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

Yıl 2023, Cilt: 72 Sayı: 3, 701 - 709, 30.09.2023

Mohamed Mowafy A. O. Mostafa Samar Mohamed

https://doi.org/10.31801/cfsuasmas.1199113

Öz

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.

Anahtar Kelimeler

Coefficient estimate subordination factor sequence q-difference and fractional operator

Kaynakça

  • 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.

Yıl 2023, Cilt: 72 Sayı: 3, 701 - 709, 30.09.2023

Mohamed Mowafy A. O. Mostafa Samar Mohamed

https://doi.org/10.31801/cfsuasmas.1199113

Öz

Kaynakça

  • 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.
Toplam 24 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Research Article
Yazarlar

Mohamed Mowafy 0000-0002-2308-6826

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

Samar Mohamed 0000-0001-7490-9901

Yayımlanma Tarihi 30 Eylül 2023
Gönderilme Tarihi 8 Kasım 2022
Kabul Tarihi 14 Şubat 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 72 Sayı: 3

Kaynak Göster

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. Eylül 2023;72(3):701-709. doi:10.31801/cfsuasmas.1199113
Chicago Mowafy, Mohamed, A. O. Mostafa, ve 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, sy. 3 (Eylül 2023): 701-9. https://doi.org/10.31801/cfsuasmas.1199113.
EndNote Mowafy M, Mostafa AO, Mohamed S (01 Eylül 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, ve S. Mohamed, “Subordination theorems for a class related to q-fractional differential operator”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 72, sy. 3, ss. 701–709, 2023, doi: 10.31801/cfsuasmas.1199113.
ISNAD Mowafy, Mohamed vd. “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 (Eylül 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 vd. “Subordination Theorems for a Class Related to Q-Fractional Differential Operator”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 72, sy. 3, 2023, ss. 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.

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