ON A FIXED POINT THEOREM IN UNIFORM SPACES AND ITS APPLICATION TO NONLINEAR VOLTERRA TYPE OPERATORS

被引：0

作者：

Angelov, Vasil ^{[1
]}

Kiskinov, Hristo ^{[2
]}

Zahariev, Andrey ^{[3
]}

Georgiev, Ljubomir ^{[1
]}

机构：

[1] Univ Min & Geol, Dept Math, St I Rilski, Sofia 1700, Bulgaria

[2] Paisij Hilendarski Univ Plovdiv, Fac Math & Informat, 236 Bulgaria Blvd, Plovdiv 4003, Bulgaria

[3] Paisij Hilendarski Univ Plovdiv, Fac Math & Informat, 236 Bulgaria Blvd, Plovdiv 4003, Bulgaria

来源：

FIXED POINT THEORY | 2017年 / 18卷 / 01期

关键词：

Fixed point; Volterra type integral equations; uniform space; pseudo metrics; Hausdorff space;

D O I：

10.24193/fpt-ro.2017.1.05

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the present work, we prove a fixed point theorem for nonlinear operators acting in Hausdorff sequentially complete uniform spaces whose uniformity is generated by a saturated family of pseudometrics. As an application we consider nonlinear abstract Volterra type integral equations of second kind in the case when the independent variable belongs to arbitrary completely regular Hausdorff space. Existence and uniqueness of the solutions of these equations in nonhomogeneous case are also proved.

引用

页码：47 / 56

页数：10

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