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ON THE CHEBYSHEV POLYNOMIAL COEFFICIENT PROBLEM OF BI-BAZILEVI C FUNCTIONS

Yıl 2020, Cilt: 10 Sayı: 1, 251 - 258, 01.01.2020

Öz

A function said to be bi-Bazilevic in the open unit disk U if both the function and its inverse are Bazilevic there. In this paper, we will study a newly constructed class of bi-Bazilevic functions. Furthermore, we establish Chebyshev polynomial bounds for the coecients, and get Fekete-Szego inequality, for the class B ; t .

Kaynakça

  • Altınkaya, S¸. and Yal¸cın, S., (2014), Fekete-Szeg¨o inequalities for certain classes of bi-univalent func- tions, Internat. Scholar. Res. Notices, (2014) Article ID 327962, pp. 1-6.
  • Altınkaya, S¸. and Yal¸cın, S., (2015), Coefficient estimates for two new subclasses of bi-univalent functions with respect to symmetric points, J. Funct. Spaces, Article ID 145242 pp. 1-5.
  • Altınkaya, S¸. and Yal¸cın, S., (2015), Faber polynomial coefficient bounds for a subclass of bi-univalent functions, C.R. Acad. Sci. Paris, Ser. I, 353, pp. 1075-1080.
  • Altınkaya, S¸. and Yal¸cın, S., (2015), Coefficient bounds for a subclass of bi-univalent functions, TWMS J. Pure Appl. Math., 6, pp. 180-185.
  • Altınkaya, S¸. and Yal¸cın, S., (2016), On the Chebyshev polynomial bounds for classes of univalent functions, Khayyam J. Math., 2, pp. 1-5.
  • Brannan, D. A. and Taha, T. S., (1986), On some classes of bi-univalent functions, Stud. Univ. Babe¸s-Bolyai Math., 31, pp. 70-77.
  • Brannan, D. A. and Clunie, J. G., (1980), Aspects of comtemporary complex analysis, (Proceedings of the NATO Advanced Study Instute Held at University of Durham:July 1-20, 1979), New York: Academic Press.
  • C¸ a˘glar, M., Deniz, E. and Srivastava, H.M., (2017), Second Hankel determinant for certain subclasses of bi-univalent functions, Turk J Math, 41, pp. 694-706.
  • Dziok, J., Raina, R. K. and Sokol, J., (2015), Application of Chebyshev polynomials to classes of analytic functions, C. R. Acad. Sci. Paris, Ser. I, 353, pp. 433-438.
  • Duren, P. L., (1983), Univalent Functions, Grundlehren der Mathematischen Wissenschaften, Springer, New York, USA, 259.
  • Doha, E. H., (1994), The first and second kind Chebyshev coefficients of the moments of the general- order derivative of an infinitely differentiable function, Intern. J. Comput. Math., 51, pp. 21-35.
  • Fekete, M. and Szeg¨o, G., (1933), Eine Bemerkung ber Ungerade Schlichte Funktionen, J. London Math. Soc., [s1-8 (2)], pp. 85-89.
  • Hamidi, S. G. and Jahangiri, J. M., (2014), Faber polynomial coefficient estimates for analytic bi- close-to-convex functions, C. R. Acad. Sci. Paris, Ser. I, 352, pp. 17-20.
  • Hayami, T. and Owa, S., (2012), Coefficient bounds for bi-univalent functions, Pan Amer. Math., 22, pp. 15-26.
  • Kowalczyk, B., Lecko, A. and Srivastava, H. M., (2017), A note on the Fekete-Szeg¨o problem for close-toconvex functions with respect to convex functions, Publications de l’Institut Math´ematique, Nouvelle S´erie, 101[115], pp. 143-149.
  • Kim, Y.C. and Srivastava, H. M., (2006), The Hardy space for a certain subclass of Bazileviˇc functions, Appl. Math. Comput., 183, pp. 1201-1207
  • Lewin, M., (1967), On a coefficient problem for bi-univalent functions, Proc. Amer. Math. Soc., 18, pp. 63-68.
  • Mason, J. C., (1967), Chebyshev polynomials approximations for the L-membrane eigenvalue problem, SIAM J. Appl. Math., 15, pp. 172-186.
