On Inclusion Properties for Certain Subclasses of Analytic Multivalent Functions Involving a New Extended Generalized Derivative Operator
Keywords:
Analytic p-valent functions, Generalized derivative operator, Inclusion properties, Quasi- convex Open unit diskAbstract
The purpose of the present paper, is making use of the principle of subordination between analytic functions, to introduce and systematically study new subclasses of analytic multivalent functions in the open unit disk E , by means of the extended generalized derivative operator {\mathcal{F}}{p,{\lambda }{1},{\lambda }_{2}}^{m,l,n}f\left(z\right). Also, inclusion properties of these subclasses of functions will be investigated. In addition, we will define the class of p-valent close-to-convex functions of order β and type α , and the class of quasi- convex functions, and will prove their inclusion properties.
References
Amer, A. and Darus, M., On some propertis for new generalized derivative operator, Jordan Journal of Mathematics and Statistics (JJMS),4(2), 91-101, (2011).
Amer, A.A , Almasri. H, and Darus, M., On neighborhoods of certain classes of p-valent functions with negative coefficients defined by a new extended generalized derivative operator, Acta Universitatis Apulensis, 78(5), 69-79, (2024).
Al-Shaqsi, K. and Darus, M., An operator defined by convolution involving polylogarithms functions, J. Math. Stat, 4(1), 46-50,(2008).
Al-Abbadi, M. H, and Darus, M., Differential Subordination for new generalized derivative operator, Acta Universitatis Apulensis, 20, 265 280, (2009).
AL-Oboudi, F. M, On univalent functions defined by a generalised Salagea Operator, Int. J. Math. Math. Sci. 27, 1429-1436, (2004).
Aouf, M. K.; Mostafa, A. O. ; El-Hawsh, G. M. Inclusion properties for classes of p−valent functions associated with linear operator, Afrika Matematika 2024, 1-11, (2024).
Aouf, M. K, On a class of p-valent close – to – convex functions od order β and type α , International Journal of Mathematics and Mathematical Sciences, 11(2), 259-266, (1988).
Ahmed, A. R. Some applications of Catas operator to p-valent starlike functions, Surman Journal for Science and Technology,401-410, (2024).
Bulut, S., On a class of analytic and multivalent functions with negative coefficients defined by Al-Oboudi differential operator, STUDIA UNIV. “BABES¸–BOLYAI”, MATHEMATICA ,(2010).
Bulboaca, T., Differential Subordinations and Superordinations, Pecent Results, House of Scientific Book Publ., Cluj-Napoca, (2005).
Catas, A., On a Certain Differential Sandwich Theorem Associated with a New Generalized Derivative Operator, General Mathematics. 4 ,83-95, (2009).
Catas, A., On certain classes of p-valent functions defined by multiplier transformations, Proceedings of the International symposium on Geometric function theory and Applications, 241- 250, (2008).
Eenigenburg. P, Miller. S, Mocanu. P, and Reade. M, On a Briot-Bouquet differential subordination, General Enequalities 3, I. S. N. M., Vol. 64, Birkh¨auser Verlag, Basel , 339-348, (1983).
Eker , S., Seker. B, On a class of multivalent functions defined by Salagean operator, General Mathematics. 15, 154-163, (2007).
Goodman, A. W., On the Shwarz- Christoffel transformation and p-valent functions, Trans. Amer. Math. Soc.,204-223, (1950).
Libera, R. J., Some radius of convexity problems, Duke Mathematical Journal, 31(1), 143-158, (1964).
Miller. S, Mocanu. P, Second-order differential inequalities in the complex plane, Journal of Mathematical Analysis and Applications, 65(2), 289-305, (1978).
Miller. S, Mocanu. P, Differential Subordination ,Theory and Applications, Series on Monographs and Textbooks in Pure and Applied Mathematics, Vol. 225, Marcel Dekker Inc., New York and Basel,( 2000).
Miller. S, Mocanu. P, Differential subordinations and univalent functions, Michigan Math. J., 28 no. 2, 157-171, (1981).
Mishra, A. K, Sahu, P., Closed convex hull of the family off multivalently close –to- convex functions of order β, Rendi Conti del Circolo Mathematico di Palermo., 209-222, (1999).
Munasser, B. M, Mostafa, A. O. , Sultan, T, Nasser, A., EL-Sherbeny and Madian, S. M., Inclusion properties for classes of p-valent functions, Journal of Function Spaces, 1-6, (2024).
Owa, S., On certain classes of p-valent functions with negative coefficients, Bull. Belg. Math. Soc. Simon stevin., 385-402, (1985).
Partil, D. A. , Thakare, N,K, On convex hulls and extreme points of p- valent starlike and convex classes with applications, Bull. Math. Soc. Sci. Math. R. S., Roumanie(N.S.)., 145-160, (1983).
Ruscheweyh, S., New criteria for univalent functions, Proc. Amer.Math. Soc. Vol. 49,109-115, (1975).
Raina, R. K., and Srivastava, H. M., Inclusion and neighborhood properties of some analytic and multivalent functions, Journal of Inequalities in Pure and Applied Mathematics, 7(1), (2006).
Salagean, G. S, Subclasses of univalent functions, Lecture Notes in Math. (Springer-Verlag), 1013, 362-372, (1983).
Silverman, H., Neighborhoods of classes of analytic functions. Far East J. Math. Sci. 3 , 165-169, (1995).
Srivastava, H.M., Aouf, M.K., EL-Ashwah, R.M.: Some inclusion relationships associated with a certain class of integral operators. Asian-European J. Math. 3(4), 667–684 (2010).
