| Title:
|
Some applications of subordination theorems associated with fractional $q$-calculus operator (English) |
| Author:
|
Kota, Wafaa Y. |
| Author:
|
El-Ashwah, Rabha Mohamed |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
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148 |
| Issue:
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2 |
| Year:
|
2023 |
| Pages:
|
131-148 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
analytic function |
| Keyword:
|
subordination principle |
| Keyword:
|
subordinating factor sequence |
| Keyword:
|
Hadamard product |
| Keyword:
|
$q$-difference operator |
| Keyword:
|
fractional $q$-calculus operator |
| MSC:
|
30C45 |
| MSC:
|
30C50 |
| idZBL:
|
Zbl 07729569 |
| idMR:
|
MR4585573 |
| DOI:
|
10.21136/MB.2022.0047-21 |
| . |
| Date available:
|
2023-05-04T17:54:47Z |
| Last updated:
|
2023-09-13 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/151680 |
| . |
| Reference:
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[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. Zbl 07342522, MR 3651242, 10.22190/FUMI1702255A |
| Reference:
|
[2] Al-Oboudi, F. M.: On univalent functions defined by a generalized Sălăgean operator.Int. J. Math. Math. Sci. 2004 (2004), 1429-1436. Zbl 1072.30009, MR 2085011, 10.1155/S0161171204108090 |
| Reference:
|
[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. Zbl 1132.30010, MR 2370683, 10.1016/j.jmaa.2007.05.087 |
| Reference:
|
[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. Zbl 07397374, MR 4259359, 10.1007/s13370-020-00849-3 |
| Reference:
|
[5] Attiya, A. A.: On some applications of a subordination theorem.J. Math. Anal. Appl. 311 (2005), 489-494. Zbl 1080.30010, MR 2168412, 10.1016/j.jmaa.2005.02.056 |
| Reference:
|
[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. |
| Reference:
|
[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. Zbl 1050.30007, MR 1959457, 10.1016/S0895-7177(03)80004-3 |
| Reference:
|
[8] Duren, P. L.: Univalent Functions.Grundlehren der Mathematischen Wissenschaften 259. Springer, New York (1983). Zbl 0514.30001, MR 0708494 |
| Reference:
|
[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. Zbl 1249.30030, MR 2893979, 10.21136/MB.2011.141652 |
| Reference:
|
[10] Gasper, G., Rahman, M.: Basic Hypergeometric Series.Encyclopedia of Mathematics and Its Applications 35. Cambridge University Press, Cambridge (1990). Zbl 0695.33001, MR 1052153 |
| Reference:
|
[11] Govindaraj, M., Sivasubramanian, S.: On a class of analytic functions related to conic domains involving $q$-calculus.Anal. Math. 43 (2017), 475-487. Zbl 1399.30047, MR 3691744, 10.1007/s10476-017-0206-5 |
| Reference:
|
[12] Ismail, M. E. H., Merkes, E., Styer, D.: A generalization of starlike functions.Complex Variables, Theory Appl. 14 (1990), 77-84. Zbl 0708.30014, MR 1048708, 10.1080/17476939008814407 |
| Reference:
|
[13] Jackson, F. H.: On $q$-definite integrals.Quart. J. 41 (1910), 193-203 \99999JFM99999 41.0317.04. |
| Reference:
|
[14] Jackson, F. H.: $q$-difference equations.Am. J. Math. 32 (1910), 305-314 \99999JFM99999 41.0502.01. MR 1506108, 10.2307/2370183 |
| Reference:
|
[15] Littlewood, J. E.: On inequalities in the theory of functions.Proc. Lond. Math. Soc. (2) 23 (1925), 481-519 \99999JFM99999 51.0247.03. MR 1575208, 10.1112/plms/s2-23.1.481 |
| Reference:
|
[16] Nishiwaki, J., Owa, S.: Coefficient inequalities for certain analytic functions.Int. J. Math. Math. Sci. 29 (2002), 285-290. Zbl 1003.30006, MR 1896244, 10.1155/S0161171202006890 |
| Reference:
|
[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. Zbl 1033.30013, MR 1966507 |
| Reference:
|
[18] Owa, S., Srivastava, H. M.: Univalent and starlike generalized hypergeometric functions.Can. J. Math. 39 (1987), 1057-1077. Zbl 0611.33007, MR 0918587, 10.4153/CJM-1987-054-3 |
| Reference:
|
[19] Purohit, S. D., Raina, R. K.: Certain subclasses of analytic functions associated with fractional $q$-calculus operators.Math. Scand. 109 (2011), 55-70. Zbl 1229.33027, MR 2831147, 10.7146/math.scand.a-15177 |
| Reference:
|
[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. Zbl 0531.30009, MR 0738107, 10.1007/BFb0066543 |
| Reference:
|
[21] Silverman, H.: Univalent functions with negative coefficients.Proc. Am. Math. Soc. 51 (1975), 109-116. Zbl 0311.30007, MR 0369678, 10.1090/S0002-9939-1975-0369678-0 |
| Reference:
|
[22] Silverman, H.: A survey with open problems on univalent functions whose coefficients are negative.Rocky Mt. J. Math. 21 (1991), 1099-1125. Zbl 0766.30011, MR 1138154, 10.1216/rmjm/1181072932 |
| Reference:
|
[23] Silverman, H.: Integral means for univalent functions with negative coefficients.Houston J. Math. 23 (1997), 169-174. Zbl 0889.30010, MR 1688819 |
| Reference:
|
[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. MR 4064730, 10.1007/s40995-019-00815-0 |
| Reference:
|
[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. Zbl 1059.30021, MR 2112435 |
| Reference:
|
[26] Uralegaddi, B. A., Ganigi, M. D., Sarangi, S. M.: Univalent functions with positive coefficients.Tamkang J. Math. 25 (1994), 225-230. Zbl 0837.30012, MR 1304483, 10.5556/j.tkjm.25.1994.4448 |
| Reference:
|
[27] Wilf, H. S.: Subordinating factor sequences for convex maps of the unit circle.Proc. Am. Math. Soc. 12 (1961), 689-693. Zbl 0100.07201, MR 0125214, 10.1090/S0002-9939-1961-0125214-5 |
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