In this article, we consider subclasses of functions with bounded turning for normalized analytic functions in the unit disk, we investigate certain conditions under which the partial sums of the modi？ed Caputo’s fractional derivative operators of analytic univalent functions of bounded turning are also of bounded turning.
References
[1]
Goodman, A.W. (1983) Univalent Functions. Vol. I & II. Polygonal Publishing House, Washinton, New Jersey.
[2]
Jahangiri, J.M. and Farahmand, K. (2004) Partial Sums of Functions of Bounded Turning. International Journal of Mathematics and Mathematical Sciences, 2004, Article ID: 451028. https://doi.org/10.1155/S0161171204305284
[3]
Liu, J.L. and Owa, S. (1997) On Partial Sums of the Libera Integral Operator. Journal of Mathematical Analysis and Applications, 213, 444-454.
https://doi.org/10.1006/jmaa.1997.5549
[4]
Darus, M. and Ibrahim, R.W. (2010) Partial Sums of Analytic Functions of Bounded Turning with Applications. Computational & Applied Mathematics, 29, 81-88.
https://doi.org/10.1590/S1807-03022010000100006
[5]
Jamal, S. (2016) A Note on the Modi？ed Caputos Fractional Calculus Derivative Operator. Far East Journal of Mathematical Sciences (FJMS), 100, 609-615.
https://doi.org/10.17654/MS100040609
[6]
Salah, J. and Darus, M. (2010) A Subclass of Uniformly Convex Functions Associated with a Fractional Calculus Operator Involving Caputos Fractional Di？erentiation. Acta Universitatis Apulensis. Mathematics-Informatics, 24, 295-306.
[7]
Gasper, G. (1969) Nonnegative Sums of Cosines, Ultraspherical and Jacobi Polynomials. Journal of Mathematical Analysis and Applications, 26, 60-68.
https://doi.org/10.1016/0022-247X(69)90176-0
