Inequalities for the m-th derivative of the (q; k)-Gamma function

Kwara Nantomah; Suleman Nasiru

doi:10.1515/mjpaa-2017-0006

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Inequalities for the m-th derivative of the (q; k)-Gamma function

Moroccan Journal of Pure and Applied Analysis

Volume 3 (2017): Issue 1 (June 2017)

By: Kwara Nantomah and Suleman Nasiru

Open Access

|Aug 2017

Abstract

By using the generalized Hölder’s and Minkowski’s integral inequalities, some inequalities for the m-th derivative of the (q; k)-Gamma function are established. Consequently, some previous results are recovered as particular cases of the present results.

References

[1] T. Batbold, Some Remarks on Results of Mortici, Kragujevac Journal of Mathematics, 36(1)(2012), 73-76.
Search in Google Scholar Back to article
[2] K. Brahim and Y. Sidomou, Some inequalities for the q; k-Gamma and Beta functions, Malaya Journal of Matematik, 2(1)(2014), 61-71.10.26637/mjm201/008
Search in Google Scholar Back to article
[3] L. M. B. de Costa Campos, Generalized Calculus with Applications to Matter and Forces, CRC Press, Taylor and Francis Group, New York, 2014.10.1201/b17019
Search in Google Scholar Back to article
[4] R. Díaz and E. Pariguan, On hypergeometric functions and Pachhammer k-symbol, Divulgaciones Matemtícas, 15(2)(2007), 179-192.
Search in Google Scholar Back to article
[5] R. Díaz and C. Teruel, q; k-generalized gamma and beta functions, Journal of Nonlinear Mathematical Physics, 12(1)(2005), 118-134.10.2991/jnmp.2005.12.1.10
Search in Google Scholar Back to article
[6] F. H. Jackson, On a q-definite integrals, Quarterly Journal of Pure and Applied Mathematics, (41)(1910), 193-203.
Search in Google Scholar Back to article
[7] C. G. Kokologiannaki, Some Properties of Γq;k(t) and Related Functions, International Journal of Contemporary Mathematical Sciences, 11(1)(2016), 1-8.10.12988/ijcms.2016.5943
Search in Google Scholar Back to article
[8] Y. Li and X-M. Gu, The Weighted AM-GM Inequality is Equivalent to the Hlder Inequality, arXiv.org, Available online at: https://arxiv.org/abs/1504.02718v2.
Search in Google Scholar Back to article
[9] C. Mortici, New inequalities for some special functions via the Cauchy-Buniakovsky-Schwarz inequality, Tamkang Journal of Mathematics, 42(1)(2011), 53-57.10.5556/j.tkjm.42.2011.608
Search in Google Scholar Back to article
[10] C. Mortici, Turan type inequalities for the Gamma and Polygamma functions, Acta Universitatis Apulensis, 23 (2010), 117-121.
Search in Google Scholar Back to article