A fixed point theorem and Ulam stability of a general linear functional equation in random normed spaces

被引：0
作者：
Chaimaa Benzarouala
Janusz Brzdęk
Lahbib Oubbi
机构：
[1] Center CeReMAR,Mohammed V University in Rabat, Faculty of Sciences, Department of Mathematics
[2] Laboratory LMSA,Faculty of Applied Mathematics
[3] Team GrAAF,Mohammed V University in Rabat, Ecole Normale Supérieure Takaddoum, Department of Mathematics
[4] AGH University of Science and Technology,undefined
[5] Center CeReMAR,undefined
[6] Laboratory LMSA,undefined
[7] Team GrAAF,undefined
来源：
Journal of Fixed Point Theory and Applications | 2023年 / 25卷
关键词：
Fixed point; function space; general linear functional equation; random normed space; Ulam stability; approximate eigenvalue; approximate eigenvector; 39B05; 39B82; 47H10; 54E70;
D O I：
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学科分类号：
摘要：
We prove a very general fixed point theorem in the space of functions taking values in a random normed space (RN-space). Next, we show several of its consequences and, among others, we present applications of it in proving Ulam stability results for the general inhomogeneous linear functional equation with several variables in the class of functions f mapping a vector space X into an RN-space. Particular cases of the equation are for instance the functional equations of Cauchy, Jensen, Jordan–von Neumann, Drygas, Fréchet, Popoviciu, the polynomials, the monomials, the p-Wright affine functions, and several others. We also show how to use the theorem to study the approximate eigenvalues and eigenvectors of some linear operators.
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