequalities in non-Archimedean Banach spaces.     

Approximate additive mappings in 2-Banach spaces and related topics

In this paper, we investigate approximate additive mappings, approximate Jensen mappings and approximate quadratic mappings in 2-Banach spaces. That is, we prove the generalized Hyers-Ulam stability of the Cauchy functional equation, the Jensen functional equation and the quadratic functional equation in 2-Banach spaces.     

直观随机赋范空间中三次泛函方程的稳定性

先引入直观随机赋范空间的概念．然后,借助这一概念,然后对任意的三角范数在该空间的框架下,研究了三次泛函方程的稳定性．另外,还介绍了随机空间理论、直观空间理论及泛函方程理论间的密切关系．     

本刊英文版Vol.31(2015),No.3论文摘要（英文）

<正>Functional Inequalities in Non-Archimedean Normed Spaces Choonkil PARK Abstract In this paper,we introduce an additive functional inequality and a quadratic functional inequality in normed spaces,and prove the Hyers-Ulam stability of the functional inequalities in Banach spaces.Furthermore,we introduce an additive functional inequality and a     

Stability of preserving lattice cubic functional equation in Menger probabilistic normed Riesz spaces

The aim of this paper is to investigate Hyers–Ulam–Rassias stability of preserving lattice functional equation in various spaces. First, we prove stability of generalized preserving lattice functional equation in Banach lattices. Next, we show stability of preserving lattice cubic functional equation in Menger probabilistic normed Riesz spaces.     

HYERS-ULAM-RASSIAS STABILITY OF FUNCTIONAL EQUATIONS IN MENGER PROBABILISTIC NORMED SPACES

We introduce the approximately quadratic functional equation in Menger probabilistic normed spaces. More precisely, we show under some suitable conditions that an approximately quadratic functional equation can be approximated by a quadratic function in above mentioned spaces. Also we consider the stability problem for approximately pexiderized functional equation in Menger probabilistic normed spaces.     

Approximation of a General Cubic Functional Equation in Felbin’s Type Fuzzy Normed Linear Spaces

In this paper, we investigate the generalized Hyers–Ulam stability of a general cubic functional equation in Felbin’s type fuzzy normed linear spaces and some applications of our results in the stability of general cubic functional equation from a linear space to a Banach space will be exhibited.     

On the stability of the quadratic mapping in normed spaces

The problem of the stability of the quadratic functional equation (including ULAM-HYERS and RASSIAS types of stability) in normed spaces is investigated.     

On an equation characterizing multi-Jensen-quadratic mappings and its Hyers–Ulam stability via a fixed point method

In this paper, we unify the system of functional equations defining a multi-Jensen-quadratic mapping to obtain a single equation. We also prove, using the fixed point method, the generalized Hyers–Ulam stability of this equation both in Banach spaces and in complete non-Archimedean normed spaces.     

Stability of Pexiderized quadratic functional equation in intuitionistic fuzzy normed space

The object of the present paper is to determine the stability of the Hyers-Ulam-Rassias type theorem concerning the Pexiderized quadratic functional equation in intuitionistic fuzzy normed spaces (IFNS).     

On the Stability of Jordan *-Derivation Pairs

In this article, the Hyers–Ulam stability of Jordan *-derivation pairs for the Cauchy additive functional equation and the Cauchy additive functional inequality is proved. A fixed point method to establish of the stability and the superstability for Jordan *-derivation pairs is also employed.     

Stability of the generalized quadratic and quartic type functional equation in non-Archimedean fuzzy normed spaces

In this paper, we prove some stability results concerning the generalized quadratic and quartic type functional equation in the context of non-Archimedean fuzzy normed spaces in the spirit of Hyers-Ulam-Rassias. As applications, we establish some results of approximately generalized quadratic and quartic type mapping in non-Archimedean normed spaces. Also, we show that the assumption of the non-Archimedean absolute value of $2$ is less than $1$ cannot be omitted in our corollaries. The results improve and extend some recent results.     

非Archimedean随机空间中混合型泛函方程的解及稳定性

在非-Archimedean 随机赋范空间的框架下,证明了Euler-Lagrange二次映象的广义稳定性．另外,文中还介绍了 随机空间理论、非-Archimedean 空间理论、以及泛函方程理论之间的联系．     

Generalized Hyers-Ulam stability for general additive functional equations in quasi-β-normed spaces

In 1940 S.M. Ulam proposed the famous Ulam stability problem. In 1941 D.H. Hyers solved the well-known Ulam stability problem for additive mappings subject to the Hyers condition on approximately additive mappings. The first author of this paper investigated the Hyers-Ulam stability of Cauchy and Jensen type additive mappings. In this paper we generalize results obtained for Jensen type mappings and establish new theorems about the Hyers-Ulam stability for general additive functional equations in quasi-β-normed spaces.     

Stability of a cubic functional equation in fuzzy normed space

In this paper, the authors investigate the general solution of a new cubic functional equation \(\begin{equation*} 3f(x+3y)-f(3x+y)=12[f(x+y)+f(x-y)]+80f(y)-48f(x) \end{equation*}\) and discuss its generalized Hyers - Ulam - Rassias stability in Banach spaces and stability in fuzzy normed spaces.     

概率赋范空间中的非线性半群与微分包含*

本文的目的是在概率赋范空间中引入和研究非线性压缩半群,并对增生映象建立Crandal-Ligget指数公式.作为应用,我们将应用这些结果研究概率赋范空间中一类具增生映象的微分包含的Cauchy问题解的存在性.