Pub Date : 2019-06-03DOI: 10.37622/ijde/14.1.2019.39-58
G. Chatzarakis, I. Jadlovská
The rapid evolution of applied science and technology, especially in the domain of computer science, control systems and communications have contributed to researchers from the science of mathematics more necessary than ever. It is because of the continuous need to develop proper software and hardware, which primarily implies the construction of components that at first make possible the digitalization of data to transfer and then recover back again in the analogue form, that man is familiar with and understand.
{"title":"Improved Oscillation Tests for Retarded Difference Equations","authors":"G. Chatzarakis, I. Jadlovská","doi":"10.37622/ijde/14.1.2019.39-58","DOIUrl":"https://doi.org/10.37622/ijde/14.1.2019.39-58","url":null,"abstract":"The rapid evolution of applied science and technology, especially in the domain of computer science, control systems and communications have contributed to researchers from the science of mathematics more necessary than ever. It is because of the continuous need to develop proper software and hardware, which primarily implies the construction of components that at first make possible the digitalization of data to transfer and then recover back again in the analogue form, that man is familiar with and understand.","PeriodicalId":36454,"journal":{"name":"International Journal of Difference Equations","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74435503","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}
Pub Date : 2019-06-02DOI: 10.37622/ijde/14.1.2019.25-38
D. Anderson
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.
{"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":null,"pages":null},"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}
Pub Date : 2019-06-01DOI: 10.37622/ijde/14.1.2019.1-24
G. Anastassiou
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.
{"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":null,"pages":null},"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}
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