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

Yıl 2016, Cilt: 4 Sayı: 1, 148 - 154, 01.04.2016

Öz

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.

Kaynakça

  • [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.
Yıl 2016, Cilt: 4 Sayı: 1, 148 - 154, 01.04.2016

Öz

Kaynakça

  • [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.
Toplam 17 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Articles
Yazarlar

Kwara Nantomah

Edward Prempeh Bu kişi benim

Stephen Boakye Twum Bu kişi benim

Yayımlanma Tarihi 1 Nisan 2016
Gönderilme Tarihi 10 Temmuz 2014
Yayımlandığı Sayı Yıl 2016 Cilt: 4 Sayı: 1

Kaynak Göster

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. Nisan 2016;4(1):148-154.
Chicago Nantomah, Kwara, Edward Prempeh, ve Stephen Boakye Twum. “THE (q; K)-EXTENSION OF SOME GAMMA FUNCTION INEQUALITIES”. Konuralp Journal of Mathematics 4, sy. 1 (Nisan 2016): 148-54.
EndNote Nantomah K, Prempeh E, Twum SB (01 Nisan 2016) THE (q; k)-EXTENSION OF SOME GAMMA FUNCTION INEQUALITIES. Konuralp Journal of Mathematics 4 1 148–154.
IEEE K. Nantomah, E. Prempeh, ve S. B. Twum, “THE (q; k)-EXTENSION OF SOME GAMMA FUNCTION INEQUALITIES”, Konuralp J. Math., c. 4, sy. 1, ss. 148–154, 2016.
ISNAD Nantomah, Kwara vd. “THE (q; K)-EXTENSION OF SOME GAMMA FUNCTION INEQUALITIES”. Konuralp Journal of Mathematics 4/1 (Nisan 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 vd. “THE (q; K)-EXTENSION OF SOME GAMMA FUNCTION INEQUALITIES”. Konuralp Journal of Mathematics, c. 4, sy. 1, 2016, ss. 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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