Existence and stability of Stieltjes quadratic functional integral equations

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• 作者：Zhi Zhang ; JinRong Wang
• 关键词：Stieltjes quadratic functional integral equations ; Existence ; Hyers–Ulam–Rassias stability ; Fixed point theorem
• 刊名：Journal of Applied Mathematics and Computing
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：53
• 期：1-2
• 页码：183-199
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Computational Mathematics and Numerical Analysis; Appl.Mathematics/Computational Methods of Engineering; Theory of Computation; Mathematics of Computing;
• 出版者：Springer Berlin Heidelberg
• ISSN：1865-2085
• 卷排序：53

文摘

In this paper, we investigate existence and generalized Hyers–Ulam–Rassias stability of Stieltjes quadratic functional integral equations. Firstly, we show some basic properties of the composite function of bounded variation. Secondly, we derive the generalized Hyers–Ulam–Rassias stability result after examining the existence and uniqueness results via the theory of measure of noncompactness and a fixed point theorem of Darbo type. Finally, two examples of functional integral equations of fractional order are given to demonstrate the applicability of our results.