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Notes on some classes of spirallike functions associated with the $q$-integral operator

Yıl 2024, Cilt: 53 Sayı: 1, 53 - 61, 29.02.2024

Tuğba Yavuz Şahsene Altınkaya

https://doi.org/10.15672/hujms.1180981

Öz

The object of the present paper is to find the essential properties for certain subfamilies of analytic and spirallike functions which are generated by $q$-integral operator. Further, we derive membership relations for functions belong to these subfamilies, and also we determine coefficient estimates.

Anahtar Kelimeler

Spirallike function convolution $q$-integral operator

Kaynakça

  • [1] O. Ahuja and A. Çetinkaya, Use of quantum calculus approach in mathematical sciences and its role in geometric function theory, AIP Conference Proceedings, 2095 (1), 1-14, 2019.
  • [2] O. Ahuja, A. Çetinkaya and N. K. Jain, Analytic functions with conic domains associated with certain generalized $q$-integral operator, arXiv preprint arXiv:2012.13776.
  • [3] S. Altınkaya, On the inclusion properties for $\vartheta $-spirallike functions involving both Mittag-Leffler and Wright function, Turkish J. Math. 46 (3), 1119-1131, 2022.
  • [4] M. K. Aouf and T. M. Seoudy, Convolution properties for classes of bounded analytic functions with complex order defined by $q$-derivative operator, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM, 113 (2), 1279-1288, 2019.
  • [5] S. D. Bernardi, Convex and starlike univalent functions, Trans. Amer. Math. Soc. 135, 429–446, 1969.
  • [6] S. Bulut, Certain subclasses of analytic and bi-univalent functions involving the $q$-derivative operator, Commun. Fac. Sci. Univ. Ank. Ser. A1. Math. Stat. 66 (1), 108- 114, 2017.
  • [7] G. Gasper and M. Rahman, Basic hypergeometric series, second edition, Encyclopedia of Mathematics and its Applications, 96, Cambridge University Press, Cambridge, 2004.
  • [8] M. Govindaraj and S. Sivasubramanian, On a class of analytic functions related to conic domains involving $q$-calculus,Anal. Math. 43 (3), 475-487, 2017.
  • [9] F. H. Jackson, On $q$-functions and a certain difference operator, Earth Environ. Sci. Trans. R. Soc. Edinb. 46, 253–281, 1908.
  • [10] F. H. Jackson, On $q$-definite integrals, Q. J. Pure Appl. Math. 14, 193-203, 1910.
  • [11] S. Mahmood, N. Raza, E. S. A. Abujarad, G. Srivastava, H. M. Srivastava, S. N. Malik, Geometric properties of certain classes of analytic functions associated with $q$-integral operators, Symmetry, 11 (5), 1-14, 2019.
  • [12] N. Mustafa and S. Korkmaz, The sharp inequality for the coefficients of certain subclass of analytic functions defined by $q$-derivative, Journal of Scientific and Engineering Research 7 (4), 209-218, 2020.
  • [13] K. I. Noor, S. Riaz and M. A. Noor, On $q$-Bernardi integral operator, TWMS J. Pure Appl. Math. 8 (1), 3–11, 2017.
  • [14] S. D. Purohit and R. K. Raina, Certain subclasses of analytic functions associated with fractional $q$-calculus operators, Math. Scand. 109 (1), 55-70, 2011.
  • [15] M. Raza, H. M. Srivastava, M. Arif and K. Ahmad, Coefficient estimates for a certain family of analytic functions involving a $q$-derivative operator, Ramanujan J. 55 (1), 53-71, 2022.
  • [16] Z. Shareef, S. Hussain and M. Darus, Convolution operators in the geometric function theory, J. Inequal. Appl. 2012 (213), 1-11, 2012.
  • [17] H. Silverman and E. M. Silvia, Subclasses of starlike functions subordinate to convex functions, Canad. J. Math. 1, 48-61, 1985.
  • [18] L. Spacek, Contribution a la theorie des fonctions univalentes, Casopis Pro Pestovani Matematiky a Fysiky, 62, 12–19, 1933.
  • [19] H. M. Srivastava, Univalent functions, fractional calculus, and associated generalized hypergeometric functions, in Univalent Functions, Fractional Calculus, and Their Applications, (H. M. Srivastava and S. Owa, Editors), Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane and Toronto, 1989.
  • [20] H. M. Srivastava, 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 (1), 327-344, 2020.
  • [21] Q. H. Xu, C. B. Lv, N. C. Luo and H. M. Srivastava, Sharp coefficient estimates for a certain general class of spirallike functions by means of differential subordination, Filomat, 27, 1351-1356, 2013.

