Implicit Linear Nonhomogeneous Difference Equation in Banach and Locally Convex Spaces

S.L. Gefter; A.L. Piven

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Implicit Linear Nonhomogeneous Difference Equation in Banach and Locally Convex Spaces

机译：Banach空间和局部凸空间中的隐式线性非齐次差分方程

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The subjects of this work are the implicit linear difference equationsAxn+1 + Bxn = gn and Axn+1 = xn ? fn, n = 0, 1, 2, . . ., where A and Bare continuous operators acting in certain locally convex spaces. The existenceand uniqueness conditions, along with explicit formulas, are obtainedfor solutions of these equations. As an application of the general theoryproduced this way, the equation Axn+1 = xn ? fn in the space R∞ of fi-nite sequences and in the space RM, where M is an arbitrary set, has beenstudied.

机译：这项工作的主题是隐式线性差分方程Axn + 1 + Bxn = gn和Axn + 1 = xn？ fn，n = 0，1，2，.. 。。，其中A和Bare连续算子在某些局部凸空间中起作用。获得这些方程解的存在性和唯一性条件，以及明确的公式。作为以这种方式产生的一般理论的应用，等式Axn + 1 = xn？已经研究了有限序列的空间R∞和RM的空间fn，其中M是任意集合。

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《Journal of Mathematical Physics, Analysis, Geometry》 |2019年第3期|共18页
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S.L. Gefter; A.L. Piven;
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中图分类高等数学;
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difference equationlocally convex spaceBanach spacelocallynilpotent operator.;

机译：差分方程局部凸空间Banach空间局部零幂算子。;

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1. IMPLICIT LINEAR q-DIFFERENCE EQUATIONS IN BANACH SPACES [J] . S. L. Gefter, A. L. Piven Journal of Mathematical Sciences . 2020,第6期

机译：Banach空间中的隐含线性Q差分方程
2. ENTIRE SOLUTIONS OF ONE LINEAR IMPLICIT DIFFERENTIAL-DIFFERENCE EQUATION IN BANACH SPACES [J] . Hefter S. L., Piven O. L. Ukrainian mathematical journal . 2019,第8期

机译：Banach空间中一个线性隐式差分方程的整个解
3. Banach-Steinhaus type theorem in locally convex spaces for linear σ-locally Lipschitzian operators [J] . S. Lahrech Miskolc Mathematical Notes . 2005,第2005期

机译：线性凸局部Lipschitzian算子的局部凸空间中的Banach-Steinhaus型定理
4. On Exponential Dichotomy of Variational Nonautonomous Difference Equations in Banach Spaces [C] . MIHAELA AURELIA TOMESCU, MIHAIL MEGAN, TRAIAN CEAUSU WSEAS International Conference on Applied Mathematics . 2013

机译：Banach空间中变分非自治差分方程的指数二分法
5. Iteration methods for approximation of solutions of nonlinear equations in Banach spaces. [D] . Chidume, Chukwudi. 2008

机译：Banach空间中非线性方程解的逼近迭代方法。
6. Multivariate systems of nonexpansive operator equations and iterative algorithms for solving them in uniformly convex and uniformly smooth Banach spaces with applications [O] . Yongchun Xu, Jinyu Guan, Yanxia Tang, -1

机译：非膨胀算子方程的多元系统及其在一致凸和一致光滑Banach空间中求解它们的迭代算法及其应用
7. Banach-Steinhaus type theorem in locally convex spaces for linear $Sigma$-locally Lipschitzian operators [O] . S. Lahrech 2005

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8. Implicit Functions from Locally Convex Spaces to Banach Spaces [R] . Hiltunen, S. 1999

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Implicit Linear Nonhomogeneous Difference Equation in Banach and Locally Convex Spaces

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