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Fixed-point results
and the Hyers–Ulam stability of linear equations of higher
orders
Bing Xu, Janusz Brzdęk and Weinian Zhang |
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Vol. 273 (2015), No. 2, 483–498
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Abstract |
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We present a general method for investigation of the Hyers–Ulam stability of linear equations (differential, difference, functional, integral) of higher orders. It is shown that in many cases, that kind of stability for such equations is a consequence of a similar property of the corresponding first-order equations. Some particular examples of applications for differential, integral, difference and functional equations are described. The method is based on some fixed-point results that are proved in this paper. |
Keywords
fixed point, Hyers–Ulam stability, linear equation, linear
operator, operator equation
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Mathematical Subject Classification 2010
Primary: 39B82, 47A63, 47J99
Secondary: 34K20, 39B12, 47H10
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Milestones
Received: 28 March 2014
Accepted: 19 August 2014
Published: 23 December 2014
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Authors |
| Bing Xu | |
| Department of Mathematics Sichuan University Chengdu, Sichuan, 610064 China |
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| Janusz Brzdęk | |
| Department of Mathematics Pedagogical University Podchorążych 2 30-084 Kraków Poland |
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| Weinian Zhang | |
| Department of Mathematics Sichuan University Chengdu, Sichuan, 610064 China |
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