Inequalities for Certain Ratios Involving the \((p,k)\)-Analogue of the Gamma function
DOI:
https://doi.org/10.26713/cma.v7i2.423Keywords:
Gamma function, \((p, k)\)-analogue, InequalityAbstract
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.Downloads
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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