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TR-Dizin İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8652

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Browsing TR-Dizin İndeksli Yayınlar Koleksiyonu by Author "109448"

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    Citation - WoS: 2
    Citation - Scopus: 6
    Diamond alpha Hardy-Copson type dynamic inequalities
    (Hacettepe Univ, Fac Sci, 2022) Kayar, Zeynep; Kaymakcalan, Billur; 109448; Matematik
    In this paper two kinds of dynamic Hardy-Copson type inequalities are derived via diamond alpha integrals. The first kind consists of twelve new integral inequalities which can be considered as mixed type in the sense that these inequalities contain delta, nabla and diamond alpha integrals together. The second kind involves another twelve new inequalities, which are composed of only diamond alpha integrals, unifying delta and nabla Hardy-Copson type inequalities. Our approach is quite new due to the fact that it uses time scale calculus rather than algebra. Therefore both kinds of our results unify some of the known delta and nabla Hardy-Copson type inequalities into one diamond alpha Hardy-Copson type inequalities and offer new Hardy-Copson type inequalities even for the special cases.
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    Citation - WoS: 12
    Citation - Scopus: 14
    Hardy—Copson type inequalities for nabla time scale calculus
    (Tubitak Scientific & Technological Research Council Turkey, 2021) Kayar, Zeynep; Kaymakcalan, Billur; 109448; Matematik
    This paper is devoted to the nabla unification of the discrete and continuous Hardy?Copson type inequalities. Some of the obtained inequalities are nabla counterparts of their delta versions while the others are new even for the discrete, continuous, and delta cases. Moreover, these dynamic inequalities not only generalize and unify the related ones in the literature but also improve them in the special cases.
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    Citation - WoS: 5
    The complementary nabla Bennett-Leindler type inequalities
    (Ankara Univ, Fac Sci, 2022) Kayar, Zeynep; Kaymakcalan, Billur; 109448; Matematik
    We aim to find the complements of the Bennett-Leindler type inequalities in nabla time scale calculus by changing the exponent from 0 < zeta < 1 to zeta > 1. Different from the literature, the directions of the new inequalities, where zeta > 1, are the same as that of the previous nabla Bennett-Leindler type inequalities obtained for 0 < zeta < 1. By these settings, we not only complement existing nabla Bennett-Leindler type inequalities but also generalize them by involving more exponents. The dual results for the delta approach and the special cases for the discrete and continuous ones are obtained as well. Some of our results are novel even in the special cases.