Research Article
BibTex RIS Cite

Subordination theorems for a class related to q-fractional differential operator

Year 2023, Volume: 72 Issue: 3, 701 - 709, 30.09.2023
https://doi.org/10.31801/cfsuasmas.1199113

Abstract

By using the definition of q-difference operator, we defined the new q-Al-Oboudi-Al-Amoudi operator, which generalize modified Al-Oboudi-Al-Amoudi operator. Using the new operator, we defined a new class of uniformly functions and obtained subordination result for functions in it. Our results not only generalize previous results but also modified some previous results.

References

  • Risha, M.A., Annaby, M.H., Mansour, Z.S., Ismail, M.E., Linear q-difference equations, Zeitschrift für Analysis und ihre Anwendungen, 26(4) (2007), 481-494. doi 10.4171/zaa/1338
  • Al-Oboudi, F.M., On univalent functions defined by a generalized Salagean operator, International Journal of Mathematics and Mathematical Sciences, 2004(27) (2004), 1429-1436. https://doi.org/10.1155/S0161171204108090
  • Al-Oboudi, F.M., Al-Amoudi, K.A., On classes of analytic functions related to conic domains, Journal of Mathematical Analysis and Applications, 339(1) (2008), 655-667. https://doi.org/10.1016/j.jmaa.2007.05.087
  • Annaby, M.H., Mansour, Z.S., Fractional q-difference equations, q-Fractional Calculus and Equations, (2012), 223-270.
  • Aouf, M.K., Mostafa, A.O., Subordination results for analytic functions associated with fractional q-calculus operators with complex order, Afrika Matematika, 31(7) (2020), 1387-1396. https://doi.org/10.1007/s13370-020-00803-3
  • Aouf, M.K., Mostafa, A.O., Some subordinating results for classes of functions defined by Salagean type q derivative operator, Filomat, 34(7) (2020), 2283-2292. https://doi.org/10.2298/FIL2007283A
  • Aouf, M.K., Mostafa, A.O., Some subordination results for classes of analytic functions defined by the Al-Oboudi–Al-Amoudi operator, Archiv der Mathematik, 92(3) (2009), 279-286. https://doi.org/10.1007/s00013-009-2984-x
  • Aouf, M.K., Mostafa, A.O., Al-Quhali, F.Y., A class of $\beta$-uniformly univalent functions defined by Salagean type q- difference operator, Acta Univ. Apulensis, 60 (2019), 19-35.
  • Aouf, M.K., Mostafa, A.O., Elmorsy, R.E, Certain subclasses of analytic functions with varying arguments associated with q-difference operator, Afrika Matematika, 32(3) (2021), 621-630. https://doi.org/10.1007/s13370-020-00849-3
  • Aouf, M.K., Mostafa, A.O., Hussain, A.A., Properties of certain class of uniformly Starlike and Convex functions defined by convolution, Int. J. Open Problems Complex Analysis, 7(2) (2015), 1-15.
  • Aouf, M.K., Mostafa, A.O., Shahin, A.M., Madian, S.M., Subordination theorem for analytic function defined by convolution, Indian J. Math., 54(1) (2012) , 1-11. https://doi.org/10.2298/FIL2007283A
  • Aouf, M.K., Shamandy, A., Mostafa, A.O., El-Emam, F., Subordination results associated with β−uniformly convex and starlike functions, Proc. Pakistan Acad. Sci, 46(2) (2009), 97-101.
  • Aouf, M.K., Shamandy, A., Mostafa, A.O., Madian, S.M., Subordination theorem for analytic function defined by convolution, Proc. Pakistan Acad. Sci., 96(4) (2009) , 227 − 232.
  • Bulboaca, T., Differential subordinations and suberordinations: Recent results, Casa Cartii de Stiinta (2005).
  • Jackson, F.H., On q-functions and a certain difference operator, Trans. R. Soc. Edinb., 46 (1908), 64–72.
  • Miller, S.S., Mocanu, P.T., Differential Subordinations: Theory and Applications, CRC Press, 2000.
  • Mostafa, A.O., Saleh, Z.M., On a class of uniformly analytic functions with q-analogue, Int. J. Open Problems Complex Analysis, 13(2) (2021), 1-13.
  • Murugusundaramoorthy, G., Vijaya, K., Sub classes of bi-univalent functions defined by Salagean type q-difference operator, arXiv preprint arXiv:1710.00143, 1 (2017), 1-10.
  • Owa, S., On the distortion theorems I, Kyungpook Mathematical Journal, 18(1) (1978), 53-59.
  • Owa, S., Srivastava, H.M., Univalent and starlike generalized hypergeometric functions, Canadian Journal of Mathematics, 39(5) (1987), 1057-1077. https://doi.org/10.4153/CJM-1987-054-3
  • Salagean, G.S., Subclasses of univalent functions, In complex analysis-fifth Romanian-Finnish seminar, part-1 (Bucharest, 1981) of Lecture Notes in Mathematics, 1013 (1983), 362-372.
  • Srivastava, H.M., Operators of basic (or q-) calculus and fractional q-calculus and their applications in geometric function theory of complex analysis, Iranian Journal of Science and Technology, Transactions A: Science, 44(1) (2020), 327-344. https://doi.org/10.1007/s40995-019-00815-0
  • Srivastava, H.M., Mostafa, A.O., Aouf, M.K., Zayed, H.M., Basic and fractional q-calculus and associated Fekete-Szeg˝o problem for p-valently q-starlike functions and p-valently q-convex functions of complex order, Miskolc Mathematical Notes, 20(1) (2019), 489-509. doi:10.18514/mmn.2019.2405
  • Wilf, H.S., Subordinating factor sequences for convex maps of the unit circle, Proceedings of the American Mathematical Society, 12(5) (1961), 689-693.
Year 2023, Volume: 72 Issue: 3, 701 - 709, 30.09.2023
https://doi.org/10.31801/cfsuasmas.1199113

