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Keywords:
uniformly convex function; subordination; conic domain; Hadamard product
uniformly convex function; subordination; conic domain; Hadamard product
Summary:
We introduce two classes of analytic functions related to conic domains, using a new linear multiplier Dziok-Srivastava operator $D_{\lambda ,\ell }^{n.q,s}$ $(n\in \mathbb N_{0}=\{ 0,1,\dots \}$, $q\leq s+1$; $q, s\in \mathbb N_{0}$, $0\leq \alpha <1$, $\lambda \geq 0$, $\ell \geq 0).$ Basic properties of these classes are studied, such as coefficient bounds. Various known or new special cases of our results are also pointed out. For these new function classes, we establish subordination theorems and also deduce some corollaries of these results.
References:
[1] Aghalary, R., Azadi, Gh.: The Dziok-Srivastava operator and k-uniformly starlike functions. J. Inequal. Pure Appl. Math. 6 (2005), 1-7. MR 2150906 | Zbl 1089.30009
[2] Al-Oboudi, F. M.: On univalent functions defined by a generalized Salagean operator. Internat. J. Math. Math Sci. 27 (2004), 1429-1436. DOI 10.1155/S0161171204108090 | MR 2085011 | Zbl 1072.30009
[3] Al-Oboudi, F. M., Al-Amoudi, K. A.: On classes of analytic functions related to conic domain. J. Math. Anal. Appl. 339 (2008), 655-667. DOI 10.1016/j.jmaa.2007.05.087 | MR 2370683
[4] Aouf, M. K., Mostafa, A. O.: Some properties of a subclass of uniformly convex functions with negative coefficients. Demonstratio Mathematica 61 (2008), 353-370. MR 2419912 | Zbl 1159.30307
[5] Aouf, M. K., Mostafa, A. M.: Some subordination results for classes of analytic functions defined by the Al-Oboudi-Al-Amoudi operator. Arch. Math. 92 (2009), 279-286. DOI 10.1007/s00013-009-2984-x | MR 2496680 | Zbl 1165.30313
[6] Aouf, M. K., Murugusundarmoorthy, G.: On a subclass of uniformly convex functions defined by the Dziok-Srivastava operator. Austral. J. Math. Anal. Appl. 5 (2008), 1-17. MR 2383651
[7] Attiya, A. A.: On some application of a subordination theorems. J. Math. Anal. Appl. 311 (2005), 489-494. DOI 10.1016/j.jmaa.2005.02.056 | MR 2168412
[8] Bulboaca, T.: Differential Subordinations and Superordinations. Recent Results, House of Scientific Book Publ., Cluj-Napoca (2005).
[9] Bernardi, S. D.: Convex and starlike univalent functions. Trans. Amer. Math. Soc. 135 (1969), 429-446. DOI 10.1090/S0002-9947-1969-0232920-2 | MR 0232920 | Zbl 0172.09703
[10] Bharati, R., Parvatham, R., Swaminathan, A.: On subclasses of uniformly cunvex functions and corresponding class of starlike functions. Tamkang J. Math. 28 (1997), 17-32. MR 1457247
[11] Catas, A.: On certain classes of $p$-valent functions defined by multiplier transformations. Proceedings of the International Symposium on Geometric Function Theory and Applications: GFTA 2007 Proceedings (İstanbul, Turkey; 20-24 August 2007) (S. Owa, Y. Polatoğlu, Eds.), pp. 241-250, TC İstanbul Kűltűr University Publications, Vol. 91, TC İstanbul Kűltűr University, İstanbul, Turkey (2008).
