THE (q; k)-EXTENSION OF SOME GAMMA FUNCTION INEQUALITIES
Year 2016,
Volume: 4 Issue: 1, 148 - 154, 01.04.2016
Kwara Nantomah
,
Edward Prempeh
Stephen Boakye Twum
Abstract
In this paper, the authors establish some inequalities for the (q; k)- extension of the classical Gamma function. The procedure utilizes a mono- tonicity property of the (q; k)-extension of the psi function. As an application, some previous results are recovered as special cases of the results of this paper.
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Journal of Inequalities and Applications, 2014,2014:191.
Year 2016,
Volume: 4 Issue: 1, 148 - 154, 01.04.2016
Kwara Nantomah
,
Edward Prempeh
Stephen Boakye Twum
References
- [1] C. Alsina and M. S. Tomas, A geometrical proof of a new inequality for the gamma function,
J. Ineq. Pure Appl. Math. 6(2) (2005), Art. 48.
- [2] T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976.
- [3] L. Bougoa, Some inequalities involving the Gamma Function, J. Ineq. Pure Appl. Math.
7(5)(2006), Art. 179.
- [4] K. Brahim and Y. Sidomou, Some inequalities for the q; k-Gamma and Beta functions,
Malaya Journal of Matematik, 1(1)(2014), 61-71.
- [5] R. Daz and E. Pariguan, On hypergeometric functions and Pachhammer k-symbol, Divulga-
ciones Matemtcas 15(2)(2007), 179-192.
- [6] R. Daz and C. Teruel, q; k-generalized gamma and beta functions, J. Nonlin. Math. Phys.
12(2005), 118-134.
- [7] F. H. Jackson, On a q-Denite Integrals, Quarterly Journal of Pure and Applied Mathematics
41(1910), 193-203.
- [8] V. Krasniqi and F. Merovci, Some Completely Monotonic Properties for the (p; q)-Gamma
Function, Mathematica Balkanica, New Series 26(2012), Fasc. 1-2.
- [9] V. Krasniqi and A. S. Shabani, Convexity properties and inequalities for a generalized gamma
function, Applied Mathematics E-Notes, 10(2010), 27-35.
- [10] K. Nantomah, Some Inequalities for the Ratios of Generalized Digamma Functions, Advances
in Inequalities and Applications, Vol . 2014 (2014), Article ID 28.
- [11] K. Nantomah and M. M. Iddrisu, The k-analogue of some inequalities for the Gamma func-
tion, Electron. J. Math. Anal. Appl., 2(2), (2014), 172-177.
- [12] J. Sandor, A note on certain inequalities for the gamma function, J. Ineq. Pure Appl. Math.
6(3)(2005), Art. 61.
- [13] A. Sh. Shabani, Some inequalities for the Gamma Function, J. Ineq. Pure Appl. Math.
8(2)(2007), Art. 49.
- [14] A. Sh. Shabani, Generalization of some inequalities for the Gamma Function, Mathematical
Communications, 13, (2008), 271-275.
- [15] A. Sh. Shabani, Generalization of some inequalities for the q-gamma function, Annales Math-
ematicae et Informaticae, 35, (2008), 129-134.
- [16] N. V. Vinh and N. P. N. Ngoc, An inequality for the Gamma Function, International Math-
ematical Forum, 4 (28),(2009), 1379-1382.
- [17] J. Zhang and H. Shi, Two double inequalities for k-gamma and k-Riemann zeta functions,
Journal of Inequalities and Applications, 2014,2014:191.