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International Journal of Difference Equations最新文献

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Improved Oscillation Tests for Retarded Difference Equations 迟滞差分方程的改进振荡试验
International Journal of Difference Equations Pub Date : 2019-06-03 DOI: 10.37622/ijde/14.1.2019.39-58
G. Chatzarakis, I. Jadlovská
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引用次数: 0
The Discrete Diamond-Alpha Imaginary Ellipse and Hyers–Ulam Stability 离散Diamond-Alpha虚椭圆与Hyers-Ulam稳定性
International Journal of Difference Equations Pub Date : 2019-06-02 DOI: 10.37622/ijde/14.1.2019.25-38
D. Anderson
{"title":"The Discrete Diamond-Alpha Imaginary Ellipse and Hyers–Ulam Stability","authors":"D. Anderson","doi":"10.37622/ijde/14.1.2019.25-38","DOIUrl":"https://doi.org/10.37622/ijde/14.1.2019.25-38","url":null,"abstract":"We introduce the imaginary diamond-alpha ellipse, which unifies and extends the left Hilger imaginary circle (forward, Delta case) and the right Hilger imaginary circle (backward, nabla case), for the discrete diamond-alpha derivative with constant step size. We then establish the Hyers–Ulam stability (HUS) of the firstorder linear complex constant coefficient discrete diamond-alpha derivative equation, proving that the imaginary diamond-alpha ellipse fails to have HUS, while inside and outside the ellipse the equation has HUS. In particular, for each parameter value not on the diamond-alpha ellipse, we determine explicitly the best (minimum) HUS constant in terms of the elliptical real part of the coefficient. AMS Subject Classifications: 30E10, 39A06, 39A30, 39A45.","PeriodicalId":36454,"journal":{"name":"International Journal of Difference Equations","volume":"45 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81301747","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
Time Scales Delta Iyengar-Type Inequalities 时间尺度Delta iyengar型不等式
International Journal of Difference Equations Pub Date : 2019-06-01 DOI: 10.37622/ijde/14.1.2019.1-24
G. Anastassiou
{"title":"Time Scales Delta Iyengar-Type Inequalities","authors":"G. Anastassiou","doi":"10.37622/ijde/14.1.2019.1-24","DOIUrl":"https://doi.org/10.37622/ijde/14.1.2019.1-24","url":null,"abstract":"Here we give the necessary background on delta time scales approach. Then we present general related time scales delta Iyengar type inequalities for all basic norms. We finish with applications to specific time scales like R, Z and qZ, q > 1. AMS Subject Classifications: 26D15, 39A12, 93C70.","PeriodicalId":36454,"journal":{"name":"International Journal of Difference Equations","volume":"13 1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87639600","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
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