Abstract

References

  • Risha, M.A., Annaby, M.H., Mansour, Z.S., Ismail, M.E., Linear q-difference equations, Zeitschrift für Analysis und ihre Anwendungen, 26(4) (2007), 481-494. doi 10.4171/zaa/1338
  • Al-Oboudi, F.M., On univalent functions defined by a generalized Salagean operator, International Journal of Mathematics and Mathematical Sciences, 2004(27) (2004), 1429-1436. https://doi.org/10.1155/S0161171204108090
  • Al-Oboudi, F.M., Al-Amoudi, K.A., On classes of analytic functions related to conic domains, Journal of Mathematical Analysis and Applications, 339(1) (2008), 655-667. https://doi.org/10.1016/j.jmaa.2007.05.087
  • Annaby, M.H., Mansour, Z.S., Fractional q-difference equations, q-Fractional Calculus and Equations, (2012), 223-270.
  • Aouf, M.K., Mostafa, A.O., Subordination results for analytic functions associated with fractional q-calculus operators with complex order, Afrika Matematika, 31(7) (2020), 1387-1396. https://doi.org/10.1007/s13370-020-00803-3
  • Aouf, M.K., Mostafa, A.O., Some subordinating results for classes of functions defined by Salagean type q derivative operator, Filomat, 34(7) (2020), 2283-2292. https://doi.org/10.2298/FIL2007283A
  • Aouf, M.K., Mostafa, A.O., Some subordination results for classes of analytic functions defined by the Al-Oboudi–Al-Amoudi operator, Archiv der Mathematik, 92(3) (2009), 279-286. https://doi.org/10.1007/s00013-009-2984-x
  • Aouf, M.K., Mostafa, A.O., Al-Quhali, F.Y., A class of $\beta$-uniformly univalent functions defined by Salagean type q- difference operator, Acta Univ. Apulensis, 60 (2019), 19-35.
  • Aouf, M.K., Mostafa, A.O., Elmorsy, R.E, Certain subclasses of analytic functions with varying arguments associated with q-difference operator, Afrika Matematika, 32(3) (2021), 621-630. https://doi.org/10.1007/s13370-020-00849-3
  • Aouf, M.K., Mostafa, A.O., Hussain, A.A., Properties of certain class of uniformly Starlike and Convex functions defined by convolution, Int. J. Open Problems Complex Analysis, 7(2) (2015), 1-15.
  • Aouf, M.K., Mostafa, A.O., Shahin, A.M., Madian, S.M., Subordination theorem for analytic function defined by convolution, Indian J. Math., 54(1) (2012) , 1-11. https://doi.org/10.2298/FIL2007283A
  • Aouf, M.K., Shamandy, A., Mostafa, A.O., El-Emam, F., Subordination results associated with β−uniformly convex and starlike functions, Proc. Pakistan Acad. Sci, 46(2) (2009), 97-101.
  • Aouf, M.K., Shamandy, A., Mostafa, A.O., Madian, S.M., Subordination theorem for analytic function defined by convolution, Proc. Pakistan Acad. Sci., 96(4) (2009) , 227 − 232.
  • Bulboaca, T., Differential subordinations and suberordinations: Recent results, Casa Cartii de Stiinta (2005).
  • Jackson, F.H., On q-functions and a certain difference operator, Trans. R. Soc. Edinb., 46 (1908), 64–72.
  • Miller, S.S., Mocanu, P.T., Differential Subordinations: Theory and Applications, CRC Press, 2000.
  • Mostafa, A.O., Saleh, Z.M., On a class of uniformly analytic functions with q-analogue, Int. J. Open Problems Complex Analysis, 13(2) (2021), 1-13.
  • Murugusundaramoorthy, G., Vijaya, K., Sub classes of bi-univalent functions defined by Salagean type q-difference operator, arXiv preprint arXiv:1710.00143, 1 (2017), 1-10.
  • Owa, S., On the distortion theorems I, Kyungpook Mathematical Journal, 18(1) (1978), 53-59.
  • Owa, S., Srivastava, H.M., Univalent and starlike generalized hypergeometric functions, Canadian Journal of Mathematics, 39(5) (1987), 1057-1077. https://doi.org/10.4153/CJM-1987-054-3
  • Salagean, G.S., Subclasses of univalent functions, In complex analysis-fifth Romanian-Finnish seminar, part-1 (Bucharest, 1981) of Lecture Notes in Mathematics, 1013 (1983), 362-372.
  • Srivastava, H.M., Operators of basic (or q-) calculus and fractional q-calculus and their applications in geometric function theory of complex analysis, Iranian Journal of Science and Technology, Transactions A: Science, 44(1) (2020), 327-344. https://doi.org/10.1007/s40995-019-00815-0
  • Srivastava, H.M., Mostafa, A.O., Aouf, M.K., Zayed, H.M., Basic and fractional q-calculus and associated Fekete-Szeg˝o problem for p-valently q-starlike functions and p-valently q-convex functions of complex order, Miskolc Mathematical Notes, 20(1) (2019), 489-509. doi:10.18514/mmn.2019.2405
  • Wilf, H.S., Subordinating factor sequences for convex maps of the unit circle, Proceedings of the American Mathematical Society, 12(5) (1961), 689-693.
There are 24 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Mohamed Mowafy 0000-0002-2308-6826

