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Argument Estimates of Multivalent Functions Involving a Certain Fractional Derivative Operator

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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.
Cite this paper
Choi, J. (2015) Argument Estimates of Multivalent Functions Involving a Certain Fractional Derivative Operator. Advances in Pure Mathematics, 5, 88-92. doi: 10.4236/apm.2015.52011.
 
References
[1]Srivastava, H.M. and Buschman, R.G. (1992) Theory and Applications of Convolution Integral Equations. Kluwer Academic Publishers, Dordrecht, Boston and London.
 
[2]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.
 
[3]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
 
[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.
 
[5]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.
 
[6]Lashin, A.Y. (2004) Applications of Nunokawa’s Theorem. Journal of Inequalities in Pure and Applied Mathematics, 5, 1-5. Art. 111.
 
[7]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.
 
[8]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
 
[9]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
 
[10]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.                            eww150215lx
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