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Partial Sums of The Miller-Ross Function

Year 2021, Volume: 6 Issue: 3, 167 - 173, 30.12.2021

Abstract

This article deals with the ratio of normalized Miller-Ross function ${{\mathbb{E}}_{\nu ,c }}\left( z \right)$ and its sequence of partial sums ${{\left( {{\mathbb{E}}_{\nu ,c }} \right)}_{m}}\left( z \right).$ Several examples which illustrate the validity of our results are also given.

References

  • [1] Brickman L, Hallenbeck DJ, MacGregor TH, Wilken D. Convex hulls and extreme points of families of starlike and convex mappings. Trans. Amer. Math. Soc. 185, 1973, 413–428.
  • [2] Çağlar M, Orhan H. On neighborhood and partial sums problem for generalized Sakaguchi type functions. The Scientifc Annals of Al.I. Cuza University of Iasi. 1, 2014, 17–28.
  • [3] Çağlar M, Deniz E. Partial sums of the normalized Lommel functions. Math. Inequal. Appl. 18, 2015, 1189–1199.
  • [4] Deniz E, Orhan H. Some Properties Of certain subclasses of analytic functions with negative coefficients by using generalized Ruscheweyh derivative operator. Czech. Math. J. 60, 2010, 699–713.
  • [5] Deniz E, Orhan H. Certain subclasses of multivalent functions dened by new multiplier transformations. Arab. J. Sci. Eng. 36, 2011, 1091–1112.
  • [6] Frasin BA. Generalization of partial sums of certain analytic and univalent functions. Appl. Math. Lett. 21, 2008, 735–741.
  • [7] Kazımoğlu S, Deniz E, Çağlar M. Partial Sums of The Bessel-Struve Kernel Function. 3rd International Conference on Mathematical and Related Sciences: Current Trend and Developments. 2020, 267–275.
  • [8] Lin LJ, Owa S. On partial sums of the Libera integral operator. J. Math. Anal. Appl. 213, 1997, 444–454.
  • [9] Miller KS, Ross B. An introduction to the fractional calculus and fractional differential equations. Wiley. 1993.
  • [10] Orhan H, Yağmur N. Partial Sums of generalized Bessel functions. J. Math. Inequal. 8, 2014, 863–877.
  • [11] Owa S, Srivastava HM, Saito N. Partial sums of certain classes of analytic functions. Int. J. Comput. Math. 81, 2014, 1239-1256.
  • [12] Ravichandran V. Geometric properties of partial sums of univalent functions. Math. Newslett. 22, 2012, 208–221.
  • [13] Rehman MS, Ahmad QZ, Srivastava HM, Khan B, Khan N. Partial sums of generalized q-Mittag-Leffler functions. Aims Math. 5, 2019, 408–420.
  • [14] Sheil-Small T. A note on partial sums of convex schlicht functions. Bull. London Math. Soc. 2, 1970, 165–168.
  • [15] Silverman H. Partial sums of starlike and convex functions. J. Math. Anal. Appl. 209, 1997, 221–227.
  • [16] Silvia EM. On partial sums of convex functions of order $\alpha$. Houston J. Math. 11, 1985, 397–404.
  • [17] Yağmur N, Orhan H. Partial sums of generalized Struve functions. Miskolc Mathematical Notes. 17, 2016, 657–670.
Year 2021, Volume: 6 Issue: 3, 167 - 173, 30.12.2021

