Argument Estimates of Multivalent Functions Involving a Certain Fractional Derivative Operator

Affiliation(s)

Department of Mathematics Education, Daegu National University of Education, Daegu, South Korea.

Department of Mathematics Education, Daegu National University of Education, Daegu, South Korea.

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.

KEYWORDS

Multivalent Analytic Functions, Argument, Integral Operator, Fractional Derivative Operator

Multivalent Analytic Functions, Argument, Integral Operator, Fractional Derivative Operator

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.

Choi, J. (2015) Argument Estimates of Multivalent Functions Involving a Certain Fractional Derivative Operator.

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.

[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.