A. O. Mostafa 0000-0002-3911-0990

Samar Mohamed 0000-0001-7490-9901

Publication Date September 30, 2023
Submission Date November 8, 2022
Acceptance Date February 14, 2023
Published in Issue Year 2023 Volume: 72 Issue: 3

Cite

APA Mowafy, M., Mostafa, A. O., & Mohamed, S. (2023). Subordination theorems for a class related to q-fractional differential operator. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 72(3), 701-709. https://doi.org/10.31801/cfsuasmas.1199113
AMA Mowafy M, Mostafa AO, Mohamed S. Subordination theorems for a class related to q-fractional differential operator. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. September 2023;72(3):701-709. doi:10.31801/cfsuasmas.1199113
Chicago Mowafy, Mohamed, A. O. Mostafa, and Samar Mohamed. “Subordination Theorems for a Class Related to Q-Fractional Differential Operator”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72, no. 3 (September 2023): 701-9. https://doi.org/10.31801/cfsuasmas.1199113.
EndNote Mowafy M, Mostafa AO, Mohamed S (September 1, 2023) Subordination theorems for a class related to q-fractional differential operator. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72 3 701–709.
IEEE M. Mowafy, A. O. Mostafa, and S. Mohamed, “Subordination theorems for a class related to q-fractional differential operator”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 72, no. 3, pp. 701–709, 2023, doi: 10.31801/cfsuasmas.1199113.
ISNAD Mowafy, Mohamed et al. “Subordination Theorems for a Class Related to Q-Fractional Differential Operator”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72/3 (September 2023), 701-709. https://doi.org/10.31801/cfsuasmas.1199113.
JAMA Mowafy M, Mostafa AO, Mohamed S. Subordination theorems for a class related to q-fractional differential operator. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2023;72:701–709.
MLA Mowafy, Mohamed et al. “Subordination Theorems for a Class Related to Q-Fractional Differential Operator”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 72, no. 3, 2023, pp. 701-9, doi:10.31801/cfsuasmas.1199113.
Vancouver Mowafy M, Mostafa AO, Mohamed S. Subordination theorems for a class related to q-fractional differential operator. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2023;72(3):701-9.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.