Applications of Fractional Derivative on a Differential Subordinations and Superordinators for Analytic Functions Associated with Differential Operator
Download PDF
Authors: A. K. WANAS AND M. DARUS
DOI: 10.46793/KgJMat2103.379W
Abstract:
The purpose of this paper is to derive subordination and superordination results involving fractional derivative of differential operator for analytic functions in the open unit disk. These results are applied to obtain sandwich results. Our results extend corresponding previously known results.
Keywords:
Analytic functions, differential subordination, differential superordination, fractional derivative, differential operator.
References:
[1] R. M. Ali, V. Ravichandran, M. H. Khan and K. G. Subramanian, Differential sandwich theorems for certain analytic functions, Far East Journal of Mathematical Sciences 15(1) (2004), 87–94.
[2] A. A. Attiya and M. F. Yassen, Some subordination and superordination results associated with generalized Srivastava-Attiya operator, Filomat 31(1) (2017), 53–60.
[3] T. Bulboacǎ, Classes of first order differential superordinations, Demonstr. Math. 35(2) (2002), 287–292.
[4] S. P. Goyal, P. Goswami and H. Silverman, Subordination and superordination results for a class of analytic multivalent functions, Journal of Inequalities in Pure and Applied Mathematics (2008), Article ID 561638, 1–12.
[5] S. S. Miller and P. T. Mocanu, Differential Subordinations: Theory and Applications, Series on Monographs and Textbooks in Pure and Applied Mathematics 225, Marcel Dekker Inc., New York, Basel, 2000.
[6] S. S. Miller and P. T. Mocanu, Subordinants of differential superordinations, Complex Variables 48(10) (2003), 815–826.
[7] G. Murugusundaramoorthy and N. Magesh, Differential subordinations and superordinations for analytic functions defined by Dziok-Srivastava linear operator, J. Ineq. Pure Appl. Math. 7(4) (2006), 1–20.
[8] V. O. Nechita, Differential subordinations and superordinations for analytic functions defined by the generalized Salagean derivative operator, Acta Univ. Apulensis Math. Inform. 16 (2008), 14–156.
[9] A. Oshah and M Darus, Differential sandwich theorems with new generalized derivative operator, Adv. Math. Sci. 3(2) (2014), 117–125.
[10] D. Răducanu and V. O. Nechita, A differential sandwich theorem for analytic functions defined by the generalized Salagean operator, Aust. J. Math. Anal. Appl. 9(1) (2012), 1–7.
[11] St. Ruscheweyh, New certain for univalent functions, Proc. Amer. Math. Soc. 49 (1975), 109–115.
[12] A. Shammaky, Differential sandwich theorems for analytic functions defined by an extended multiplier transformation, Advances in Pure Mathematics 2 (2012), 323–329.
[13] T. N. Shanmugam, V. Ravichandran and S. Sivasubramanian, Differential sandwich theorems for some subclasses of analytic functions, Aust. J. Math. Anal. Appl. 3(1) (2006), 1–11.
[14] T. N. Shanmugam, S. Sivasubramanian and H. Silverman, On sandwich theorems for some classes of analytic functions, Int. J. Math. Math. Sci. (2006), Article ID 29684, 1–13.
[15] H. M. Srivastava and S. Owa (Eds.), Current Topics in Analytic Function Theory, World Scientific Publishing Company, Singapore, 1992.
[16] N. Tuneski, On certain sufficient conditions for starlikeness, Int. J. Math. Math. Sci. 23(8) (2000), 521–527.
[17] A. K. Wanas, Differential sandwich theorems for integral operator of certain analytic functions, General Mathematics Notes 15(1) (2013), 72–83.
[18] A. K. Wanas, On sandwich theorems for higher-order derivatives of multivalent analytic functions associated with the generalized Noor integral operator, Asian-Eur. J. Math. 8(1) (2015), 1–14.
Login:
