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Some new refinements of the generalized Holder inequality and applications | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 25، دوره 13، شماره 2، مهر 2022، صفحه 265-276 اصل مقاله (422.98 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.20201.2134 | ||
| نویسندگان | ||
| Mohamed Amine Ighachane* ؛ Mohamed Akkouchi | ||
| Department of Mathematics, Faculty of Sciences-Semlalia, University Cadi Ayyad, Av. Prince My. Abdellah, BP: 2390, Marrakesh (40.000-Marrakech), Morocco | ||
| تاریخ دریافت: 25 فروردین 1399، تاریخ بازنگری: 24 آبان 1400، تاریخ پذیرش: 24 آذر 1400 | ||
| چکیده | ||
| The main goal of this article is to present some new refinements of the generalized classical Holder's inequality. As applications, we present some refinements to several inequalities for the $(q,s)$-Polygamma functions, the $s$-Extension of Nielsen's $\beta$-function, the derivatives of the $s$-Extension of Nielsen's $\beta$-function, the extended Gamma function, the $r$-Gamma functions and the $r$-Riemann Zeta function. | ||
| کلیدواژهها | ||
| Generalized Holder's inequality؛ (q,k)-Polygamma Functions؛ Nielsen’s beta-function؛ Gamma function؛ zeta function | ||
| مراجع | ||
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[1] M. Akkouchi and M.A. Ighachane, Some refinements to H¨older’s inequality and applications, Proyecciones J. Math. 39 (2020), no. 1, 153–166. [2] E.F. Beckenbach and R. Bellman, Inequalities, Springer Verlag, Berlin, 1961. [3] M.A. Chaudhry and S.M. Zubair, On a class of incomplete gamma functions with applications, Chapman and Hall/CRC, 2002. [4] Z. Cvetkovski, Inequalities: Theorems techniques and selected problems, Springer: Berlin/Heidelberg, Germany, 2012. [5] R. Dıaz and C. Teruel, q, k-generalized gamma and beta functions, J. Nonlinear Math. Sci. 11 (2016), no. 1. [6] M.A. Ighachane, M. Akkouchi and El. H. Benabdi, A new generalized refinement of the weighted arithmetic-geometric mean inequality, Math. Ineq. Appl. 23 (2020), no. 3, 1079–1085. [7] F. Merovci, Turan type inequalities for some (q, k)-special functions, Acta Univer. Apulensis 34 (2013), 69–76. [8] K. Nantomah, K. S. Nisar and K. S. Gehlot, On a k-extension of the Nielsen’s β-function Int. J. Nonlinear Anal. Appl. 9 (2018) 191–201. [9] K. Nantomah, Generalized Turan-type inequalities for the (q, k)-poly gamma functions, Commun. Mathe. Appl. 9 (2018), no. 2, 87–92. [10] W. T. Sulaiman, Turan inequalities for the Riemann Zeta functions, AIP Conf. Proc. 1389 (2011), 1763–1797. [11] Y. I. Kim and X.Yang Turan inequalities for the Riemann Zeta functions, Appl. Math. Lett. 25 (2012), no. 7, 1094–1097. [12] X. Yang, Holder’s inequality, Appl. Math. Lett. 16 (2003), 897—903. | ||
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