Research Article
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A new approach to the bi-univalent analytic functions connected with q-analogue of Noor integral operator

Year 2021, Volume: 70 Issue: 2, 940 - 949, 31.12.2021

Arzu Akgül

https://doi.org/10.31801/cfsuasmas.846485
Cited By: 1

Abstract

Recently, q-analogue of Noor integral operator and other special operators became importance in the field of Geometric Function Theory. In this study, by connecting this operators and the principle of subordination we introduced an interesting class of bi-univalent functions and obtained coefficient estimates for this new class.

Keywords

Bi-univalent analytic functions Noor integral operator coefficient estimates subordination

References

  • Akgül, A., Sakar, F. M., A certain subclass of bi-univalent analytic functions introduced by means of the q-analogue of Noor integral operator and Horadam polynomials, Turkish Journalof Mathematics, 43(5) (2019), 2275-2286. https://doi.org/10.3906/mat-1905-17.
  • Aldweby, H., Darus, M., A subclass of harmonic univalent functions associated with q-analogue of Dziok-Srivastava operator, ISRN Mathematical Analysis, 2013 (2013), Article ID 382312, 6 pages. https://doi.org/10.1155/2013/382312
  • Altınkaya, Ş., Inclusion properties of Lucas polynomials for bi-univalent functions introduced through the q-analogue of Noor integral operator, Turkish Journal of Mathematics. 43(2) (2019), 620-629. doi:10.3906/mat-1805-86, https://doi.10.3906/mat-1805-86
  • Arif, M., Ul Haq M, Liu J-L., Subfamily of univalent functions associated with q-analogue of Noor integral operator, J Funct Spaces 2018 (2018), 1-5. https://doi.org/10.1155/2018/3818915
  • Bulut, S.,Coefficient estimates for a class of analytic and bi-univalent functions, Novi Sad J. Math. 43(2) (2013), 59-65.
  • Duren, P. L., Univalent Functions, vol. 259 of Grundlehren der Mathematischen Wissenschaften, Springer, New York, NY, USA, 1983.
  • Brannan, D. A., Taha, T. S., On some classes of bi-univalent functions, in Mathematical Analysis and Its Applications, S. M. Mazhar, A. Hamoui, and N. S. Faour, Eds., vol. 3 of KFAS Proceedings Series, pp. 53-60, Pergamon Press, Elsevier Science, Oxford, UK, 1988.
  • Brannan, D. A., Taha, T. S., On some classes of bi-univalent functions, Studia Universitatis Babeş-Bolyai Mathematica, 31(2) (1986), 70-77.
  • Çağlar M., Orhan, H., Yağmur, N., Coefficient bounds for new subclasses of bi-univalent functions, Filomat, 27(7) (2013), 1165-1171. DOI 10.2298/FIL1307165C
  • Frasin, B. A., Aouf, M. K., New subclasses of bi-univalent functions, Applied Mathematics Letters, 24(9) (2011), 1569-1573. doi:10.1016/j.aml.2011.03.048, http://dx.doi.org/10.1016/j.joems.2012.08.020.
  • Goyal, S. P., Goswami, P., Estimate for initial Maclaurin coefficients of bi-univalent functions for a class defined by fractional derivatives, Journal of the Egyptian Mathematical Society, 20(3) (2012), 179-182. http://dx.doi.org/10.1016/j.joems.2012.08.020
  • Hayami, T., Owa, S., Coefficient bounds for bi-univalent functions, Pan-American Mathematical Journal, 22(4) (2012), 15-26.
  • Jackson, F.H., On q-functions and a certain difference operator, Trans. R. Soc. Edinb., 46 (1908), 253-281.
  • Orhan, H., Magesh, N., Balaji, V. K., Initial coefficient bounds for a general class of biunivalent functions, Filomat, 29(6) (2015), 1259-126. DOI 10.2298/FIL1506259O
  • Noor K. I., On new classes of integral operators, J Natur Geom, 16 (1999), 71-80.
  • Noor, K. I., Altinkaya, S.., Yalcin, S., Coefficient inequalities of analytic functions equipped with conic domains involving q-analogue of Noor integral operator, Tbilisi Mathematical Journal, 14(1) (2021), 1-14. DOI: 10.32513/tmj/1932200811
  • Goyal, S. P., Goswami, P., Estimate for initial Maclaurin coefficients of bi-univalent functions for a class defined by fractional derivatives, Journal of the Egyptian Mathematical Society, 20(3) (2012). http://dx.doi.org/10.1016/j.joems.2012.08.020
  • Rogosinski, W., On the coefficients of subordinate functions, Proceedings of the London Mathematical Society, 48(2) (1943), 48-82.
  • Salagean G. S., Subclasses of univalent functions, in Complex Analysis-Fifth Romanian-Finnish Seminar, Part 1 (Bucharest, 1981), vol. 1013 of Lecture Notes in Mathematics, 362-372, Springer, Berlin, Germany, 1983. https://doi.org/10.1007/BFb0066543
  • Srivastava, H. M., Mishra A. K., Gochhayat P., Certain subclasses of analytic and bi-univalent functions, Applied Mathematics Letters, 23(10) (2010), 1188-1192. doi:10.1016/j.aml.2010.05.009
  • Xu, Q. H., Gui, Y. C., Srivastava, H. M., Coefficient estimates for a certain subclass of analytic and bi-univalent functions, Applied Mathematics Letters, 25(6) (2012), 990-994. doi:10.1016/j.aml.2011.11.013
  • Xu, Q. H., Xiao, H. G., Srivastava, H. M., A certain general subclass of analytic and biunivalent functions and associated coefficient estimate problems, Applied Mathematics and Computation, 218(23) (2012), 11461-11465. http://dx.doi.org/10.1016/j.amc.2012.05.034

