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Hadamard product of holomorphic mappings associated with the conic shaped domain

Yıl 2023, Cilt: 72 Sayı: 1, 105 - 117, 30.03.2023

Syed Zakar Hussain Bukhari , Aamir Shahzad

https://doi.org/10.31801/cfsuasmas.1061950
Cited By: 1

Öz

We define certain subclasses $\delta-\mathcal{UM}(\ell,\eta_{1},\eta_{2})$ and
$\delta-\mathcal{UM}_{\Im}(\ell,\eta_{1},\eta_{2})$ of holomorphic mappings
involving some differential inequalities. These functions are actually
generalizations of some basic families of starlike and convex mappings. We
study sufficient conditions for $f\in \delta-\mathcal{UM}(\ell,\eta_{1}%
,\eta_{2}).$ We also discuss the characterization for $f\in \delta
-\mathcal{UM}_{\Im}(\ell,\eta_{1},\eta_{2})$ along with the coefficient bounds
and other problems. Using certain conditions for functions in the class
$\delta-\mathcal{UM}(\ell,\eta_{1},\eta_{2}),$ we also define another class
$\delta-\mathcal{UM}^{\ast}(\ell,\eta_{1},\eta_{2})$ and study some
subordination related result.

Anahtar Kelimeler

Caratheodory functions convolution subordination

Destekleyen Kurum

N/A

Kaynakça

  • Aouf, M. K., Mostafa, A. O., Some properties of a subclass of uniformly convex functions with negative coefficients, Demonstration Math., 2 (2008), 353-370. https://doi.org/10.1515/dema-2008-0212
  • Aouf, M. K., El-Ashwah, R. M., El-Deeb, S. M., Subordination results for certain subclasses of uniformly starlike and convex functions defined by convolution, European J. Pure Appl. Math., 3(5) (2010), 903-917.
  • Attiya, A. A., On some application of a subordination theorems, J. Math. Anal. Appl., 311 (2005), 489-494. https://doi.org/10.1016/j.jmaa.2005.02.056
  • Bukhari, S. Z. H., Bulboaca, T., Shabbir, M. S., Subordination and superordination results for analytic functions with respect to symmetrical points, Quaest. Math., 41(1) (2018), 1-15. https://doi.org/10.2989/16073606.2017.1372528
  • Bukhari, S. Z. H., Raza, M., Nazir, M., Some generalizations of the class of analytic functions with respect to δ-symmetric points, Hacet. J. Math. Stat., 45(1) (2016), 1-14.
  • Bukhari, S. Z. H., Sokol, J., Zafar, S., Unified approach to starlike and convex functions involving convolution between analytic functions, Results in Math., 73 (2018), 30. https://doi.org/10.1007/s00025-018-0782-0
  • Goodman, A. W., On uniformly starlike functions, J. Math. Anal. Appl., 155 (1991), 364-370. https://doi.org/10.1016/0022-247X(91)90006-L
  • Janowski, W., Some extremal problems for certain classes of analytic functions, Ann. Polon. Math., 28 (1973), 297-326. 10.4064/AP-28-3-297-326
  • Kanas, S., Wisniowska, A., Conic domains and starlike functions, Rev. Roumaine Math. Pures Appl., 45 (2000), 647-657.
  • Miller, S. S., Mocanu, P. T., Differential Subordinations Theory and Applications, Series on Monographs and Textbooks in Pure and Appl Math, No. 255 Marcel Dekker, Inc., New York, 2000. https://doi.org/10.1201/9781482289817
  • Noor, K. I., Malik, S. N., On coefficient inequalities of functions associated with conic domains, Comp. Math. Appl., 62 (2011), 2209-2217. https://doi.org/10.1016/j.camwa.2011.07.006
  • Raina, R. K., Deepak, B., Some properties of a new class of analytic functions defined in terms of a Hadamard product, J. Inequal Pure Appl. Math., 9 (2008), 1-9.
  • Ronning, F., Uniformly convex functions and a corresponding class of starlike functions, Proc. Amer. Math. Soc., 118 (1993), 189-196. https://doi.org/10.2307/2160026
  • Silverman, H., Univalent functions with negative coefficients, Proc. Amer. Math. Soc., 51 (1975), 109-116.
  • Srivastava, H. M., Attiya, A. A., Some subordination results associated with certain subclass of analytic functions, J. Inequal Pure Appl. Math., 5(4) (2004), 1-6.
  • Wilf, H. S., Subordinating factor sequence for convex maps of the unit circle, Proc. Amer. Math. Soc., 129 (1961), 689-693.

