Research Article
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Year 2016, , 23 - 28, 30.10.2016
https://doi.org/10.36753/mathenot.421447

Abstract

References

  • [1] C. Alsina and M. S. Tomás, 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] R. Díaz and E. Pariguan, On hypergeometric functions and Pachhammer k-symbol, Divulgaciones Matemtícas, 15(2)(2007), 179-192.
  • [4] R. Díaz and C. Teruel, q, k-generalized gamma and beta functions, J. Nonlin. Math. Phys., 12(2005), 118-134.
  • [5] F. H. Jackson, On a q-Definite Integrals, Quarterly Journal of Pure and Applied Mathematics, 41(1910), 193-203.
  • [6] V. Krasniqi and F. Merovci, Some Completely Monotonic Properties for the (p, q)-Gamma Function, Mathematica Balkanica, New Series, 26(2012), Fasc. 1-2.
  • [7] K. Nantomah, Some Inequalities for the Ratios of Generalized Digamma Functions, Advances in Inequalities and Applications, 2014(2014), Article ID 28.
  • [8] 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.
  • [9] K. Nantomah, E. Prempeh and S. B. Twum, The (q, k)-extension of some Gamma function inequalities, Konuralp Journal of Mathematics, 4(1)(2016), 148-154.
  • [10] N. V. Vinh and N. P. N. Ngoc, An inequality for the Gamma Function, International Mathematical Forum, 4(28)(2009), 1379-1382.
  • [11] N. P. N. Ngoc, N. V. Vinh and P. T. T. Hien, Generalization of Some Inequalities for the Gamma Function, Int. J. Open Problems Compt. Math., 2(4)(2009), 532-535.
  • [12] J. Zhang and H. Shi, Two double inequalities for k-gamma and k-Riemann zeta functions, Journal of Inequalities and Applications, 2014, 2014:191.

On (p, q) and (q, k)-extensions of a double-inequality bounding a ratio of Gamma functions

Year 2016, , 23 - 28, 30.10.2016
https://doi.org/10.36753/mathenot.421447

Abstract

In this paper, the authors present the (p, q) and (q, k)-extensions of a double inequality involving a ratio of
Gamma functions. The method is based on some monotonicity properties of certain functions associated
with the (p, q) and (q, k)-extensions of the Gamma function.

References

  • [1] C. Alsina and M. S. Tomás, 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] R. Díaz and E. Pariguan, On hypergeometric functions and Pachhammer k-symbol, Divulgaciones Matemtícas, 15(2)(2007), 179-192.
  • [4] R. Díaz and C. Teruel, q, k-generalized gamma and beta functions, J. Nonlin. Math. Phys., 12(2005), 118-134.
  • [5] F. H. Jackson, On a q-Definite Integrals, Quarterly Journal of Pure and Applied Mathematics, 41(1910), 193-203.
  • [6] V. Krasniqi and F. Merovci, Some Completely Monotonic Properties for the (p, q)-Gamma Function, Mathematica Balkanica, New Series, 26(2012), Fasc. 1-2.
  • [7] K. Nantomah, Some Inequalities for the Ratios of Generalized Digamma Functions, Advances in Inequalities and Applications, 2014(2014), Article ID 28.
  • [8] 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.
  • [9] K. Nantomah, E. Prempeh and S. B. Twum, The (q, k)-extension of some Gamma function inequalities, Konuralp Journal of Mathematics, 4(1)(2016), 148-154.
  • [10] N. V. Vinh and N. P. N. Ngoc, An inequality for the Gamma Function, International Mathematical Forum, 4(28)(2009), 1379-1382.
  • [11] N. P. N. Ngoc, N. V. Vinh and P. T. T. Hien, Generalization of Some Inequalities for the Gamma Function, Int. J. Open Problems Compt. Math., 2(4)(2009), 532-535.
  • [12] 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 12 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Kwara Nantomah

Edward Prempeh This is me

Stephen Boakye Twum This is me

Publication Date October 30, 2016
Submission Date January 16, 2016
Published in Issue Year 2016

Cite

APA Nantomah, K., Prempeh, E., & Twum, S. B. (2016). On (p, q) and (q, k)-extensions of a double-inequality bounding a ratio of Gamma functions. Mathematical Sciences and Applications E-Notes, 4(2), 23-28. https://doi.org/10.36753/mathenot.421447
AMA Nantomah K, Prempeh E, Twum SB. On (p, q) and (q, k)-extensions of a double-inequality bounding a ratio of Gamma functions. Math. Sci. Appl. E-Notes. October 2016;4(2):23-28. doi:10.36753/mathenot.421447
Chicago Nantomah, Kwara, Edward Prempeh, and Stephen Boakye Twum. “On (p, Q) and (q, K)-Extensions of a Double-Inequality Bounding a Ratio of Gamma Functions”. Mathematical Sciences and Applications E-Notes 4, no. 2 (October 2016): 23-28. https://doi.org/10.36753/mathenot.421447.
EndNote Nantomah K, Prempeh E, Twum SB (October 1, 2016) On (p, q) and (q, k)-extensions of a double-inequality bounding a ratio of Gamma functions. Mathematical Sciences and Applications E-Notes 4 2 23–28.
IEEE K. Nantomah, E. Prempeh, and S. B. Twum, “On (p, q) and (q, k)-extensions of a double-inequality bounding a ratio of Gamma functions”, Math. Sci. Appl. E-Notes, vol. 4, no. 2, pp. 23–28, 2016, doi: 10.36753/mathenot.421447.
ISNAD Nantomah, Kwara et al. “On (p, Q) and (q, K)-Extensions of a Double-Inequality Bounding a Ratio of Gamma Functions”. Mathematical Sciences and Applications E-Notes 4/2 (October 2016), 23-28. https://doi.org/10.36753/mathenot.421447.
JAMA Nantomah K, Prempeh E, Twum SB. On (p, q) and (q, k)-extensions of a double-inequality bounding a ratio of Gamma functions. Math. Sci. Appl. E-Notes. 2016;4:23–28.
MLA Nantomah, Kwara et al. “On (p, Q) and (q, K)-Extensions of a Double-Inequality Bounding a Ratio of Gamma Functions”. Mathematical Sciences and Applications E-Notes, vol. 4, no. 2, 2016, pp. 23-28, doi:10.36753/mathenot.421447.
Vancouver Nantomah K, Prempeh E, Twum SB. On (p, q) and (q, k)-extensions of a double-inequality bounding a ratio of Gamma functions. Math. Sci. Appl. E-Notes. 2016;4(2):23-8.

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