Some applications of subordination theorems associated with fractional q -calculus operator

Wafaa Y. Kota; Rabha Mohamed El-Ashwah

Mathematica Bohemica (2023)

  • Volume: 148, Issue: 2, page 131-148
  • ISSN: 0862-7959

Abstract

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Using the operator 𝔇 q , ϱ m ( λ , l ) , we introduce the subclasses 𝔜 q , ϱ * m ( l , λ , γ ) and 𝔎 q , ϱ * m ( l , λ , γ ) 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.

How to cite

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Kota, Wafaa Y., and El-Ashwah, Rabha Mohamed. "Some applications of subordination theorems associated with fractional $q$-calculus operator." Mathematica Bohemica 148.2 (2023): 131-148. <http://eudml.org/doc/299546>.

@article{Kota2023,
abstract = {Using the operator $\mathfrak \{D\}_\{q,\varrho \}^\{m\}(\lambda ,l)$, we introduce the subclasses $\mathfrak \{Y\}^\{*m\}_\{q,\varrho \}(l,\lambda ,\gamma )$ and $\mathfrak \{K\}^\{*m\}_\{q,\varrho \}(l,\lambda ,\gamma )$ 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.},
author = {Kota, Wafaa Y., El-Ashwah, Rabha Mohamed},
journal = {Mathematica Bohemica},
keywords = {analytic function; subordination principle; subordinating factor sequence; Hadamard product; $q$-difference operator; fractional $q$-calculus operator},
language = {eng},
number = {2},
pages = {131-148},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Some applications of subordination theorems associated with fractional $q$-calculus operator},
url = {http://eudml.org/doc/299546},
volume = {148},
year = {2023},
}

TY - JOUR
AU - Kota, Wafaa Y.
AU - El-Ashwah, Rabha Mohamed
TI - Some applications of subordination theorems associated with fractional $q$-calculus operator
JO - Mathematica Bohemica
PY - 2023
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 148
IS - 2
SP - 131
EP - 148
AB - Using the operator $\mathfrak {D}_{q,\varrho }^{m}(\lambda ,l)$, we introduce the subclasses $\mathfrak {Y}^{*m}_{q,\varrho }(l,\lambda ,\gamma )$ and $\mathfrak {K}^{*m}_{q,\varrho }(l,\lambda ,\gamma )$ 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.
LA - eng
KW - analytic function; subordination principle; subordinating factor sequence; Hadamard product; $q$-difference operator; fractional $q$-calculus operator
UR - http://eudml.org/doc/299546
ER -

