On certain subclass of univalent functions with finitely many fixed coefficients defined by Bessel function

R. Ezhilarasi; T.V. Sudharsan; S. Sivasubramanian

doi:10.26637/MJM0803/0061

Abstract

In this present investigation, we study a new class of functions that are analytic and Univalent with finitely many fixed coefficients defined by modified Hadamard product involving Bessel function. Further, we also establish coefficient condition, radii of starlikeness and convexity, extreme points and integral operators applied to functions in this class.

Keywords:

Analytic, Starlike, Convex, Bessel Function

Mathematics Subject Classification:

Mathematics

Authors Imprint References Funding Related Articles Downloads

R. Ezhilarasi Department of Mathematics, S.I.V.E.T College, Chennai-600073, Tamil Nadu, India.
T.V. Sudharsan Department of Mathematics, S.I.V.E.T College, Chennai-600073, Tamil Nadu, India. https://orcid.org/0000-0002-6882-3367
S. Sivasubramanian Department of Mathematics, University College of Engineering Tindivanam, Anna University, Tindivanam-604001, Tamil Nadu, India. https://orcid.org/0000-0002-7294-5922

Pages: 1085-1091
Date Published: 01-07-2020
Vol. 8 No. 03 (2020): Malaya Journal of Matematik (MJM)

J. W. Alexander, Functions which map the interior of the unit circle upon simple regions, Ann. of Math., (2) $17(1)(1915), 12-22$.

E. Deniz, Convexity of integral operators involving generalized Bessel functions, Integral Transforms Spec. Funct., 24(3)(2013), 201-216.

E. Deniz, H. Orhan and H. M. Srivastava, Some sufficient conditions for univalence of certain families of integral operators involving generalized Bessel functions, Taiwanese J. Math., 15(2)(2011), 883-917.

K. K. Dixit and I. B. Misra, A class of uniformly convex functions of order $alpha$ with negative and fixed finitely many coefficients, Indian J. Pure Appl. Math., 32(5)(2001), $711-716$.

S. Owa and H. M. Srivastava, A class of analytic functions with fixed finitely many coefficients, J. Fac. Sci. Tech. Kinki Univ., 23(1987), 1-10.

C.Ramachandran, K.Dhanalakshmi and L. Vanitha, Certain aspects of univalent functions with negative coefficients defined by Bessel function, International Journal of Brazilian Archive of Biology and Technology, Vol 59, e 16161044, Jan - Dec - 2016.

M. I. S. Robertson, On the theory of univalent functions, Ann. of Math., (2)37(1936), 374-408.

T. Rosy, Studies on Subclasses of Starlike and Convex Functions, Ph.D. Thesis, submitted to University of Madras, Chennai, India, 2001.

H. Silverman, Univalent functions with negative coefficients, Proc. Amer. Math. Soc., 51(1975), 109-116.

T. N. Shanmugam, C. Ramachandran and R. A. Prabhu, Certain aspects of univalent functions with negative coefficients defined by Rafid operator, Int. J. Math. Anal., 7(9-12)(2013), 499-509.

H. M. Srivastava et al., A new subclass of $k$-uniformly convex functions with negative coefficients, J. Inequal. Pure Appl. Math., 8(2)(2007), Article ID 43, 14 pp.

S. Sunil Varma and T. Rosy, Certain properties of a sub- class of univalent functions with finitely many fixed coefficients, Khayyam J. Math., 3(1)(2017), 25-32.