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Some Extended Nabla and Delta Hardy–Copson Type Inequalities with Applications in Oscillation Theory

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Abstract

We extend classical nabla and delta Hardy–Copson type inequalities from \(\zeta >1\) to \(0<\zeta <1\) and also use these novel inequalities to find necessary and sufficient condition for the nonoscillation of the related half linear dynamic equations. Since ordinary differential equations and difference equations are special cases of dynamic equations, our results cover these equations as well. Moreover, the obtained inequalities are not only novel but also unify the continuous and discrete cases for which the case \(0<\zeta <1\) has not been considered so far.

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Authors and Affiliations

  1. Department of Mathematics, Van Yüzüncü Yıl University, 65080, Van, Turkey

    Zeynep Kayar

  2. Department of Mathematics, Çankaya University, 06810, Ankara, Turkey

    Billur Kaymakçalan

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  1. Zeynep Kayar
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  2. Billur Kaymakçalan
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Correspondence to Zeynep Kayar.

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Communicated by Majid Gazor.

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Kayar, Z., Kaymakçalan, B. Some Extended Nabla and Delta Hardy–Copson Type Inequalities with Applications in Oscillation Theory. Bull. Iran. Math. Soc. 48, 2407–2439 (2022). https://doi.org/10.1007/s41980-021-00651-2

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