Research ArticleOpen AccessGoogle Scholar indexed
Argument Estimates of Multivalent Functions Involving a Certain Fractional Derivative Operator
Department of Mathematics Education, Daegu National University of Education, Daegu, South Korea
- 1 Department of Mathematics Education, Daegu National University of Education, Daegu, South Korea
Advances in Pure Mathematics·Volume 05 (2015)·Pages 88–92·Published 26 January 2015·DOI10.4236/apm.2015.52011
Copy link · social · email
Abstract
The object of the present paper is to investigate various argument results of analytic and multivalent functions which are defined by using a certain fractional derivative operator. Some interesting applications are also considered.
KeywordsMultivalent Analytic FunctionsArgumentIntegral OperatorFractional Derivative Operator
- Srivastava, H.M. and Buschman, R.G. (1992) Theory and Applications of Convolution Integral Equations. Kluwer Academic Publishers, Dordrecht, Boston and London.
- Samko, S.G., Kilbas, A.A. and Marichev, O.I. (1993) Fractional Integral and Derivatives, Theory and Applications. Gordon and Breach, New York, Philadelphia, London, Paris, Montreux, Toronto and Melbourne.
- Raina, R.K. and Srivastava, H.M. (1996) A Certain Subclass of Analytic Functions Associated with Operators of Fractional Calculus. Computers & Mathematics with Applications, 32, 13-19. http://dx.doi.org/10.1016/0898-1221(96)00151-4
- Raina, R.K. and Choi, J.H. (2002) On a Subclass of Analytic and Multivalent Functions Associated with a Certain Fractional Calculus Operator. Indian Journal of Pure and Applied Mathematics, 33, 55-62.
- Srivastava, H.M. and Aouf, M.K. (1992) A Certain Fractional Derivative Operator and Its Applications to a New Class of Analytic and Multivalent Functions with Negative Coefficients. I and II. Journal of Mathematical Analysis and Applications, 171, 1-13.
- Lashin, A.Y. (2004) Applications of Nunokawa’s Theorem. Journal of Inequalities in Pure and Applied Mathematics, 5, 1-5. Art. 111.
- Goyal, S.P. and Goswami, P. (2010) Argument Estimate of Certain Multivalent Analytic Functions Defined by Integral Operators. Tamsui Oxford Journal of Mathematical Sciences, 25, 285-290.
- Bernardi, S.D. (1969) Convex and Starlike Univalent Functions. Transaction of the American Mathematical Society, 135, 429-446. http://dx.doi.org/10.1090/S0002-9947-1969-0232920-2
- Libera, R.J. (1965) Some Classes of Regular Univalent Functions. Proceedings of the American Mathematical Society, 16, 755-758. http://dx.doi.org/10.1090/S0002-9939-1965-0178131-2
- Srivastava, H.M. and Owa, S. (Eds.) (1992) Current Topics in Analytic Function Theory. World Scientific Publishing Company, Singapore, New Jersey, London, and Hong Kong.