[12] Choi, J. H., Saigo, M., Srivastava, H. M.: Some inclusion properties of a certain family of integral operators. J. Math. Anal. Appl. 276 (2002), 432-445. DOI 10.1016/S0022-247X(02)00500-0 | MR 1944360 | Zbl 1035.30004
[13] Dziok, J., Srivastava, H. M.: Classes of analytic functions with the generalized hypergeometric function. Applied Math. Comput. 103 (1999), 1-13. DOI 10.1016/S0096-3003(98)10042-5 | MR 1686354
[14] Frasin, B. A.: Subordination results for a class of analytic functions defined by linear operator. J. Inequal. Pure. Appl. Math. 7 (2006), 1-7. MR 2268588
[15] Goodmen, A. W.: On uniformly convex functions. Ann. Polon. Math. 56 (1991), 87-92. DOI 10.4064/ap-56-1-87-92
[16] Kanas, S., Wisniowska, A.: Conic regions and k-uniform convexity. Comput. Appl. Math. 105 (1999), 327-336. DOI 10.1016/S0377-0427(99)00018-7 | MR 1690599 | Zbl 0944.30008
[17] Kanas, S., Wisniowska, A.: Conic domains and starlike functions. Rev. Roum. Math. Pures Appl. 45 (2000), 647-657. MR 1836295 | Zbl 0990.30010
[18] Kanas, S., Yuguchi, T.: Subclasses of k-uniformly convex and starlike functions defined by generalized derivative II. Publ. Inst. Math. 69 (2001), 91-100. MR 1847833
[19] Libera, R. J.: Some classes of regular univalent function. Proc. Amer. Math. Soc. 16 (1965), 755-758. DOI 10.1090/S0002-9939-1965-0178131-2 | MR 0178131
[20] Livingston, A. E.: On the radius of univalence of certain analytic functions. Proc. Amer. Math. Soc. 17 (1966), 352-357. DOI 10.1090/S0002-9939-1966-0188423-X | MR 0188423 | Zbl 0158.07701
[21] Ma, W., Minda, D.: Uniformly convex functions. Ann. Polon. Math. 57 (1992), 165-175. DOI 10.4064/ap-57-2-165-175 | MR 1182182 | Zbl 0760.30004
[22] Miller, S. S., Mocanu, P. T.: Differential subordinations and univalent functions. Michigan Math. J. 28 (1981), 157-171. DOI 10.1307/mmj/1029002507 | MR 0616267 | Zbl 0439.30015
[23] Miller, S. S., Mocanu, P. T.: Differential Subordinations: Theory and Applications. Series of Monographs and Texbooks in Pure and Applied Mathematics, Vol. 225, Marcel Dekker, New York (2000). MR 1760285 | Zbl 0954.34003
[24] Murugusundaramoorthy, G., Magesh, N.: A new subclass of uniformly convex functions and a corresponding subclass of starlike functions with fixed second coefficient. J. Inequal. Pure Appl. Math. 5 (2004), 1-20. MR 2112438 | Zbl 1059.30010
[25] Noor, K. I., Noor, M. A.: On integral operators. J. Math. Anal. Appl. 238 (1999), 341-352. DOI 10.1006/jmaa.1999.6501 | MR 1715487 | Zbl 0934.30007
[26] Prajapat, J. K., Raina, R. K.: Subordination theorem for a certain subclass of analytic functions involving a linear multiplier operator. Indian J. Math. 51 (2009), 267-276. MR 2537946 | Zbl 1178.30017
[27] Rogosinski, W.: On the coefficients of subordinate functions. Proc. London Math. Soc. 48 (1943), 48-82. MR 0008625 | Zbl 0028.35502
[28] Ronning, F.: On starlike functions associated with parabolic regions. Ann. Univ. Mariae Curie-Sklodowska Sect. A 45 (1991), 117-122. MR 1322145
[29] Ronning, F.: Uniformly convex functions and a corresponding class of starlike functions. Proc. Amer. Math. Soc. 118 (1993), 189-196. DOI 10.1090/S0002-9939-1993-1128729-7 | MR 1128729
[30] Rosy, T., Murugsundarmoorthy, G.: Fractional calculus and its applications to certain subclassof uniformly convex functions. Far East J. Math. Sci. 15 (2004), 231-242. MR 2133425
[31] Rosy, T., Subramanian, K. G., Murugsundarmoorthy, G.: Neighbourhoods and partial sums of starlike functions based on Ruscheweyh derivatives. J. Inequal. Pure. Appl. Math. 4 (2003), 1-19. MR 2051565
[32] Salagean, G. S.: Subclasses of univalent functions. Complex Analysis---Fifth Romanian-Finish Seminar, Part I, Bucharest, 1981. Lecture Notes in Math., Vol. 1013, Springer, Berlin, 1983, pp. 362-372. MR 0738107
[33] Singh, S.: A subordination theorems for starlike functions. Internat. J. Math. Math. Sci. 24 (2000), 433-435. DOI 10.1155/S0161171200004634
[34] Singh, S.: A subordination theorems for spirallike functions. Internat. J. Math. Math. Sci. 24 (2004), 433-435. DOI 10.1155/S0161171200004634 | MR 1781509
[35] Srivastava, H. M., Attiya, A. A.: Some subordination result associated with certain subclasses of analytic functions. J. Inequal. Pure Appl. Math. 5 (2004), 1-6. MR 2112435
[36] Srivastava, H. M., Karlsson, P. W.: Multiple Gaussian Hypergeometric Series. Ellis Horwood Ltd., Chichester, Halsted Press (John Wiley & Sons), New York (1985). MR 0834385 | Zbl 0552.33001
[37] Srivastava, H. M., Mishra, A. K.: Applications of fractional calculus to parabolic starlike and uniformly convex functions. Comput. Math. Appl. 39 (2000), 57-69. DOI 10.1016/S0898-1221(99)00333-8 | MR 1740907 | Zbl 0948.30018
[38] Srivastava, H. M., Li, Shu-Hai, Tang, H.: Certain classes of k-uniformly close-to-convex functions and other related functions defined by using the Dziok-Srivastava operator. Bull. Math. Anal. Appl. 3 (2009), 49-63. MR 2578116
[39] Wilf, H. S.: Subordinating factor sequence for convex maps of the unit circle. Proc. Amer. Math. Soc. vol 12 (1961), 689-693. DOI 10.1090/S0002-9939-1961-0125214-5 | MR 0125214
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