  • Netanyahu, E., (1969), The minimal distance of the image boundary from the origin and the second coefficient of a univalent function in |z| < 1, Arch. Ration. Mech. Anal., 32, pp. 100-112.
  • Singh, R., (1973), On Bazilevi˘c Functions, Proc. Amer. Math. Soc., 38, pp. 261-271.
  • Srivastava, H. M., Mishra, A. K. and Gochhayat, P., (2010), Certain subclasses of analytic and bi- univalent functions, Appl. Math. Lett., 23, pp. 1188-1192.
  • Srivastava, H. M. and Bansal, D., (2015), Coefficient estimates for a subclass of analytic and bi- univalent functions, J. Egyptian Math. Soc., 23, pp. 242-246.
  • Srivastava, H. M., Bulut, S., C¸ a˘glar, M. and Ya˘gmur, N., (2013), Coefficient estimates for a general subclass of analytic and bi-univalent functions, Filomat, 27, pp. 831-842.
  • Srivastava, H. M., Joshi, S. B., Joshi, S. S. and Pawar, H., (2016), Coefficient estimates for certain subclasses of meromorphically bi-univalent functions, Palest. J. Math., 5, pp. 250-258.
  • Srivastava, H. M., Gaboury, S. and Ghanim, F., (2016), Initial coefficient estimates for some subclasses of m-fold symmetric bi-univalent functions, Acta Math. Sci. Ser. B Engl. Ed., 36, pp. 863–871.
  • Srivastava, H. M., Gaboury, S. and Ghanim, F., (2017), Coefficient estimates for some general sub- classes of analytic and bi-univalent functions, Afrika Matematika, 28, pp. 693-706.
  • Srivastava, H. M., Mishra, A. K. and Das, M. K., (2001), The Fekete-Szeg¨o problem for a subclass of close-to-convex functions, Complex Var. Theory Appl., 44, pp. 145-163.
  • Srivastava, H. M., Murugusundaramoorthy, G. and Vijaya, K., (2013), Coefficient estimates for some families of bi-Bazileviˇc functions of the Ma-Minda type involving the Hohlov operator, J. Class. Anal., 2, pp. 167-181.
  • Srivastava, H. M., S¨umer Eker, S. and Ali, R. M., (2015), Coefficient bounds for a certain class of analytic and bi-univalent functions, Filomat, 29, pp. 1839-1845.
  • Srivastava, H. M., Sivasubramanian, S. and Sivakumar, R., (2014), Initial coefficient bounds for a subclass of m-fold symmetric bi-univalent functions, Tbilisi Math. J., 7, pp. 1-10.
  • Tang, H., Srivastava, H. M., Sivasubramanian, S. and Gurusamy, P., (2016), The Fekete-Szeg¨o func- tional problems for some subclasses of m-fold symmetric bi-univalent functions, Journal of Mathe- matical Inequalities, 10, pp. 1063-1092.
  • Xu, Q.-H., Gui, Y.-C. and Srivastava, H. M., (2012), Coefficient estimates for a certain subclass of analytic and bi-univalent functions, Appl. Math. Lett., 25, pp. 990-994.
  • Xu, Q.-H., Xiao, H.-G. and Srivastava, H. M., (2012), A certain general subclass of analytic and bi-univalent functions and associated coefficient estimates problems, Appl. Math. Comput., 218, pp. 11461-11465.
  • Zaprawa, P., (2014), On Fekete-Szeg problem for classes of bi-univalent functions, Bull. Belg. Math. Soc. Simon Stevin, 21, pp. 169-178.
  • Zireh, A., Hajiparvaneh, S. and Bulut, S., (2016), Faber polynomial coefficient estimates for a com- prehensive subclass of analytic bi-univalent functions defined by subordination, Bull. Belg. Math. Soc. Simon Stevin, 23, pp. 487-504.
  • S¸ahsene Altınkaya for the photography and short autobiography, see TWMS J. App. Eng. Math.V.8, N.1a, 2018.
Yıl 2020, Cilt: 10 Sayı: 1, 251 - 258, 01.01.2020

