Stability of Generalized Jensen Equation on Restricted Domains

Approximation of a Cauchy-Jensen additive mapping in various normed spaces

In this paper, using the fixed point and direct methods, we prove the generalized Hyers-Ulam-Rassias stability of a Cauchy-Jensen additive functional equation in various normed spaces. The concept of Hyers-Ulam-Rassias stability originated from Th. M. Rassias stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300.

混合型加性-三次Jensen泛函方程在非阿基米德$(n, β)$赋范空间中的稳定性

Stability of Mixed Type Additive-Cubic Jensen Functional Equation in Non-Archimedean $(n, β)$ Normed Spaces

本文研究了混合型加性-三次Jensen泛函方程在非阿基米德$(n, β)$赋范空间中的Hyers-Ulam稳定性。

Approximation of general 3-variable Jensen $ρ$-functional inequalities in complex Banach spaces

In this paper, we introduce and investigate general 3-variable Jensen $ρ$-functional equation, and prove the Hyers-Ulam stability of the Jensen functional equations associated with the general 3-variable Jensen $ρ$-functional inequalities in complex Banach spaces.

Satbility of Ternary Homomorphisms via Generalized Jensen Equation

In this paper, we establish the generalized Hyers--Ulam--Rassias stability of homomorphisms between ternary algebras associted to the generalized Jensen functional equation $r f(\frac{sx+ty}{r}) = s f(x) + t f(y)$.

On the stability of J$^*-$derivations

In this paper, we establish the stability and superstability of $J^*-$derivations in $J^*-$algebras for the generalized Jensen--type functional equation $$rf(\frac{x+y}{r})+rf(\frac{x-y}{r})= 2f(x).$$ Finally, we investigate the stability of $J^*-$derivations by using the fixed point alternative.

用不动点方法研究巴拿赫代数上对合的稳定性

Stability of involutions on Banach Algebra by fixed point method

该研究采用Jensen函数方程稳定性的不动点方法，证明巴拿赫代数上对合的Hyers-Ulam-Rassias稳定性与超稳定性，还得到使带近似对合的巴拿赫代数成为$C^*$-代数的条件。

带参数的函数方程的Hyers-Ulam-Rassias稳定性

Hyers-Ulam-Rassias stability of functional equations with parameters

本文在β-齐次F-空间中研究广义Jensen加性和二次函数方程的Hyers-Ulam稳定性，证明近似映射存在唯一精确近似解。

$\boldsymbol{\text{ℓ}_p}$-直和下限制中心性质的稳定性及限制中心映射的连续性研究

On stability of restricted center properties and continuity of restricted center map under $\ell_p$-direct sum

该研究聚焦ℓₚ-直和下限制中心相关性质的稳定性与映射连续性，明确了多类性质在有限/无限ℓₚ-直和下的稳定情况，还提出性质-(lP₂)作为连续性充分条件并验证其稳定性。

混合下传输不等式与受限对数Sobolev不等式的稳定性

Stability under mixtures of transportation inequalities and restricted log-Sobolev inequalities

本文研究传输-熵不等式与受限泛函不等式在混合下的稳定性，给出将不等式从混合分量转移到混合本身的充分条件。

Approximately Quadratic Mappings on Restricted Domains

In this paper, we introduce a generalized quadratic functional equation $f(rx + sy) = rf(x) + sf(y) - rsf(x - y)$ where $r, s$ are nonzero real numbers with $r + s = 1.$ We show that this functional equation is quadratic if $r, s$ are rational numbers. We also investigate its stability problem on restricted domains. These results are applied to study of an asymptotic behavior of these generalized quadratic mappings.

Some stability properties of restricted Chebyshev centers in Banach spaces

In this paper, we discuss the stability of (restricted) Chebyshev centers in few function spaces. For an extremally disconnected compact Hausdorff space $K$ and a finite dimensional Banach space $X$, we prove the existence of Chebyshev centers of closed bounded subsets of the space of $X$-valued continuous functions on $K$, $C(K,X)$ and that of compact subsets of $M$-ideals in $C(K,X)$. It is also proved that the existence of restricted Chebyshev centers is stable in the space of vector-valued bounded functions on an arbitrary set. Furthermore, the stability of continuity properties of the Che…