BibTex RIS Kaynak Göster

CONVEXITY PROPERTIES AND INEQUALITIES CONCERNING THE(p; k)-GAMMA FUNCTION

Yıl 2017, Cilt: 66 Sayı: 2, 130 - 140, 01.08.2017
https://doi.org/10.1501/Commua1_0000000807

Öz

In this paper, some convexity properties and some inequalities forthe (p; k)-analogue of the Gamma function,a (p; k)-analogue of the celebrated Bohr-Mollerup theorem is given. Furthermore, a (p; k)-analogue of the Riemann zeta function,p;k(x)is introduced andsome associated inequalities are derived. The established results provide the(p; k)-generalizations of some known results concerning the classical Gammafunction

Kaynakça

  • S. S. Dragomir, R. P. Agarwal and N. S. Barnett, Inequalities for Beta and Gamma Functions via Some Classical and New Integral Inequalities, Journal of Inequalities and Applications, 5 (2000), 103-165.
  • B. N. Guo and F. Qi, Sharp bounds for harmonic numbers, Applied Mathematics and Com- putation, 218(3)(2011), 991-995.
  • J. D. Keµcki´c and P. M. Vasi´c, Some inequalities for the Gamma function, Publ. Inst. Math. Beograd N. S., 11(1971), 107-114.
  • C. G. Kokologiannaki and V. Krasniqi, Some properties of the k-Gamma function, Le Matem- atiche, LXVIII (2013), Fasc. I, 13-22.
  • V. Krasniqi, T. Mansour and A. Sh. Shabani, Some Monotonicity Properties and Inequalities for and
  • Functions, Mathematical Communications, 15(2)(2010), 365-376.
  • V. Krasniqi and A. S. Shabani, Convexity Properties and Inequalities for a Generalized Gamma Function, Applied Mathematics E-Notes, 10(2010), 27-35.
  • A. Laforgia and P. Natalini, Turan type inequalities for some special functions, J. Ineq. Pure Appl. Math., 7(1)(2006), Art. 22, 1-5.
  • F. Merovci, Turan type inequalities for p-Polygamma functions, Le Matematiche, LXVIII (2013), Fasc. II, 99-106.
  • K. Nantomah, Some inequalities bounding certain ratios of the (p; k)-Gamma function, New Trends in Mathematical Sciences, 4(4)(2016), 329-336.
  • K. Nantomah. E. Prempeh and S. B. Twum, On a (p; k)-analogue of the Gamma function and some associated Inequalities, Moroccan Journal of Pure and Applied Analysis, 2(2)(2016), 79-90.
  • E. Neuman, Inequalities involving a logarithmically convex function and their applications to special functions, J. Inequal. Pure Appl. Math., 7(1)(2006) Art. 16.
  • C. P. Nilculescu, Convexity according to the geometric mean, Mathematical Inequalities and Applications, 3(2)(2000), 155-167.
  • C. Niculescu and L. E. Persson, Convex Functions and their Applications, A Contemporary Approach, CMS Books in Mathematics, Vol. 23, Springer-Verlag, New York, 2006.
  • J. Sandor, Selected Chapters of Geometry, Analysis and Number Theory, RGMIA Mono- graphs, Victoria University, 2005.
  • Xiao-Ming Zhang, Tie-Quan Xu and Ling-bo Situ, Geometric convexity of a function in- volving Gamma function and application to inequality theory, J. Inequal. Pure Appl. Math., 8(1)(2007), Art. 17.
  • Current address : Kwara Nantomah: Department of Mathematics, Faculty of Mathematical Sciences, University for Development Studies, Navrongo Campus, P. O. Box 24, Navrongo, UE/R, Ghana.
  • E-mail address : mykwarasoft@yahoo.com, knantomah@uds.edu.gh
Yıl 2017, Cilt: 66 Sayı: 2, 130 - 140, 01.08.2017
https://doi.org/10.1501/Commua1_0000000807

