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Keywords:
analytic function; subordination principle; subordinating factor sequence; Hadamard product; $q$-difference operator; fractional $q$-calculus operator
analytic function; subordination principle; subordinating factor sequence; Hadamard product; $q$-difference operator; fractional $q$-calculus operator
Summary:
Using the operator $\frak {D}_{q,\varrho }^{m}(\lambda ,l)$, we introduce the subclasses $\frak {Y}^{*m}_{q,\varrho }(l,\lambda ,\gamma )$ and $\frak {K}^{*m}_{q,\varrho }(l,\lambda ,\gamma )$ of normalized analytic functions. Among the results investigated for each of these function classes, we derive some subordination results involving the Hadamard product of the associated functions. The interesting consequences of some of these subordination results are also discussed. Also, we derive integral means results for these classes.
References:
[1] Abelman, S., Selvakumaran, K. A., Rashidi, M. M., Purohit, S. D.: Subordination conditions for a class of non-Bazilević type defined by using fractional $q$-calculus operators. Facta Univ., Ser. Math. Inf. 32 (2017), 255-267. DOI 10.22190/FUMI1702255A | MR 3651242 | Zbl 07342522
[2] Al-Oboudi, F. M.: On univalent functions defined by a generalized Sălăgean operator. Int. J. Math. Math. Sci. 2004 (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 domains. J. Math. Anal. Appl. 339 (2008), 655-667. DOI 10.1016/j.jmaa.2007.05.087 | MR 2370683 | Zbl 1132.30010
[4] Aouf, M. K., Mostafa, A. O., Elmorsy, R. E.: Certain subclasses of analytic functions with varying arguments associated with $q$-difference operator. Afr. Mat. 32 (2021), 621-630. DOI 10.1007/s13370-020-00849-3 | MR 4259359 | Zbl 07397374
[5] Attiya, A. A.: On some applications of a subordination theorem. J. Math. Anal. Appl. 311 (2005), 489-494. DOI 10.1016/j.jmaa.2005.02.056 | MR 2168412 | Zbl 1080.30010
[6] Cătaş, A.: On certain classes of $p$-valent functions defined by multiplier transformations. Proceedings of the International Symposium on Geometric Function Theory and Applications S. Owa, Y. Polatoglu Istanbul Kültür University Publications, Istanbul (2007), 241-250.
[7] Cho, N. E., Srivastava, H. M.: Argument estimates of certain analytic functions defined by a class of multiplier transformations. Math. Comput. Modelling 37 (2003), 39-49. DOI 10.1016/S0895-7177(03)80004-3 | MR 1959457 | Zbl 1050.30007
[8] Duren, P. L.: Univalent Functions. Grundlehren der Mathematischen Wissenschaften 259. Springer, New York (1983). MR 0708494 | Zbl 0514.30001
[9] El-Ashwah, R. M., Aouf, M. K., Shamandy, A., Ali, E. E.: Subordination results for some subclasses of analytic functions. Math. Bohem. 136 (2011), 311-331. DOI 10.21136/MB.2011.141652 | MR 2893979 | Zbl 1249.30030
[10] Gasper, G., Rahman, M.: Basic Hypergeometric Series. Encyclopedia of Mathematics and Its Applications 35. Cambridge University Press, Cambridge (1990). MR 1052153 | Zbl 0695.33001
[11] Govindaraj, M., Sivasubramanian, S.: On a class of analytic functions related to conic domains involving $q$-calculus. Anal. Math. 43 (2017), 475-487. DOI 10.1007/s10476-017-0206-5 | MR 3691744 | Zbl 1399.30047
[12] Ismail, M. E. H., Merkes, E., Styer, D.: A generalization of starlike functions. Complex Variables, Theory Appl. 14 (1990), 77-84. DOI 10.1080/17476939008814407 | MR 1048708 | Zbl 0708.30014
[13] Jackson, F. H.: On $q$-definite integrals. Quart. J. 41 (1910), 193-203 \99999JFM99999 41.0317.04.
[14] Jackson, F. H.: $q$-difference equations. Am. J. Math. 32 (1910), 305-314 \99999JFM99999 41.0502.01. DOI 10.2307/2370183 | MR 1506108
[15] Littlewood, J. E.: On inequalities in the theory of functions. Proc. Lond. Math. Soc. (2) 23 (1925), 481-519 \99999JFM99999 51.0247.03. DOI 10.1112/plms/s2-23.1.481 | MR 1575208
[16] Nishiwaki, J., Owa, S.: Coefficient inequalities for certain analytic functions. Int. J. Math. Math. Sci. 29 (2002), 285-290. DOI 10.1155/S0161171202006890 | MR 1896244 | Zbl 1003.30006
[17] Owa, S., Nishiwaki, J.: Coefficient estimates for certain classes of analytic functions. JIPAM, J. Inequal. Pure Appl. Math. 3 (2002), Article ID 72, 5 pages. MR 1966507 | Zbl 1033.30013
[18] Owa, S., Srivastava, H. M.: Univalent and starlike generalized hypergeometric functions. Can. J. Math. 39 (1987), 1057-1077. DOI 10.4153/CJM-1987-054-3 | MR 0918587 | Zbl 0611.33007
[19] Purohit, S. D., Raina, R. K.: Certain subclasses of analytic functions associated with fractional $q$-calculus operators. Math. Scand. 109 (2011), 55-70. DOI 10.7146/math.scand.a-15177 | MR 2831147 | Zbl 1229.33027
[20] Sălăgean, G. S.: Subclasses of univalent functions. Complex Analysis - Fifth Romanian-Finnish Seminar. Part 1 Lecture Notes in Mathematics 1013. Springer, Berlin (1983), 362-372. DOI 10.1007/BFb0066543 | MR 0738107 | Zbl 0531.30009
[21] Silverman, H.: Univalent functions with negative coefficients. Proc. Am. Math. Soc. 51 (1975), 109-116. DOI 10.1090/S0002-9939-1975-0369678-0 | MR 0369678 | Zbl 0311.30007
[22] Silverman, H.: A survey with open problems on univalent functions whose coefficients are negative. Rocky Mt. J. Math. 21 (1991), 1099-1125. DOI 10.1216/rmjm/1181072932 | MR 1138154 | Zbl 0766.30011
[23] Silverman, H.: Integral means for univalent functions with negative coefficients. Houston J. Math. 23 (1997), 169-174. MR 1688819 | Zbl 0889.30010
[24] Srivastava, H. M.: Operators of basic (or $q$-) calculus and fractional $q$-calculus and their applications in geometric function theory of complex analysis. Iran. J. Sci. Technol., Trans. A, Sci. 44 (2020), 327-344. DOI 10.1007/s40995-019-00815-0 | MR 4064730
[25] Srivastava, H. M., Attiya, A. A.: Some subordination results associated with certain subclasses of analytic functions. JIPAM, J. Inequal. Pure Appl. Math. 5 (2004), Article ID 82, 6 pages. MR 2112435 | Zbl 1059.30021
[26] Uralegaddi, B. A., Ganigi, M. D., Sarangi, S. M.: Univalent functions with positive coefficients. Tamkang J. Math. 25 (1994), 225-230. DOI 10.5556/j.tkjm.25.1994.4448 | MR 1304483 | Zbl 0837.30012
[27] Wilf, H. S.: Subordinating factor sequences for convex maps of the unit circle. Proc. Am. Math. Soc. 12 (1961), 689-693. DOI 10.1090/S0002-9939-1961-0125214-5 | MR 0125214 | Zbl 0100.07201
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