DOI QR코드

DOI QR Code

INEQUALITIES FOR THE (q, k)-DEFORMED GAMMA FUNCTION EMANATING FROM CERTAIN PROBLEMS OF TRAFFIC FLOW

  • Nantomah, Kwara (Department of Mathematics, University for Development Studies, Navrongo Campus) ;
  • Prempeh, Edward (Department of Mathematics, Kwame Nkrumah University of Science and Technology)
  • 투고 : 2015.03.20
  • 심사 : 2015.12.22
  • 발행 : 2016.03.25

초록

In this paper, the authors establish some double inequalities concerning the (q, k)-deformed Gamma function. These inequalities emanate from certain problems of traffic flow. The procedure makes use of the integral representation of the (q, k)-deformed Gamma function.

키워드

참고문헌

  1. R. Askey, The q-Gamma and q-Beta Functions, Appl. Anal. 8(2)(1978), 125-141. https://doi.org/10.1080/00036817808839221
  2. W. S. Chung, T. Kim and T. Mansour, The q-deformed Gamma function and q-deformed Polygamma function, Bull. Korean Math. Soc. 51(4)(2014), 1155-1161. https://doi.org/10.4134/BKMS.2014.51.4.1155
  3. R. Diaz and E. Pariguan, On hypergeometric functions and Pachhammer k-symbol, Divulg. Mat., 15(2)(2007), 179-192.
  4. R. Diaz and C. Teruel, q, k-generalized gamma and beta functions, J. Nonlinear Math. Phys., 12(2005), 118-134. https://doi.org/10.2991/jnmp.2005.12.1.10
  5. I. Ege, E. Yyldyrym, Some generalized equalities for the q-gamma function, Filomat, 26(6)(2012), 1221-1226.
  6. H. Elmonster, K. Brahim, A. Fitouhi, Relationship between characterizations of the q-Gamma function, J. Inequal. Spec. Funct., 3(4)(2012), 50-58.
  7. F. H. Jackson, On a q-Definite Integrals, Quart. J. Pure Appl. Math., 41(1910), 193-203.
  8. J. Lew, J. Frauenthal, N. Keyfitz, On the Average Distances in a Circular Disc, SIAM Rev., 20(3)(1978), 584-592. https://doi.org/10.1137/1020073
  9. K. Nantomah, Some Inequalities for the Ratios of Generalized Digamma Functions, Adv. Inequal. Appl., 2014(2014), Article ID 28.
  10. K. Nantomah and E. Prempeh, Certain Inequalities Involving the q-Deformed Gamma Function , Probl. Anal. Issues Anal., 4(22)(1)(2015), 57-65.
  11. F. Qi, and Q. M. Luo, Bounds for the ratio of two Gamma functions - From Wendel's and related inequalities to logarithmically completely monotonic functions, Banach J. Math. Anal., 6(2)(2012), 123-158.
  12. J. Sandor, On certain inequalities for the Gamma function, RGMIA Res. Rep. Coll. 9(1)(2006), Art. 11.
  13. J.G. Wendel, Note on the gamma function, Amer. Math. Monthly, 55(1948), 563-564. https://doi.org/10.2307/2304460