Partial Sums of The Miller-Ross Function

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.

Keywords:

Analytic functions, Partial sums, Miller-Ross function Univalent function,

PDF

___

[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.