On Ulam Stability of the Inhomogeneous Version of the General Linear Functional Equation

被引:11
作者
Benzarouala, Chaimaa [1 ]
Brzdek, Janusz [2 ]
El-hady, El-sayed [3 ,4 ]
Oubbi, Lahbib [5 ]
机构
[1] Mohammed V Univ Rabat, Fac Sci, Ctr CeReMAR, Dept Math,Lab LMSA,Team GrAAF, Box 1014, 4 Ave Ibn Batouta, Rabat, Morocco
[2] AGH Univ Sci & Technol, Fac Appl Math, Mickiewicza 30, PL-30059 Krakow, Poland
[3] Jouf Univ, Coll Sci, Math Dept, POB 2014, Sakaka, Saudi Arabia
[4] Suez Canal Univ, Fac Comp & Informat, Basic Sci Dept, Ismailia 41522, Egypt
[5] Mohammed V Univ Rabat, Ecole Normale Super Takaddoum, Ctr CeReMAR, Dept Math,Lab LMSA,Team GrAAF, POB 5118, Rabat 10105, Morocco
关键词
Fixed point; function space; general linear functional equation; Ulam stability; SCHRODER EQUATION; RASSIAS STABILITY; HYPERSTABILITY; POPOVICIU;
D O I
10.1007/s00025-023-01840-7
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The Ulam stability concerns the following issue: how much an approximate solution to an equation differs from an exact solution to the equation. We prove a general Ulam stability result for the functional equation sigma(m)(i=1) A(i)f (sigma(n)(j=1)a(ij)x(j ))= D(x(1), . . . , x(n)),in the class of functions f mapping a module X, over a commutative ring K, into a Banach space Y, where m and n are fixed positive integers, a(ij) is an element of K for every i is an element of {1,. .., m} and j is an element of {1,. .., n}, A(1),..., A(m) are scalars, and the function D : X-n -> Y is fixed. In this way we generalize an earlier result of A. Bahyrycz and J. Olko. We also show some interesting consequences of this outcome, including conditions sufficient for the existence of solutions to the equation. Particular cases of the equation that we investigate are for instance the functional equations of Cauchy, Jensen, Jordan-von Neumann, Drygas, Fre & acute;chet, Popoviciu, Wright and many others.
引用
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页数:32
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