Topological Properties for Harmonic τ-Uniformly Convex Functions of Order ρ Associated with Wanas Differential Operator

  • Abbas Kareem Wanas Department of Mathematics, College of Science, University of Al-Qadisiyah, Iraq
Keywords: harmonic function, uniformly convex function, extreme points, closed convex hull, compact set


The purpose of the present paper is to establish some topological properties for a certain family of harmonic τ-uniformly convex functions of order ρ associated with Wanas differential operatordefined in the open unit disk U.


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

F. M. Al-Oboudi, On univalent functions defined by a generalized Salagean operator, Int. J. Math. Math. Sci. 27 (2004), 1429-1436.

S. D. Bernardi, Convex and starlike univalent functions, Trans. Amer. Math. Soc. 135 (1969), 429-446.

N. E. Cho and H. M. Srivastava, Argument estimates of certain analytic functions defined by a class of multiplier transformations, Math. Comput. Modeling 37(1-2) (2003), 39-49.

N. E. Cho and T. H. Kim, Multiplier transformations and strongly close-to-convex functions, Bull. Korean Math. Soc. 40(3) (2003), 399-410.

J. Clunie and T. Sheil-Small, Harmonic univalent functions, Ann. Acad. Aci. Fenn. Ser. A I Math. 9 (1984), 3-25.

J. Dziok, On Janowski harmonic functions, J. Appl. Anal. 21(2) (2015), 99-107.

I. B. Jung, Y. C. Kim and H. M. Srivastava, The Hardy space of analytic functions associated with certain one-parameter families of integral operators, J. Math. Anal. Appl. 176 (1993), 138-147.

P. Montel, Sur les familles de fonctions analytiques qui admettent des valeurs exceptionnelles dans un domaine, Ann. Sci. Ecole Norm. Sup. 29 (1912), 487-535.

G. S. Salagean, Subclasses of univalent functions, Lecture Notes in Math., Springer Verlag, Berlin 1013 (1983), 362-372.

T. Sheil-Small, Constants for planer Harmonic mappings, J. London Math. Soc. 42(2) (1990), 237-248.

H. M. Srivastava and A. A. Attiya, An integral operator associated with the Hurwitz-Lerch Zeta function and differential subordination, Integral Transforms and Special Functions 18(3) (2007), 207-216.

S. R. Swamy, Inclusion properties of certain subclasses of analytic functions, Int. Math. Forum 7(36) (2012), 1751-1760.

B. A. Uralegaddi and C. Somanatha, Certain classes of univalent functions, in: Current Topics in Analytic Function Theory, (Edited by H. M. Srivastava and S. Own), 371-374, World Scientific, Singapore, 1992.

A. K. Wanas, New differential operator for holomorphic functions, Earthline J. Math. Sci. 2(2) (2019), 527-537.

A. K. Wanas and G. Murugusundaramoorthy, Differential sandwich results for Wanas operator of analytic functions, Mathematica Moravica 24(1) (2020), 17-28.

How to Cite
Wanas, A. K. (2020). Topological Properties for Harmonic τ-Uniformly Convex Functions of Order ρ Associated with Wanas Differential Operator. Earthline Journal of Mathematical Sciences, 4(2), 333-346.

Most read articles by the same author(s)

1 2 3 > >>