Abstract

References

  • [1] Brickman L, Hallenbeck DJ, MacGregor TH, Wilken D. Convex hulls and extreme points of families of starlike and convex mappings. Trans. Amer. Math. Soc. 185, 1973, 413–428.
  • [2] Çağlar M, Orhan H. On neighborhood and partial sums problem for generalized Sakaguchi type functions. The Scientifc Annals of Al.I. Cuza University of Iasi. 1, 2014, 17–28.
  • [3] Çağlar M, Deniz E. Partial sums of the normalized Lommel functions. Math. Inequal. Appl. 18, 2015, 1189–1199.
  • [4] Deniz E, Orhan H. Some Properties Of certain subclasses of analytic functions with negative coefficients by using generalized Ruscheweyh derivative operator. Czech. Math. J. 60, 2010, 699–713.
  • [5] Deniz E, Orhan H. Certain subclasses of multivalent functions dened by new multiplier transformations. Arab. J. Sci. Eng. 36, 2011, 1091–1112.
  • [6] Frasin BA. Generalization of partial sums of certain analytic and univalent functions. Appl. Math. Lett. 21, 2008, 735–741.
  • [7] Kazımoğlu S, Deniz E, Çağlar M. Partial Sums of The Bessel-Struve Kernel Function. 3rd International Conference on Mathematical and Related Sciences: Current Trend and Developments. 2020, 267–275.
  • [8] Lin LJ, Owa S. On partial sums of the Libera integral operator. J. Math. Anal. Appl. 213, 1997, 444–454.
  • [9] Miller KS, Ross B. An introduction to the fractional calculus and fractional differential equations. Wiley. 1993.
  • [10] Orhan H, Yağmur N. Partial Sums of generalized Bessel functions. J. Math. Inequal. 8, 2014, 863–877.
  • [11] Owa S, Srivastava HM, Saito N. Partial sums of certain classes of analytic functions. Int. J. Comput. Math. 81, 2014, 1239-1256.
  • [12] Ravichandran V. Geometric properties of partial sums of univalent functions. Math. Newslett. 22, 2012, 208–221.
  • [13] Rehman MS, Ahmad QZ, Srivastava HM, Khan B, Khan N. Partial sums of generalized q-Mittag-Leffler functions. Aims Math. 5, 2019, 408–420.
  • [14] Sheil-Small T. A note on partial sums of convex schlicht functions. Bull. London Math. Soc. 2, 1970, 165–168.
  • [15] Silverman H. Partial sums of starlike and convex functions. J. Math. Anal. Appl. 209, 1997, 221–227.
  • [16] Silvia EM. On partial sums of convex functions of order $\alpha$. Houston J. Math. 11, 1985, 397–404.
  • [17] Yağmur N, Orhan H. Partial sums of generalized Struve functions. Miskolc Mathematical Notes. 17, 2016, 657–670.
There are 17 citations in total.

Details

Primary Language English
Journal Section Volume VI Issue III
Authors

Sercan Kazımoğlu 0000-0002-1023-4500

Publication Date December 30, 2021
Published in Issue Year 2021 Volume: 6 Issue: 3

Cite

APA Kazımoğlu, S. (2021). Partial Sums of The Miller-Ross Function. Turkish Journal of Science, 6(3), 167-173.
AMA Kazımoğlu S. Partial Sums of The Miller-Ross Function. TJOS. December 2021;6(3):167-173.
Chicago Kazımoğlu, Sercan. “Partial Sums of The Miller-Ross Function”. Turkish Journal of Science 6, no. 3 (December 2021): 167-73.
EndNote Kazımoğlu S (December 1, 2021) Partial Sums of The Miller-Ross Function. Turkish Journal of Science 6 3 167–173.
IEEE S. Kazımoğlu, “Partial Sums of The Miller-Ross Function”, TJOS, vol. 6, no. 3, pp. 167–173, 2021.
ISNAD Kazımoğlu, Sercan. “Partial Sums of The Miller-Ross Function”. Turkish Journal of Science 6/3 (December 2021), 167-173.
JAMA Kazımoğlu S. Partial Sums of The Miller-Ross Function. TJOS. 2021;6:167–173.
MLA Kazımoğlu, Sercan. “Partial Sums of The Miller-Ross Function”. Turkish Journal of Science, vol. 6, no. 3, 2021, pp. 167-73.
Vancouver Kazımoğlu S. Partial Sums of The Miller-Ross Function. TJOS. 2021;6(3):167-73.