SciELO - Scientific Electronic Library Online

 
vol.41 issue3Structure of a quotient ring R/P and its relation with generalized derivations of RStability and instability analysis for the standing waves for a generalized Zakharov-Rubenchik system author indexsubject indexarticles search
Home Pagealphabetic serial listing  

Services on Demand

Journal

Article

Indicators

Related links

  • On index processCited by Google
  • Have no similar articlesSimilars in SciELO
  • On index processSimilars in Google

Share


Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.41 no.3 Antofagasta June 2022

http://dx.doi.org/10.22199/issn.0717-6279-4538 

Artículos

A new refinement of the generalized Hölder’s inequality with applications

Mohamed Amine Ighachane1 

El Hassan Benabdi2 

Mohamed Akkouchi3 

1 Department of Mathematics, Faculty of Sciences-Semlalia, University Cadi Ayyad, Av. Prince My. Abdellah, BP: 2390, Marrakesh (40.000-Marrakech), Morocco (Maroc). e-mail: mohamedamineighachane@gmail.com

2 Department of Mathematics, Laboratory of Mathematics, Statistics and Applications Faculty of Sciences, Mohammed V University in Rabat, Morocco (Maroc). e-mail: elhassan.benabdi@gmail.com

3 Department of Mathematics, Faculty of Sciences-Semlalia, University Cadi Ayyad, Av. Prince My. Abdellah, BP: 2390, Marrakesh (40.000-Marrakech), Morocco (Maroc). e-mail: akkm555@yahoo.fr

Abstract

In this paper, we prove a further generalized refinement of the weighted arithmetic-geometric mean inequality. As application, we show a new refinement of the generalized classical Hölder’s inequality and we give refinements to several inequalities for some special functions.

Keywords: arithmetic-geometric mean inequality; generalized Hölder’s inequality; gamma function; (q, k)-polygamma functions; Nielsen’s β-function

Texto completo disponible sólo en PDF

Full text available only in PDF format.

References

[1] M. Akkouchi and M. A. Ighachane, “Some refinements to Hölder’s inequality and applications”, Proyecciones (Antofagasta), vol. 39, no. 1, pp. 153-166, 2020. doi: 10.22199/issn.0717-6279-2020-01-0010 [ Links ]

[2] Y. Al-Manasrah and F. Kittaneh, “Further generalizations, refinements, and reverses of the young and Heinz Inequalities”, Results in Mathematics, vol. 71, no. 3-4, pp. 1063-1072, 2016. doi: 10.1007/s00025-016-0611-2 [ Links ]

[3] M. A. Chaudhry and S. M. Zubair, On a class of incomplete gamma functions with applications. Chapman and Hall/CRC, 2002. [ Links ]

[4] R. Díaz and C. Teruel, “q,k-generalized gamma and beta functions”, Journal of Nonlinear Mathematical Physics, vol. 12, no. 1, p. 118, 2005. doi: 10.2991/jnmp.2005.12.1.10 [ Links ]

[5] S. Furuichi, “On refined young inequalities and reverse inequalities”, Journal of Mathematical Inequalities, no. 1, pp. 21-31, 2011. doi: 10.7153/jmi-05-03 [ Links ]

[6] G. H. Hardy, J. E. Littlewood and G. Pólya, Inequalities, 2nd ed. Cambridge: Cambridge University Press, 1988. [ Links ]

[7] M. A. Ighachane, M. Akkouchi, and E. H. Benabdi, “A new generalized refinement of the weighted arithmetic-geometric mean inequality”, Mathematical Inequalities and Applications, no. 3, pp. 1079-1085, 2020. doi: 10.7153/mia-2020-23-82 [ Links ]

[8] F. Merovci, “Turan type inequalities for some (q, k)-special functions”, Acta Universitatis Apulensis, vol. 34, pp. 69-76, 2013. [ Links ]

[9] K. Nantomah, K. S. Nisarb and K. S. Gehlotc, “On a k-extension of the Nielsen’s β-function”, International Journal of Nonlinear Analysis and Applications, vol. 9, no. 2, pp. 191-201, 2018. doi: 10.22075/ijnaa.2018.12972.1668 [ Links ]

[10] K. Nantomah , “Generalized Turan-type inequalities for the (q, k)-polygamma functions”, Communications in Mathematics and Applications, vol. 9, no. 2, pp. 87-92, 2018. [ Links ]

[11] W. T. Sulaiman, “Turan inequalites for the Riemann zeta functions”, AIP Conference Proceedings, 2011. doi: 10.1063/1.3636956 [ Links ]

Received: October 30, 2020; Accepted: December 30, 2021

Creative Commons License This is an open-access article distributed under the terms of the Creative Commons Attribution License