Öz

Kaynakça

  • S. S. Dragomir, R. P. Agarwal and N. S. Barnett, Inequalities for Beta and Gamma Functions via Some Classical and New Integral Inequalities, Journal of Inequalities and Applications, 5 (2000), 103-165.
  • B. N. Guo and F. Qi, Sharp bounds for harmonic numbers, Applied Mathematics and Com- putation, 218(3)(2011), 991-995.
  • J. D. Keµcki´c and P. M. Vasi´c, Some inequalities for the Gamma function, Publ. Inst. Math. Beograd N. S., 11(1971), 107-114.
  • C. G. Kokologiannaki and V. Krasniqi, Some properties of the k-Gamma function, Le Matem- atiche, LXVIII (2013), Fasc. I, 13-22.
  • V. Krasniqi, T. Mansour and A. Sh. Shabani, Some Monotonicity Properties and Inequalities for and
  • Functions, Mathematical Communications, 15(2)(2010), 365-376.
  • V. Krasniqi and A. S. Shabani, Convexity Properties and Inequalities for a Generalized Gamma Function, Applied Mathematics E-Notes, 10(2010), 27-35.
  • A. Laforgia and P. Natalini, Turan type inequalities for some special functions, J. Ineq. Pure Appl. Math., 7(1)(2006), Art. 22, 1-5.
  • F. Merovci, Turan type inequalities for p-Polygamma functions, Le Matematiche, LXVIII (2013), Fasc. II, 99-106.
  • K. Nantomah, Some inequalities bounding certain ratios of the (p; k)-Gamma function, New Trends in Mathematical Sciences, 4(4)(2016), 329-336.
  • K. Nantomah. E. Prempeh and S. B. Twum, On a (p; k)-analogue of the Gamma function and some associated Inequalities, Moroccan Journal of Pure and Applied Analysis, 2(2)(2016), 79-90.
  • E. Neuman, Inequalities involving a logarithmically convex function and their applications to special functions, J. Inequal. Pure Appl. Math., 7(1)(2006) Art. 16.
  • C. P. Nilculescu, Convexity according to the geometric mean, Mathematical Inequalities and Applications, 3(2)(2000), 155-167.
  • C. Niculescu and L. E. Persson, Convex Functions and their Applications, A Contemporary Approach, CMS Books in Mathematics, Vol. 23, Springer-Verlag, New York, 2006.
  • J. Sandor, Selected Chapters of Geometry, Analysis and Number Theory, RGMIA Mono- graphs, Victoria University, 2005.
  • Xiao-Ming Zhang, Tie-Quan Xu and Ling-bo Situ, Geometric convexity of a function in- volving Gamma function and application to inequality theory, J. Inequal. Pure Appl. Math., 8(1)(2007), Art. 17.
  • Current address : Kwara Nantomah: Department of Mathematics, Faculty of Mathematical Sciences, University for Development Studies, Navrongo Campus, P. O. Box 24, Navrongo, UE/R, Ghana.
  • E-mail address : mykwarasoft@yahoo.com, knantomah@uds.edu.gh
Toplam 18 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

Kwara Nantomah Bu kişi benim

Yayımlanma Tarihi 1 Ağustos 2017
Yayımlandığı Sayı Yıl 2017 Cilt: 66 Sayı: 2

Kaynak Göster

APA Nantomah, K. (2017). CONVEXITY PROPERTIES AND INEQUALITIES CONCERNING THE(p; k)-GAMMA FUNCTION. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 66(2), 130-140. https://doi.org/10.1501/Commua1_0000000807
AMA Nantomah K. CONVEXITY PROPERTIES AND INEQUALITIES CONCERNING THE(p; k)-GAMMA FUNCTION. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Ağustos 2017;66(2):130-140. doi:10.1501/Commua1_0000000807
Chicago Nantomah, Kwara. “CONVEXITY PROPERTIES AND INEQUALITIES CONCERNING THE(p; K)-GAMMA FUNCTION”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 66, sy. 2 (Ağustos 2017): 130-40. https://doi.org/10.1501/Commua1_0000000807.
EndNote Nantomah K (01 Ağustos 2017) CONVEXITY PROPERTIES AND INEQUALITIES CONCERNING THE(p; k)-GAMMA FUNCTION. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 66 2 130–140.
IEEE K. Nantomah, “CONVEXITY PROPERTIES AND INEQUALITIES CONCERNING THE(p; k)-GAMMA FUNCTION”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 66, sy. 2, ss. 130–140, 2017, doi: 10.1501/Commua1_0000000807.
ISNAD Nantomah, Kwara. “CONVEXITY PROPERTIES AND INEQUALITIES CONCERNING THE(p; K)-GAMMA FUNCTION”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 66/2 (Ağustos 2017), 130-140. https://doi.org/10.1501/Commua1_0000000807.
JAMA Nantomah K. CONVEXITY PROPERTIES AND INEQUALITIES CONCERNING THE(p; k)-GAMMA FUNCTION. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2017;66:130–140.
MLA Nantomah, Kwara. “CONVEXITY PROPERTIES AND INEQUALITIES CONCERNING THE(p; K)-GAMMA FUNCTION”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 66, sy. 2, 2017, ss. 130-4, doi:10.1501/Commua1_0000000807.
Vancouver Nantomah K. CONVEXITY PROPERTIES AND INEQUALITIES CONCERNING THE(p; k)-GAMMA FUNCTION. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2017;66(2):130-4.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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