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Hyers-Ulam 稳定性及其应用的研究
  • 项目名称：Hyers-Ulam 稳定性及其应用的研究
  • 项目类别：面上项目
  • 批准号：11171022
  • 申请代码：A010701
  • 项目来源：国家自然科学基金
  • 研究期限：2012-01-01-2015-12-31
  • 项目负责人：许天周
  • 依托单位：北京理工大学
  • 批准年度：2011
中文摘要：

本项目结合算子理论、不动点理论、极小极大原理研究高阶混合型函数方程的一般解和Hyers-Ulam稳定性问题；研究混合型函数方程所对应函数不等式的Hyers-Ulam 稳定性问题；研究混合型函数方程在广义函数空间上的Hyers-Ulam稳定性问题；研究多值函数方程的集值解及其Hyers-Ulam稳定性和与该问题有关的集值映射的选择定理，寻求新的迭代算法和技巧；研究微分方程、泛函微分方程的Hyers-Ulam稳定性理论，给出精确解与扰动解的误差分析，寻求定理的表述形式和最佳刻画。期望通过对上述问题的研究，作出具有创新性的成果，推进非线性分析理论与应用的发展，课题所发展的迭代方法和技巧适用于函数逼近、集值变分包含、计算机程序的近似检查、自测试和自纠错等领域。

中文主题词： Hyers-Ulam稳定性；函数方程；微分算子；分数阶微分方程；非线性发展方程
英文摘要：

Hyers-Ulam stability；functional equation；differential operator；fractional differential equation；nonlinear evolution equation

英文主题词： Hyers-Ulam stability；functional equation；differential operator；fractional differential equation；nonlinear evolution equation
结论摘要：

本项目研究Hyers-Ulam 稳定性的若干问题。主要研究了混合型函数方程的一般解和Hyers-Ulam稳定性问题，在拟Banach空间、Banach模、n-Banach空间和 F-空间中建立了一般可加三次方程及AQ方程的Ulam型稳定性定理；研究了多可加映射、多Jensen映射和多二次映射的一般解及Hyers-Ulam稳定性问题；研究了整函数Hilbert空间上微分算子的Hyers-Ulam稳定性，给出了在整函数空间上判别微分算子Hyers-Ulam稳定性的一个充分必要条件，得到了微分算子Hyers-Ulam稳定性的最佳常数；研究了再生核函数空间上微分算子的Hyers-Ulam稳定性，得到了微分算子具有Hyers-Ulam稳定性的一个充分必要条件；研究了带有Riemman-Liouville导数和Caputo导数的几类分数阶微分方程的Hyers-Ulam稳定性问题；研究了几类非线性发展方程的不变群和对称等问题。

成果综合统计
成果类型
数量
  • 期刊论文
  • 会议论文
  • 专利
  • 获奖
  • 著作
  • 40
  • 0
  • 0
  • 0
  • 0
期刊论文
A fixed point approach to the Hyers-Ulam stability of an AQ functional equation on β -Banach modules
A Generalized Mixed Quadratic-Quartic Functional Equation
On the stability of multi-Jensen mappings in β-normed spaces
On the Hyers-Ulam Stability of a General Mixed Additive and Cubic Functional Equation in n-Banach Sp
Stability of a general mixed additive-cubic equation in F-spaces
Approximate septic and octic mappings in quasi-beta-normed spaces
On fuzzy approximately cubic type mapping in fuzzy Banach spaces
Lie Symmetry Analysis and Explicit Solutions of the Time Fractional Fifth-Order KdV Equation
Approximate multi-Jensen and multi-quadratic mappings in 2-Banach spaces
A fixed point approach to the intuitionistic fuzzy stability of quintic and sextic functional equati
Group Analysis and New Explicit Solutions of Simplified Modified Kawahara Equation with Variable Coe
Hyers-Ulam stability of a class of fractional linear differential equations
Optical soliton of time fractional Schrodinger equations with He's semi-inverse method
Group analysis, explicit solutions and conservation laws of the Logarithmic-KdV equation
On the stability of multi-additive mappings in non-Archimedean normed spaces
On New Existence Results for Fractional Differential Equations in Quaternionic Analysis
Invariant analysis and explicit solutions of the time fractional nonlinear perturbed Burgers equatio
The Cauchy problem for quaternion fuzzy fractional differential equation
A fixed point approach to the stability of a general mixed additive-cubic equation on Banach modules
Stability of general multi-Euler-Lagrange quadratic functional equations in non-Archimedean fuzzy no
Stability of multi-Jensen mappings in non-Archimedean normed spaces
On the Mazur-Ulam Theorem in Non-Archimedean Fuzzy n-Normed Spaces
Approximate Multi-Jensen, Multi-Euler-Lagrange Additive and Quadratic Mappings in n-Banach Spaces
Hyers-Ulam stability of fractional linear differential equations involving Caputo fractional derivat
Direct and fixed point approaches to the stability of an AQ-functional equation in non-Archimedean n
Invariant analysis and exact solutions of nonlinear time fractional Sharma-Tasso-Olver equation by L
Singular solitons, shock waves, and other solutions to potential KdV equation
Topological solitons and conservation laws of the coupled Burgers equations
Solitons and Lie group analysis to an extended quantum Zakharov-Kuznetsov equation
Shock Waves and Other Solutions to the Benjamin-Bona-Mahoney-Burgers Equation with Dual Power-Law No
Hyers-Ulam stability of differentiation operator on Hilbert spaces of entire functions
Hyers-Ulam stability of differentiation operator on Hilbert spaces of entire function
The Modified Fractional Sub-Equation Method and Its Applications to Nonlinear Fractional Partial Dif
The improved fractional sub-equation method and its applications to nonlinear fractional partial dif
Generalized Hyers–Ulam Stability of a General Mixed Additive-cubic Functional Equation in Quasi-Bana
A fixed point approach to the stability of an AQ-functional equation on beta-Banach modules
Symmetry properties and explicit solutions of the nonlinear time fractional KdV equation
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