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THE (q; k)-EXTENSION OF SOME GAMMA FUNCTION INEQUALITIES

Year 2016, Volume: 4 Issue: 1, 148 - 154, 01.04.2016

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.

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. Bougo a, 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-De nite 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.
Year 2016, Volume: 4 Issue: 1, 148 - 154, 01.04.2016

Abstract

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. Bougo a, 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-De nite 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.
There are 17 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Kwara Nantomah

Edward Prempeh This is me

Stephen Boakye Twum This is me

Publication Date April 1, 2016
Submission Date July 10, 2014
Published in Issue Year 2016 Volume: 4 Issue: 1

Cite

APA Nantomah, K., Prempeh, E., & Twum, S. B. (2016). THE (q; k)-EXTENSION OF SOME GAMMA FUNCTION INEQUALITIES. Konuralp Journal of Mathematics, 4(1), 148-154.
AMA Nantomah K, Prempeh E, Twum SB. THE (q; k)-EXTENSION OF SOME GAMMA FUNCTION INEQUALITIES. Konuralp J. Math. April 2016;4(1):148-154.
Chicago Nantomah, Kwara, Edward Prempeh, and Stephen Boakye Twum. “THE (q; K)-EXTENSION OF SOME GAMMA FUNCTION INEQUALITIES”. Konuralp Journal of Mathematics 4, no. 1 (April 2016): 148-54.
EndNote Nantomah K, Prempeh E, Twum SB (April 1, 2016) THE (q; k)-EXTENSION OF SOME GAMMA FUNCTION INEQUALITIES. Konuralp Journal of Mathematics 4 1 148–154.
IEEE K. Nantomah, E. Prempeh, and S. B. Twum, “THE (q; k)-EXTENSION OF SOME GAMMA FUNCTION INEQUALITIES”, Konuralp J. Math., vol. 4, no. 1, pp. 148–154, 2016.
ISNAD Nantomah, Kwara et al. “THE (q; K)-EXTENSION OF SOME GAMMA FUNCTION INEQUALITIES”. Konuralp Journal of Mathematics 4/1 (April 2016), 148-154.
JAMA Nantomah K, Prempeh E, Twum SB. THE (q; k)-EXTENSION OF SOME GAMMA FUNCTION INEQUALITIES. Konuralp J. Math. 2016;4:148–154.
MLA Nantomah, Kwara et al. “THE (q; K)-EXTENSION OF SOME GAMMA FUNCTION INEQUALITIES”. Konuralp Journal of Mathematics, vol. 4, no. 1, 2016, pp. 148-54.
Vancouver Nantomah K, Prempeh E, Twum SB. THE (q; k)-EXTENSION OF SOME GAMMA FUNCTION INEQUALITIES. Konuralp J. Math. 2016;4(1):148-54.
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