In this scientific note, an operator, which is the well-known Tremblay operator in the literature, is first introduced and some of its applications to certain analytic complex functions, which are normalized and analytic in the open unit disk, are then determined. In addition, certain special results of the related applications are also emphasized.
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 O. Altıntaş, H. Irmak, H. M. Srivastava, Fractional calculus and certain starlike functions with negative coefficients, Comput. Math. Appl., vol. 30, no. 2, 1995, 9-15.
 M. P. Chen, H. Irmak, H. M. Srivastava, Some families of multivalently analytic functions with negative coefficients, J. Math. Anal. Appl., vol. 214, no. 2, 1997, 674-690.
 M. P. Chen, H. Irmak, H. M. Srivastava, A certain subclass of analytic functions involving operators of fractional calculus, Comput. Math. Appl., vol. 35, no. 2, 1998, 83-91.
 P. L. Duren, Grundlehren der Mathematischen Wissencha en, Springer-Verlag, New York, Berlin, Heidelberg, Tokyo, 1983.
 Z. Esa, H. M. Srivastava, A. Kılıçman, R. W. Ibrahim, A novel subclass of analytic functions specified by a family of fractional derivatives in the complex domain, Filomat, vol. 31, no. 9, 2017, 2837-2849.
 H. Irmak, Certain complex equations and some of their implications in relation with normalized analytic functions, Filomat, vol. 30, no. 12, 2016, 3371-3376.
 H. Irmak, Some novel applications in relation with certain equations and inequalities in the complex plane, Math. Commun., vol. 23, no. 1, 2018, 9-14.
 H. Irmak, The ordinary differential operator and some of its applications to pvalently analytic functions, Electron. J. Math. Anal. Appl., vol. 4, no. 1, 2016, 205-210.
 H. Irmak, The fractional differ-integral operators and some of their applications to certain multivalent functions, J. Fract. Calc. Appl., vol. 8, no. 1, 2017, 99-107.
 H. Irmak, R. K. Raina, Some applications of generalized fractional calculus operators to a novel class of analytic functions with negative coefficients, Taiwanese J. Math., vol. 8, no. 3, 2004, 443-452.
 H. Irmak, B. A. Frasin, An application of fractional calculus and its implications relating to certain analytic functions and complex equations, J. Fract. Calc. Appl., vol. 6, no. 2, 2015, 94-100.
 H. Irmak, P. Agarwal, Some comprehensive inequalities consisting of Mittag-Leffler type functions in the complex plane, Math. Model. Nat. Phenom., vol. 12, no. 3, 2017, 65-71.
 H. Irmak, P. Agarwal, Comprehensive Inequalities and Equations Specified by the Mittag-Leffler Functions and Fractional Calculus in the Complex Plane. In: Agarwal P., Dragomir S., Jleli M., Samet B. (eds) Advances in Mathematical Inequalities and Applications. Trends in Mathematics. Birkhauser, Singapore, 2018.
 M. Şan, H. Irmak, A note on some relations between certain inequalities and normalized analytic functions, Acta Univ. Sapientiae Math., vol. 10, no. 2, 2018, 368-374.
 M. Nunokawa, On properties of non-Caratheodory functions, Proc. Japan Acad. Ser. A Math. Sci., vol. 68, no. 6, 1992, 152-153.
 S. Owa, On the distortion theorems. I, Kyungpook Math. J., vol. 8, no. 1, 1978, 53-59.
 H. M. Srivastava, S. Owa (Editors), Univalent functions, fractional calculus and their applications, Halsted Press, John Wiley and Sons., New york, Chieschester, Brisbane, Toronto, 1989.
 R. W. Ibrahim, J. M. Jahangiri, Boundary fractional differential equation in a complex domain, Boundary Value Prob., Article ID 66, 2014, 1-11.