Year 2021, Volume: 70 Issue: 2, 940 - 949, 31.12.2021

Arzu Akgül

https://doi.org/10.31801/cfsuasmas.846485
Cited By: 1

Abstract

References

  • Akgül, A., Sakar, F. M., A certain subclass of bi-univalent analytic functions introduced by means of the q-analogue of Noor integral operator and Horadam polynomials, Turkish Journalof Mathematics, 43(5) (2019), 2275-2286. https://doi.org/10.3906/mat-1905-17.
  • Aldweby, H., Darus, M., A subclass of harmonic univalent functions associated with q-analogue of Dziok-Srivastava operator, ISRN Mathematical Analysis, 2013 (2013), Article ID 382312, 6 pages. https://doi.org/10.1155/2013/382312
  • Altınkaya, Ş., Inclusion properties of Lucas polynomials for bi-univalent functions introduced through the q-analogue of Noor integral operator, Turkish Journal of Mathematics. 43(2) (2019), 620-629. doi:10.3906/mat-1805-86, https://doi.10.3906/mat-1805-86
  • Arif, M., Ul Haq M, Liu J-L., Subfamily of univalent functions associated with q-analogue of Noor integral operator, J Funct Spaces 2018 (2018), 1-5. https://doi.org/10.1155/2018/3818915
  • Bulut, S.,Coefficient estimates for a class of analytic and bi-univalent functions, Novi Sad J. Math. 43(2) (2013), 59-65.
  • Duren, P. L., Univalent Functions, vol. 259 of Grundlehren der Mathematischen Wissenschaften, Springer, New York, NY, USA, 1983.
  • Brannan, D. A., Taha, T. S., On some classes of bi-univalent functions, in Mathematical Analysis and Its Applications, S. M. Mazhar, A. Hamoui, and N. S. Faour, Eds., vol. 3 of KFAS Proceedings Series, pp. 53-60, Pergamon Press, Elsevier Science, Oxford, UK, 1988.
  • Brannan, D. A., Taha, T. S., On some classes of bi-univalent functions, Studia Universitatis Babeş-Bolyai Mathematica, 31(2) (1986), 70-77.
  • Çağlar M., Orhan, H., Yağmur, N., Coefficient bounds for new subclasses of bi-univalent functions, Filomat, 27(7) (2013), 1165-1171. DOI 10.2298/FIL1307165C
  • Frasin, B. A., Aouf, M. K., New subclasses of bi-univalent functions, Applied Mathematics Letters, 24(9) (2011), 1569-1573. doi:10.1016/j.aml.2011.03.048, http://dx.doi.org/10.1016/j.joems.2012.08.020.
  • Goyal, S. P., Goswami, P., Estimate for initial Maclaurin coefficients of bi-univalent functions for a class defined by fractional derivatives, Journal of the Egyptian Mathematical Society, 20(3) (2012), 179-182. http://dx.doi.org/10.1016/j.joems.2012.08.020
  • Hayami, T., Owa, S., Coefficient bounds for bi-univalent functions, Pan-American Mathematical Journal, 22(4) (2012), 15-26.
  • Jackson, F.H., On q-functions and a certain difference operator, Trans. R. Soc. Edinb., 46 (1908), 253-281.
  • Orhan, H., Magesh, N., Balaji, V. K., Initial coefficient bounds for a general class of biunivalent functions, Filomat, 29(6) (2015), 1259-126. DOI 10.2298/FIL1506259O
  • Noor K. I., On new classes of integral operators, J Natur Geom, 16 (1999), 71-80.
  • Noor, K. I., Altinkaya, S.., Yalcin, S., Coefficient inequalities of analytic functions equipped with conic domains involving q-analogue of Noor integral operator, Tbilisi Mathematical Journal, 14(1) (2021), 1-14. DOI: 10.32513/tmj/1932200811
  • Goyal, S. P., Goswami, P., Estimate for initial Maclaurin coefficients of bi-univalent functions for a class defined by fractional derivatives, Journal of the Egyptian Mathematical Society, 20(3) (2012). http://dx.doi.org/10.1016/j.joems.2012.08.020
  • Rogosinski, W., On the coefficients of subordinate functions, Proceedings of the London Mathematical Society, 48(2) (1943), 48-82.
  • Salagean G. S., Subclasses of univalent functions, in Complex Analysis-Fifth Romanian-Finnish Seminar, Part 1 (Bucharest, 1981), vol. 1013 of Lecture Notes in Mathematics, 362-372, Springer, Berlin, Germany, 1983. https://doi.org/10.1007/BFb0066543
  • Srivastava, H. M., Mishra A. K., Gochhayat P., Certain subclasses of analytic and bi-univalent functions, Applied Mathematics Letters, 23(10) (2010), 1188-1192. doi:10.1016/j.aml.2010.05.009
  • Xu, Q. H., Gui, Y. C., Srivastava, H. M., Coefficient estimates for a certain subclass of analytic and bi-univalent functions, Applied Mathematics Letters, 25(6) (2012), 990-994. doi:10.1016/j.aml.2011.11.013
  • Xu, Q. H., Xiao, H. G., Srivastava, H. M., A certain general subclass of analytic and biunivalent functions and associated coefficient estimate problems, Applied Mathematics and Computation, 218(23) (2012), 11461-11465. http://dx.doi.org/10.1016/j.amc.2012.05.034
There are 22 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences, Applied Mathematics
Journal Section Research Article
Authors

