Welcome to Open Science
Contact Us
Home Books Journals Submission Open Science Join Us News
A Class of Harmonic Univalent Functions Defined by Linear Operator
Current Issue
Volume 3, 2015
Issue 4 (August)
Pages: 101-109   |   Vol. 3, No. 4, August 2015   |   Follow on         
Paper in PDF Downloads: 50   Since Aug. 28, 2015 Views: 1720   Since Aug. 28, 2015
Authors
[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.
Abstract
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.
Keywords
Harmonic Univalent Functions, Coefficient Estimate, Extreme Points, Distortion Bounds, Integral Operator, Inclusion Relations
Reference
[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.
Open Science Scholarly Journals
Open Science is a peer-reviewed platform, the journals of which cover a wide range of academic disciplines and serve the world's research and scholarly communities. Upon acceptance, Open Science Journals will be immediately and permanently free for everyone to read and download.
CONTACT US
Office Address:
228 Park Ave., S#45956, New York, NY 10003
Phone: +(001)(347)535 0661
E-mail:
LET'S GET IN TOUCH
Name
E-mail
Subject
Message
SEND MASSAGE
Copyright © 2013-, Open Science Publishers - All Rights Reserved