Harmonic functions of class of Bazilevi´c type Related to new derivative operator

Abdul Rahman S. Juma, Mushtaq S. Abdulhussain, Saba Nazar Al-khafaji


In this paper, we define and investigate subclass of Bazilevi´c type harmonic univalent functions related with a new linear operator. Also, we have obtained the harmonic structures in terms of its coefficient bounds, extreme points, distortion bound, convolution and we proved the function belongs to this class be closed under an integral operator.


Analytic function, Univalent function, Bazilevi´c function, Harmonic mapping.

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F. M. Al-Oboudi, On univalent functions defined by a generalized Salagean operator, Int. J. Math. Math. Sci. (2004), no. 25-28, 1429-1436.

I. E. Bazilevi´c, Ueber einen Fall der Integrierbarkeit der Loewner-

Kufarevschen Gleichungen durch Quadraturen [On a case of integrability

in quadratures of the Loewner- Kufarev equation], Mat. Sb. (N.S.) 37(79)

(1955), 471476.

J. Clunie and T. Sheil-Small, Harmonic univalent functions, Ann. Acad.

Aci. Fenn. Ser. A. I. Math., 9 (1984), 3-25.

M. Gregorczyk and J. Widomski, Harmonic mappings in the exterior of

the unit disk, Annales Universitatis Mariae Curie-Sklodowska, VOL. LXIV,

NO. 1, (2010), 63-73.

S. Hussain, A. Rasheed, and M. Darus, A Subclass of Harmonic Functions Related to a Convolution Operator, Journal of Function Spaces Volume (2016), 1-6.

J. M. Jahangiri and H. Silverman, Harmonic univalent functions with varying arguments, Internat. J. Appl. Math., 8 (2002), 267-275.

S. S. Miller and P.T. Mocanu, Differential Subordination:Theory and Applications, Series on Monographs and Texbooks in Pure and Applied Mathematics, Vol.225, Marcel Dekker Incorporated, New York and Basel, (2000).

G. Murugusundaramoorthy and K. Vijaya, Starlike harmonic functions in

parabolic region associated with a convolution structure, Acta Univ. Sapientiae, Mathematica, 2, 2 (2010) 168-183.

A. T. Oladipo and D. Breaz, A Brief Study of Certain Class of Harmonic

Functions of Bazilevi´c Type, ISRN Mathematical Analysis, Vol. (2013),


H. Silverman, Harmonic Univalent Functions with Negative Coefficients, Journal of mathematical analysis and applications 220, (1998), 283-289.

G. S. Salagean, Subclasses of univalent functions, Complex analysis-fifth Romanian-Finnish seminar, Part 1 (Bucharest, 1981), 362-372.

DOI: http://dx.doi.org/10.23851/mjs.v30i1.565


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