Arzu Akgül 0000-0001-7934-0339

Submission Date December 25, 2020
Acceptance Date April 25, 2021
Publication Date December 31, 2021
Published in Issue Year 2021 Volume: 70 Issue: 2

Cite

APA Akgül, A. (2021). A new approach to the bi-univalent analytic functions connected with q-analogue of Noor integral operator. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 70(2), 940-949. https://doi.org/10.31801/cfsuasmas.846485
AMA Akgül A. A new approach to the bi-univalent analytic functions connected with q-analogue of Noor integral operator. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. December 2021;70(2):940-949. doi:10.31801/cfsuasmas.846485
Chicago Akgül, Arzu. “A New Approach to the Bi-Univalent Analytic Functions Connected With Q-Analogue of Noor Integral Operator”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70, no. 2 (December 2021): 940-49. https://doi.org/10.31801/cfsuasmas.846485.
EndNote Akgül A (December 1, 2021) A new approach to the bi-univalent analytic functions connected with q-analogue of Noor integral operator. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70 2 940–949.
IEEE A. Akgül, “A new approach to the bi-univalent analytic functions connected with q-analogue of Noor integral operator”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 70, no. 2, pp. 940–949, 2021, doi: 10.31801/cfsuasmas.846485.
ISNAD Akgül, Arzu. “A New Approach to the Bi-Univalent Analytic Functions Connected With Q-Analogue of Noor Integral Operator”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70/2 (December2021), 940-949. https://doi.org/10.31801/cfsuasmas.846485.
JAMA Akgül A. A new approach to the bi-univalent analytic functions connected with q-analogue of Noor integral operator. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2021;70:940–949.
MLA Akgül, Arzu. “A New Approach to the Bi-Univalent Analytic Functions Connected With Q-Analogue of Noor Integral Operator”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 70, no. 2, 2021, pp. 940-9, doi:10.31801/cfsuasmas.846485.
Vancouver Akgül A. A new approach to the bi-univalent analytic functions connected with q-analogue of Noor integral operator. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2021;70(2):940-9.

Cited By

Subordination Method for the Estimation of Certain Subclass of Analytic Functions Defined by the q -Derivative Operator
Journal of Function Spaces
https://doi.org/10.1155/2022/5078060

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

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