Yıl 2024, Cilt: 53 Sayı: 1, 53 - 61, 29.02.2024

Tuğba Yavuz Şahsene Altınkaya

https://doi.org/10.15672/hujms.1180981

Öz

Kaynakça

  • [1] O. Ahuja and A. Çetinkaya, Use of quantum calculus approach in mathematical sciences and its role in geometric function theory, AIP Conference Proceedings, 2095 (1), 1-14, 2019.
  • [2] O. Ahuja, A. Çetinkaya and N. K. Jain, Analytic functions with conic domains associated with certain generalized $q$-integral operator, arXiv preprint arXiv:2012.13776.
  • [3] S. Altınkaya, On the inclusion properties for $\vartheta $-spirallike functions involving both Mittag-Leffler and Wright function, Turkish J. Math. 46 (3), 1119-1131, 2022.
  • [4] M. K. Aouf and T. M. Seoudy, Convolution properties for classes of bounded analytic functions with complex order defined by $q$-derivative operator, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM, 113 (2), 1279-1288, 2019.
  • [5] S. D. Bernardi, Convex and starlike univalent functions, Trans. Amer. Math. Soc. 135, 429–446, 1969.
  • [6] S. Bulut, Certain subclasses of analytic and bi-univalent functions involving the $q$-derivative operator, Commun. Fac. Sci. Univ. Ank. Ser. A1. Math. Stat. 66 (1), 108- 114, 2017.
  • [7] G. Gasper and M. Rahman, Basic hypergeometric series, second edition, Encyclopedia of Mathematics and its Applications, 96, Cambridge University Press, Cambridge, 2004.
  • [8] M. Govindaraj and S. Sivasubramanian, On a class of analytic functions related to conic domains involving $q$-calculus,Anal. Math. 43 (3), 475-487, 2017.
  • [9] F. H. Jackson, On $q$-functions and a certain difference operator, Earth Environ. Sci. Trans. R. Soc. Edinb. 46, 253–281, 1908.
  • [10] F. H. Jackson, On $q$-definite integrals, Q. J. Pure Appl. Math. 14, 193-203, 1910.
  • [11] S. Mahmood, N. Raza, E. S. A. Abujarad, G. Srivastava, H. M. Srivastava, S. N. Malik, Geometric properties of certain classes of analytic functions associated with $q$-integral operators, Symmetry, 11 (5), 1-14, 2019.
  • [12] N. Mustafa and S. Korkmaz, The sharp inequality for the coefficients of certain subclass of analytic functions defined by $q$-derivative, Journal of Scientific and Engineering Research 7 (4), 209-218, 2020.
  • [13] K. I. Noor, S. Riaz and M. A. Noor, On $q$-Bernardi integral operator, TWMS J. Pure Appl. Math. 8 (1), 3–11, 2017.
  • [14] S. D. Purohit and R. K. Raina, Certain subclasses of analytic functions associated with fractional $q$-calculus operators, Math. Scand. 109 (1), 55-70, 2011.
  • [15] M. Raza, H. M. Srivastava, M. Arif and K. Ahmad, Coefficient estimates for a certain family of analytic functions involving a $q$-derivative operator, Ramanujan J. 55 (1), 53-71, 2022.
  • [16] Z. Shareef, S. Hussain and M. Darus, Convolution operators in the geometric function theory, J. Inequal. Appl. 2012 (213), 1-11, 2012.
  • [17] H. Silverman and E. M. Silvia, Subclasses of starlike functions subordinate to convex functions, Canad. J. Math. 1, 48-61, 1985.
  • [18] L. Spacek, Contribution a la theorie des fonctions univalentes, Casopis Pro Pestovani Matematiky a Fysiky, 62, 12–19, 1933.
  • [19] H. M. Srivastava, Univalent functions, fractional calculus, and associated generalized hypergeometric functions, in Univalent Functions, Fractional Calculus, and Their Applications, (H. M. Srivastava and S. Owa, Editors), Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane and Toronto, 1989.
  • [20] H. M. Srivastava, 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 (1), 327-344, 2020.
  • [21] Q. H. Xu, C. B. Lv, N. C. Luo and H. M. Srivastava, Sharp coefficient estimates for a certain general class of spirallike functions by means of differential subordination, Filomat, 27, 1351-1356, 2013.
Toplam 21 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik
Yazarlar

