Inequalities for Certain Ratios Involving the \((p,k)\)-Analogue of the Gamma function

Authors

  • Kwara Nantomah University for Development Studies

DOI:

https://doi.org/10.26713/cma.v7i2.423

Keywords:

Gamma function, \((p, k)\)-analogue, Inequality

Abstract

Recently, a \((p,k)\)-analogue of the classical Gamma function was introduced and investigated. In this paper, we establish some inequalities for certain ratios involving the new analogue. The method is based on the monotonicity properties of some functions associated the \((p,k)\)-Gamma function.

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Author Biography

Kwara Nantomah, University for Development Studies

Department of Mathematics, Faculty of Mathematical Sciences

References

T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976.

R. Diaz and E. Pariguan, On hypergeometric functions and Pachhammer k-symbol, Divul-

gaciones Matemticas, 15(2)(2007), 179-192.

A. Sh. Shabani, Generalization of some inequalities for the Gamma Function, Mathematical

Communications, 13(2008), 271-275.

V. Krasniqi and A. S. Shabani, Convexity properties and inequalities for a generalized gamma function, Applied Mathematics E-Notes, 10(2010), 27-35.

K. Nantomah, On Certain Inequalities Concerning the Classical Euler's Gamma Function, Advances in Inequalities and Applications, Vol 2014 (2014), Article ID 42.

K. Nantomah, Generalized Inequalities Related to the Classical Euler's Gamma function,

Turkish Journal of Analysis and Number Theory, 2(6)(2014), 226-229.

K. Nantomah and M. M. Iddrisu, The k-analogue of some inequalities for the Gamma function, Electron. J. Math. Anal. Appl., 2(2)(2014), 172-177.

K. Nantomah and M. M. Iddrisu, Some Inequalities Involving the Ratio of Gamma Functions, RGMIA Res. Rep. Coll., 19(2016), Art. 20.

K. Nantomah, M. M. Iddrisu and E. Prempeh, Generalization of Some Inequalities for the Ratio of Gamma Functions, RGMIA Res. Rep. Coll., 19(2016), Art. 40.

K. Nantomah and E. Prempeh, Generalizations of Some Inequalities for the p-Gamma, q-Gamma and k-Gamma Functions, Electron. J. Math. Anal. Appl., 3(1)(2015), 158-163.

K. Nantomah and E. Prempeh, Some Sharp Inequalities for the Ratio of Gamma Functions, Math. Aeterna, 4(5)(2014), 501-507.

K. Nantomah and E. Prempeh, Generalizations of Some Sharp Inequalities for the Ratio of Gamma Functions, Math. Aeterna, 4(5)(2014), 539-544.

K. Nantomah. E. Prempeh and S. B. Twum, On a (p; k)-analogue of the Gamma function and some associated Inequalities, Moroccan Journal of Pure and Applied Analysis,

(2)(2016), 79-90.

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Published

04-11-2016
CITATION

How to Cite

Nantomah, K. (2016). Inequalities for Certain Ratios Involving the \((p,k)\)-Analogue of the Gamma function. Communications in Mathematics and Applications, 7(2), 121–128. https://doi.org/10.26713/cma.v7i2.423

Issue

Section

Research Article