A Class of Harmonic Univalent Functions Defined by Linear Operator
[1]
R. M. EL-Ashwah, Department of Mathematics, Faculty of Science, Damietta University, New Damietta, Egypt.
[2]
M. E. Drbuk, Department of Mathematics, Faculty of Science, Damietta University, New Damietta, Egypt.
In this paper we study some properties of harmonic univalent functions which are defined by linear operator. Among the results presented here including the coefficient bounds, distortion inequality and cover property, extreme points, convolution properties and inclusion relations for this generalized class of functions are obtained.
Harmonic Univalent Functions, Coefficient Estimate, Extreme Points, Distortion Bounds, Integral Operator, Inclusion Relations
[1]
R. A. Al-Khal, Goodman-Ronning-type harmonic univalent functions based on Dziok-Srivastava operator, Appl. Math. Sci., 5 (2011), no. 12, 573-584.
[2]
H. A. Al-Kharsani and R. A. Al-Khal, Univalent harmonic functions, J. Inequal. Pure Appl. Math., 8 (2007), no. 2, Art. 59, 1-8.
[3]
K. Al-Shaqsi and M. Darus, On harmonic functions defined by derivative operator, J. Ineq. Appl, 2008, Art. ID 263413.
[4]
S. D. Bernardi, Convex and starlike univalent functions, Trans. Amer. Math. Soc., 135(1969), 429-446.
[5]
D. Breaz, Certain integral operators on the classes and , J. Inequal. Appl., (2008), Art. ID 719354.
[6]
R. Chandrashekar, G. Murugusundaramoorthy, S. K. Lee and K. G. Subramanian, A class of complex-valued harmonic functions defined by Dziok-Srivastava operator, Chamchuri J. Math., 1 (2009), no. 2, 31-42.
[7]
J. Clunie and T. Sheil-Small, Harmonic univalent functions, Annales Academiae Scientiarum Fennicae A, 9,(1984), 3-25.
[8]
K. K. Dixit and V. Chandra, On subclass of univalent functions with positive coefficients, The Aligarh Bulletin of Mathematics, 27 (2008), no. 2, 87-93.
[9]
K. K. Dixit and S. Porwal, A subclass of harmonic univalent functions with positive coefficients, Tamkang Journal of Mathematics, 41 (2010), no. 3, 261-269.
[10]
R. M. El-Ashwah and E. E. Ali, A class of complex-valued harmonic functions defined by extended multiplier Dizok-Srivastava operator, (Submitted).
[11]
J. M. Jahangiri, Harmonic functions starlike in the unit disk, J. Math. Anal. Appl., 235 (1999), no. 2, 470-477.
[12]
R. J. Libera, Some classes of regular univalent functions, Proc. Amer. Math. Soc., 16 (1965), no. 4, 755-758.
[13]
A. E. Livingston, On the radius of univalence of cerain analytic functions, Proc. Amer. Math. Soc., 17 (1966), 352-357.
[14]
S. Owa, H.M. Srivastava, Some generalized convolution properties associated with certain subclasses of analytic functions, J. Inequal. Pure Appl. Math., 3 (2002), no. 3, 1-13. Art. 42.
[15]
S. Porwal and K. K. Dixit, New Subclasses of harmonic starlike and convex functions, Kyungpook Math. J., 53 (2013), 467-478.
[16]
S. Porwal, K. K. Dixit, V. Kumar, and P. Dixit, On a subclass of analytic functions defined by convolution, General Mathematics, 19 (2011), no. 3, 57-65.
[17]
B. A. Uralegaddi, M. D. Ganigi and S. M. Sarangi, Univalent functions with positive coefficients, Tamkang J. Math., 25 (1994), no. 3, 225-233.
[18]
K.Vijaya, G. Murugusundaramoorthy, and M. Kasthuri, Pascu-type harmonic functions with positive coefficients involving Salagean operator, Inter. J. Anal., 2014 (2014), Art. 793709, 1-10.