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．     

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.     

ON THE HYERS-ULAM STABILITY OF AN EQUATION CHARACTERIZING MULTI-QUADRATIC MAPPINGS

In this article,we prove,both in complete non-Archimedean normed spaces and in 2-Banach spaces,the generalized Hyers-Ulam stability of an equation characterizing multiquadratic mappings.Our results generalize some known outcomes.     

A Mazur–Ulam theorem in non-Archimedean normed spaces

The classical Mazur–Ulam theorem which states that every surjective isometry between real normed spaces is affine is not valid for non-Archimedean normed spaces. In this paper, we establish a Mazur–Ulam theorem in the non-Archimedean strictly convex normed spaces.     

On some fixed-point theorems for generalized contractions and their perturbations

The aim of this paper is to prove a collection of fixed-point theorems for mappings which can be roughly called generalized contractions or their perturbations. In particular, we are going to consider operators (single-valued or multi-valued) in Banach spaces with a quasimodulus, in hyperconvex subsets of normed spaces, or finally in non-Archimedean spaces. A particular attention will be paid to Krasnoselskii-type fixed-point theorems as well as to a Schaefer-type fixed-point theorem. Some applications to nonlinear functional-integral equations will be given. Our results extend and complement some commonly known theorems.     

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.     

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.     

Some inequalities in inner product spaces related to the generalized triangle inequality

In this paper we obtain some inequalities related to the generalized triangle and quadratic triangle inequalities for vectors in inner product spaces. Some results that employ the Ostrowski discrete inequality for vectors in normed linear spaces are also obtained.     

On Hyers–Ulam stability of two functional equations in non-Archimedean spaces

In this paper we prove, using the fixed point method, the generalized Hyers–Ulam stability of two functional equations in complete non-Archimedean normed spaces. One of these equations characterizes multi-Cauchy–Jensen mappings, and the other gives a characterization of multi-additive-quadratic mappings.     

概率收缩偶与非阿基米德Menger概率赋范空间中非线性方程组的解*

本文在非阿基米德Menger概率赋范空间中引入了概率收缩偶的概念,研究了非阿基米德Menger概率赋范空间中具概率收缩偶的非线性方程组的解的存在性与唯一性.发展和改进了引文[1～5]的相应结果.     

On the Best Approximation in Non-Archimedean Normed Linear Spaces

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Non-Archimedean stability of a quadratic functional equation

Recently the Hyers–Ulam stability of the quadratic functional equation $ f(kx+y)+f(kx+\sigma (y))- 2k^2 f(x)-2f(y)=0 $ where $\sigma $ is an involution of the normed space $E$ and $k$ is a fixed positive integer greater that 1, has been proved in the earlier work. In this paper, using fixed point and direct methods, we prove the Hyers–Ulam stability of the above functional equation in non-Archimedean normed 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.     

On orthocomplemented subspaces in p-adic Banach spaces

For linear subspaces of finite-dimensional normed spaces over K, where K is a non-Archimedean complete valued field which is not spherically complete, we study orthocomplementation as related to strictness and the Hahn-Banach property. We prove that there exist finite-dimensional normed spaces which possess non-orthocomplemented, strict HB-subspaces.     

On the Mazur-Ulam theorem in non-Archimedean fuzzy normed spaces

We prove that the Mazur-Ulam theorem holds under some conditions in non-Archimedean fuzzy normed space.     

On stationary points of multivalued strongly contractive mappings in partially ordered ultrametric spaces and non-Archimedean

The purpose of this paper is to present a fixed point theorem for multivalued strongly contractive mappings in partially ordered ultrametric spaces. Also a consequence is obtained for these mappings in partially ordered non-Archimedean normed spaces. Finally, two supporting examples of these results are given.     

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.     

赋范线性空间中广义Φ-半压缩映射的迭代逼近

研究了实赋范线性空间中一致连续广义Φ-半压缩映射带误差的Ishikawa序列迭代逼近问题,改进和推广了现有的结果.     

Stability of multi-additive mappings in non-Archimedean normed spaces

A function f:Vn→W, where V is a commutative semigroup, W is a linear space and n?1 is an integer, is called multi-additive if it is additive in each variable. In this paper we prove the generalized Hyers-Ulam stability of multi-additive mappings in non-Archimedean normed spaces, using the so-called direct method.     

二维严格凸赋范空间单位球面间等距映射的线性延拓

主要研究二维严格凸实赋范空间E和F的单位球面S_1(E)和S_1(F)之间的等距映射的线性延拓问题.利用二维严格凸赋范空间单位球面的性质得到:若等距映射V_0:S_1(E)→S_1(F)满足一定条件,则V_0可延拓为全空间E上的线性等距映射V:E→F.