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.
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
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
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
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
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 (December 2021), 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.