References

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  1. Abelman, S., Selvakumaran, K. A., Rashidi, M. M., Purohit, S. D., 10.22190/FUMI1702255A, Facta Univ., Ser. Math. Inf. 32 (2017), 255-267. (2017) Zbl07342522MR3651242DOI10.22190/FUMI1702255A
  2. Al-Oboudi, F. M., 10.1155/S0161171204108090, Int. J. Math. Math. Sci. 2004 (2004), 1429-1436. (2004) Zbl1072.30009MR2085011DOI10.1155/S0161171204108090
  3. Al-Oboudi, F. M., Al-Amoudi, K. A., 10.1016/j.jmaa.2007.05.087, J. Math. Anal. Appl. 339 (2008), 655-667. (2008) Zbl1132.30010MR2370683DOI10.1016/j.jmaa.2007.05.087
  4. Aouf, M. K., Mostafa, A. O., Elmorsy, R. E., 10.1007/s13370-020-00849-3, Afr. Mat. 32 (2021), 621-630. (2021) Zbl07397374MR4259359DOI10.1007/s13370-020-00849-3
  5. Attiya, A. A., 10.1016/j.jmaa.2005.02.056, J. Math. Anal. Appl. 311 (2005), 489-494. (2005) Zbl1080.30010MR2168412DOI10.1016/j.jmaa.2005.02.056
  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. (2007) 
  7. Cho, N. E., Srivastava, H. M., 10.1016/S0895-7177(03)80004-3, Math. Comput. Modelling 37 (2003), 39-49. (2003) Zbl1050.30007MR1959457DOI10.1016/S0895-7177(03)80004-3
  8. Duren, P. L., Univalent Functions, Grundlehren der Mathematischen Wissenschaften 259. Springer, New York (1983). (1983) Zbl0514.30001MR0708494
  9. El-Ashwah, R. M., Aouf, M. K., Shamandy, A., Ali, E. E., 10.21136/MB.2011.141652, Math. Bohem. 136 (2011), 311-331. (2011) Zbl1249.30030MR2893979DOI10.21136/MB.2011.141652
  10. Gasper, G., Rahman, M., Basic Hypergeometric Series, Encyclopedia of Mathematics and Its Applications 35. Cambridge University Press, Cambridge (1990). (1990) Zbl0695.33001MR1052153
  11. Govindaraj, M., Sivasubramanian, S., 10.1007/s10476-017-0206-5, Anal. Math. 43 (2017), 475-487. (2017) Zbl1399.30047MR3691744DOI10.1007/s10476-017-0206-5
  12. Ismail, M. E. H., Merkes, E., Styer, D., 10.1080/17476939008814407, Complex Variables, Theory Appl. 14 (1990), 77-84. (1990) Zbl0708.30014MR1048708DOI10.1080/17476939008814407
  13. Jackson, F. H., On q -definite integrals, Quart. J. 41 (1910), 193-203 9999JFM99999 41.0317.04. (1910) 
  14. Jackson, F. H., 10.2307/2370183, Am. J. Math. 32 (1910), 305-314 9999JFM99999 41.0502.01. (1910) MR1506108DOI10.2307/2370183
  15. Littlewood, J. E., 10.1112/plms/s2-23.1.481, Proc. Lond. Math. Soc. (2) 23 (1925), 481-519 9999JFM99999 51.0247.03. (1925) MR1575208DOI10.1112/plms/s2-23.1.481
  16. Nishiwaki, J., Owa, S., 10.1155/S0161171202006890, Int. J. Math. Math. Sci. 29 (2002), 285-290. (2002) Zbl1003.30006MR1896244DOI10.1155/S0161171202006890
  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. (2002) Zbl1033.30013MR1966507
  18. Owa, S., Srivastava, H. M., 10.4153/CJM-1987-054-3, Can. J. Math. 39 (1987), 1057-1077. (1987) Zbl0611.33007MR0918587DOI10.4153/CJM-1987-054-3
  19. Purohit, S. D., Raina, R. K., 10.7146/math.scand.a-15177, Math. Scand. 109 (2011), 55-70. (2011) Zbl1229.33027MR2831147DOI10.7146/math.scand.a-15177
  20. Sălăgean, G. S., 10.1007/BFb0066543, Complex Analysis - Fifth Romanian-Finnish Seminar. Part 1 Lecture Notes in Mathematics 1013. Springer, Berlin (1983), 362-372. (1983) Zbl0531.30009MR0738107DOI10.1007/BFb0066543
  21. Silverman, H., 10.1090/S0002-9939-1975-0369678-0, Proc. Am. Math. Soc. 51 (1975), 109-116. (1975) Zbl0311.30007MR0369678DOI10.1090/S0002-9939-1975-0369678-0
  22. Silverman, H., 10.1216/rmjm/1181072932, Rocky Mt. J. Math. 21 (1991), 1099-1125. (1991) Zbl0766.30011MR1138154DOI10.1216/rmjm/1181072932
  23. Silverman, H., Integral means for univalent functions with negative coefficients, Houston J. Math. 23 (1997), 169-174. (1997) Zbl0889.30010MR1688819
  24. Srivastava, H. M., 10.1007/s40995-019-00815-0, Iran. J. Sci. Technol., Trans. A, Sci. 44 (2020), 327-344. (2020) MR4064730DOI10.1007/s40995-019-00815-0
  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. (2004) Zbl1059.30021MR2112435
  26. Uralegaddi, B. A., Ganigi, M. D., Sarangi, S. M., 10.5556/j.tkjm.25.1994.4448, Tamkang J. Math. 25 (1994), 225-230. (1994) Zbl0837.30012MR1304483DOI10.5556/j.tkjm.25.1994.4448
  27. Wilf, H. S., 10.1090/S0002-9939-1961-0125214-5, Proc. Am. Math. Soc. 12 (1961), 689-693. (1961) Zbl0100.07201MR0125214DOI10.1090/S0002-9939-1961-0125214-5

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