Some refinements to Hölder’s inequality and applications

• Akkouchi, Mohamed ^[1] ; Ighachane, Mohamed Amine ^[1]
  1. [1] Cadi Ayyad University

     Cadi Ayyad University

     Marrakech-Medina, Marruecos

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 39, Nº. 1, 2020, págs. 153-166
• Idioma: inglés
• DOI: 10.22199/issn.0717-6279-2020-01-0010
• Enlaces
  • Texto completo
• Resumen

  • We establish some new refinements to the Hölder inequality. We then apply them to provide some refinements to the extended Euler’s gamma and beta functions. As another application of our results, we give a new proof of the equivalence between the Hölder inequality and the Cauchy-Schwarz inequality.

• Referencias bibliográficas
  • M. Akkouchi, “Inequalities for real random variables connected with Jensen’s inequality and applications”, Rivista di matematica della Universitá...
  • M. Akkouchi, “Cauchy-Schwarz inequality implies Hölder’s inequality”, RGMIA Research report collection, vol 21, Art. ID. 48, 2018. [On line]....
  • J. M. Aldaz, “Self improvement of the inequality between arithmetic and geometric means”, Journal of mathematical inequalities, vol. 3, no....
  • R. M. Ali, S. R. Mondal, and K. S. Nisar, “Monotonicity properties of the generalized Struve functions”, Journal of korean mathematical society,...
  • P. K. Bhandari and S. K. Bissu, “Inequalities via Hölder’s inequality”, Scholars journal of research in mathematics and computer science,...
  • M. A. Chaudhry, A. Qadir, M. Rafique, and S. M. Zubair, “Extension of Euler’s beta function”, Journal of computational and applied mathematics,...
  • M. A. Chaudhry and S. M. Zubair, On a class of incomplete gamma functions with applications. Boca Raton, FL: Chapman & Hall/CRC, 2002.
  • S. S. Dragomir, R. P. Agarwal and N. S. Barnett, “Inequalities for beta and gamma functions via some classical and new integral inequalities”,...
  • C. Finol and M. Wojtowicz, “Cauchy-Schwarz and Hölder’s inequalities are equivalent”, Divulgaciones matemáticas, vol. 15, no. 2, pp. 143-147,...
  • C. A. Infantozzi, “An introduction to relations among inequalities. The November Meeting in Cleveland, Ohio November 25, 1972”, Notices of...
  • Y-C. Li and S-Y. Shaw, “A proof of Hölder’s inequality using the Cauchy-Schwarz inequality”, Journal of inequalities in pure and applied mathematics,...
  • A. W. Marshall and I. Olkin, Inequalities: theory of majorization and its applications. New York, NY: Academic Press, 1979.
  • D. S. Mtirinovic, J. E. Pečarić and A. M. Fink, Classical and new inequalities in analysis. Dordrecht: Kluwer Academic Publishers, 1993.
  • K. S. Nisar, S. R. Mondal, and J. Choi, “Certain inequalities involving the k-Struve function”, Journal of inequalities and applications,...
  • K. S. Nisar, F. Qi, G. Rahman, S. Mubeen, and M. Arshad, “Some inequalities involving the extended gamma function and the Kummer confluent...