Tuğba Yavuz 0000-0002-0490-9313

Şahsene Altınkaya 0000-0002-7950-8450

Erken Görünüm Tarihi 10 Ocak 2024
Yayımlanma Tarihi 29 Şubat 2024
Yayımlandığı Sayı Yıl 2024 Cilt: 53 Sayı: 1

Kaynak Göster

APA Yavuz, T., & Altınkaya, Ş. (2024). Notes on some classes of spirallike functions associated with the $q$-integral operator. Hacettepe Journal of Mathematics and Statistics, 53(1), 53-61. https://doi.org/10.15672/hujms.1180981
AMA Yavuz T, Altınkaya Ş. Notes on some classes of spirallike functions associated with the $q$-integral operator. Hacettepe Journal of Mathematics and Statistics. Şubat 2024;53(1):53-61. doi:10.15672/hujms.1180981
Chicago Yavuz, Tuğba, ve Şahsene Altınkaya. “Notes on Some Classes of Spirallike Functions Associated With the $q$-Integral Operator”. Hacettepe Journal of Mathematics and Statistics 53, sy. 1 (Şubat 2024): 53-61. https://doi.org/10.15672/hujms.1180981.
EndNote Yavuz T, Altınkaya Ş (01 Şubat 2024) Notes on some classes of spirallike functions associated with the $q$-integral operator. Hacettepe Journal of Mathematics and Statistics 53 1 53–61.
IEEE T. Yavuz ve Ş. Altınkaya, “Notes on some classes of spirallike functions associated with the $q$-integral operator”, Hacettepe Journal of Mathematics and Statistics, c. 53, sy. 1, ss. 53–61, 2024, doi: 10.15672/hujms.1180981.
ISNAD Yavuz, Tuğba - Altınkaya, Şahsene. “Notes on Some Classes of Spirallike Functions Associated With the $q$-Integral Operator”. Hacettepe Journal of Mathematics and Statistics 53/1 (Şubat 2024), 53-61. https://doi.org/10.15672/hujms.1180981.
JAMA Yavuz T, Altınkaya Ş. Notes on some classes of spirallike functions associated with the $q$-integral operator. Hacettepe Journal of Mathematics and Statistics. 2024;53:53–61.
MLA Yavuz, Tuğba ve Şahsene Altınkaya. “Notes on Some Classes of Spirallike Functions Associated With the $q$-Integral Operator”. Hacettepe Journal of Mathematics and Statistics, c. 53, sy. 1, 2024, ss. 53-61, doi:10.15672/hujms.1180981.
Vancouver Yavuz T, Altınkaya Ş. Notes on some classes of spirallike functions associated with the $q$-integral operator. Hacettepe Journal of Mathematics and Statistics. 2024;53(1):53-61.

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