Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2016, Cilt: 4 Sayı: 2, 23 - 28, 30.10.2016
https://doi.org/10.36753/mathenot.421447

Öz

Kaynakça

  • [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

Yıl 2016, Cilt: 4 Sayı: 2, 23 - 28, 30.10.2016
https://doi.org/10.36753/mathenot.421447

Öz

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.

Kaynakça

  • [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.
Toplam 12 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Articles
Yazarlar

Kwara Nantomah

Edward Prempeh Bu kişi benim

Stephen Boakye Twum Bu kişi benim

Yayımlanma Tarihi 30 Ekim 2016
Gönderilme Tarihi 16 Ocak 2016
Yayımlandığı Sayı Yıl 2016 Cilt: 4 Sayı: 2

Kaynak Göster

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. Ekim 2016;4(2):23-28. doi:10.36753/mathenot.421447
Chicago Nantomah, Kwara, Edward Prempeh, ve 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, sy. 2 (Ekim 2016): 23-28. https://doi.org/10.36753/mathenot.421447.
EndNote Nantomah K, Prempeh E, Twum SB (01 Ekim 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, ve 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, c. 4, sy. 2, ss. 23–28, 2016, doi: 10.36753/mathenot.421447.
ISNAD Nantomah, Kwara vd. “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 (Ekim 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 vd. “On (p, Q) and (q, K)-Extensions of a Double-Inequality Bounding a Ratio of Gamma Functions”. Mathematical Sciences and Applications E-Notes, c. 4, sy. 2, 2016, ss. 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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