Yıl 2023, Cilt: 72 Sayı: 1, 105 - 117, 30.03.2023

Syed Zakar Hussain Bukhari , Aamir Shahzad

https://doi.org/10.31801/cfsuasmas.1061950
Cited By: 1

Öz

Kaynakça

  • Aouf, M. K., Mostafa, A. O., Some properties of a subclass of uniformly convex functions with negative coefficients, Demonstration Math., 2 (2008), 353-370. https://doi.org/10.1515/dema-2008-0212
  • Aouf, M. K., El-Ashwah, R. M., El-Deeb, S. M., Subordination results for certain subclasses of uniformly starlike and convex functions defined by convolution, European J. Pure Appl. Math., 3(5) (2010), 903-917.
  • Attiya, A. A., On some application of a subordination theorems, J. Math. Anal. Appl., 311 (2005), 489-494. https://doi.org/10.1016/j.jmaa.2005.02.056
  • Bukhari, S. Z. H., Bulboaca, T., Shabbir, M. S., Subordination and superordination results for analytic functions with respect to symmetrical points, Quaest. Math., 41(1) (2018), 1-15. https://doi.org/10.2989/16073606.2017.1372528
  • Bukhari, S. Z. H., Raza, M., Nazir, M., Some generalizations of the class of analytic functions with respect to δ-symmetric points, Hacet. J. Math. Stat., 45(1) (2016), 1-14.
  • Bukhari, S. Z. H., Sokol, J., Zafar, S., Unified approach to starlike and convex functions involving convolution between analytic functions, Results in Math., 73 (2018), 30. https://doi.org/10.1007/s00025-018-0782-0
  • Goodman, A. W., On uniformly starlike functions, J. Math. Anal. Appl., 155 (1991), 364-370. https://doi.org/10.1016/0022-247X(91)90006-L
  • Janowski, W., Some extremal problems for certain classes of analytic functions, Ann. Polon. Math., 28 (1973), 297-326. 10.4064/AP-28-3-297-326
  • Kanas, S., Wisniowska, A., Conic domains and starlike functions, Rev. Roumaine Math. Pures Appl., 45 (2000), 647-657.
  • Miller, S. S., Mocanu, P. T., Differential Subordinations Theory and Applications, Series on Monographs and Textbooks in Pure and Appl Math, No. 255 Marcel Dekker, Inc., New York, 2000. https://doi.org/10.1201/9781482289817
  • Noor, K. I., Malik, S. N., On coefficient inequalities of functions associated with conic domains, Comp. Math. Appl., 62 (2011), 2209-2217. https://doi.org/10.1016/j.camwa.2011.07.006
  • Raina, R. K., Deepak, B., Some properties of a new class of analytic functions defined in terms of a Hadamard product, J. Inequal Pure Appl. Math., 9 (2008), 1-9.
  • Ronning, F., Uniformly convex functions and a corresponding class of starlike functions, Proc. Amer. Math. Soc., 118 (1993), 189-196. https://doi.org/10.2307/2160026
  • Silverman, H., Univalent functions with negative coefficients, Proc. Amer. Math. Soc., 51 (1975), 109-116.
  • Srivastava, H. M., Attiya, A. A., Some subordination results associated with certain subclass of analytic functions, J. Inequal Pure Appl. Math., 5(4) (2004), 1-6.
  • Wilf, H. S., Subordinating factor sequence for convex maps of the unit circle, Proc. Amer. Math. Soc., 129 (1961), 689-693.
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Research Article
Yazarlar

Syed Zakar Hussain Bukhari 0000-0002-5243-4252

Aamir Shahzad 0000-0001-5255-0176

Yayımlanma Tarihi 30 Mart 2023
Gönderilme Tarihi 23 Ocak 2022
Kabul Tarihi 31 Mayıs 2022
Yayımlandığı Sayı Yıl 2023 Cilt: 72 Sayı: 1

Kaynak Göster

APA Hussain Bukhari, S. Z., & Shahzad, A. (2023). Hadamard product of holomorphic mappings associated with the conic shaped domain. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 72(1), 105-117. https://doi.org/10.31801/cfsuasmas.1061950
AMA Hussain Bukhari SZ, Shahzad A. Hadamard product of holomorphic mappings associated with the conic shaped domain. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Mart 2023;72(1):105-117. doi:10.31801/cfsuasmas.1061950
Chicago Hussain Bukhari, Syed Zakar, ve Aamir Shahzad. “Hadamard Product of Holomorphic Mappings Associated With the Conic Shaped Domain”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72, sy. 1 (Mart 2023): 105-17. https://doi.org/10.31801/cfsuasmas.1061950.
EndNote Hussain Bukhari SZ, Shahzad A (01 Mart 2023) Hadamard product of holomorphic mappings associated with the conic shaped domain. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72 1 105–117.
IEEE S. Z. Hussain Bukhari ve A. Shahzad, “Hadamard product of holomorphic mappings associated with the conic shaped domain”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 72, sy. 1, ss. 105–117, 2023, doi: 10.31801/cfsuasmas.1061950.
ISNAD Hussain Bukhari, Syed Zakar - Shahzad, Aamir. “Hadamard Product of Holomorphic Mappings Associated With the Conic Shaped Domain”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72/1 (Mart 2023), 105-117. https://doi.org/10.31801/cfsuasmas.1061950.
JAMA Hussain Bukhari SZ, Shahzad A. Hadamard product of holomorphic mappings associated with the conic shaped domain. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2023;72:105–117.
MLA Hussain Bukhari, Syed Zakar ve Aamir Shahzad. “Hadamard Product of Holomorphic Mappings Associated With the Conic Shaped Domain”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 72, sy. 1, 2023, ss. 105-17, doi:10.31801/cfsuasmas.1061950.
Vancouver Hussain Bukhari SZ, Shahzad A. Hadamard product of holomorphic mappings associated with the conic shaped domain. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2023;72(1):105-17.

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