Öz

Kaynakça

  • Altınkaya, S¸. and Yal¸cın, S., (2014), Fekete-Szeg¨o inequalities for certain classes of bi-univalent func- tions, Internat. Scholar. Res. Notices, (2014) Article ID 327962, pp. 1-6.
  • Altınkaya, S¸. and Yal¸cın, S., (2015), Coefficient estimates for two new subclasses of bi-univalent functions with respect to symmetric points, J. Funct. Spaces, Article ID 145242 pp. 1-5.
  • Altınkaya, S¸. and Yal¸cın, S., (2015), Faber polynomial coefficient bounds for a subclass of bi-univalent functions, C.R. Acad. Sci. Paris, Ser. I, 353, pp. 1075-1080.
  • Altınkaya, S¸. and Yal¸cın, S., (2015), Coefficient bounds for a subclass of bi-univalent functions, TWMS J. Pure Appl. Math., 6, pp. 180-185.
  • Altınkaya, S¸. and Yal¸cın, S., (2016), On the Chebyshev polynomial bounds for classes of univalent functions, Khayyam J. Math., 2, pp. 1-5.
  • Brannan, D. A. and Taha, T. S., (1986), On some classes of bi-univalent functions, Stud. Univ. Babe¸s-Bolyai Math., 31, pp. 70-77.
  • Brannan, D. A. and Clunie, J. G., (1980), Aspects of comtemporary complex analysis, (Proceedings of the NATO Advanced Study Instute Held at University of Durham:July 1-20, 1979), New York: Academic Press.
  • C¸ a˘glar, M., Deniz, E. and Srivastava, H.M., (2017), Second Hankel determinant for certain subclasses of bi-univalent functions, Turk J Math, 41, pp. 694-706.
  • Dziok, J., Raina, R. K. and Sokol, J., (2015), Application of Chebyshev polynomials to classes of analytic functions, C. R. Acad. Sci. Paris, Ser. I, 353, pp. 433-438.
  • Duren, P. L., (1983), Univalent Functions, Grundlehren der Mathematischen Wissenschaften, Springer, New York, USA, 259.
  • Doha, E. H., (1994), The first and second kind Chebyshev coefficients of the moments of the general- order derivative of an infinitely differentiable function, Intern. J. Comput. Math., 51, pp. 21-35.
  • Fekete, M. and Szeg¨o, G., (1933), Eine Bemerkung ber Ungerade Schlichte Funktionen, J. London Math. Soc., [s1-8 (2)], pp. 85-89.
  • Hamidi, S. G. and Jahangiri, J. M., (2014), Faber polynomial coefficient estimates for analytic bi- close-to-convex functions, C. R. Acad. Sci. Paris, Ser. I, 352, pp. 17-20.
  • Hayami, T. and Owa, S., (2012), Coefficient bounds for bi-univalent functions, Pan Amer. Math., 22, pp. 15-26.
  • Kowalczyk, B., Lecko, A. and Srivastava, H. M., (2017), A note on the Fekete-Szeg¨o problem for close-toconvex functions with respect to convex functions, Publications de l’Institut Math´ematique, Nouvelle S´erie, 101[115], pp. 143-149.
  • Kim, Y.C. and Srivastava, H. M., (2006), The Hardy space for a certain subclass of Bazileviˇc functions, Appl. Math. Comput., 183, pp. 1201-1207
  • Lewin, M., (1967), On a coefficient problem for bi-univalent functions, Proc. Amer. Math. Soc., 18, pp. 63-68.
  • Mason, J. C., (1967), Chebyshev polynomials approximations for the L-membrane eigenvalue problem, SIAM J. Appl. Math., 15, pp. 172-186.
  • Netanyahu, E., (1969), The minimal distance of the image boundary from the origin and the second coefficient of a univalent function in |z| < 1, Arch. Ration. Mech. Anal., 32, pp. 100-112.
  • Singh, R., (1973), On Bazilevi˘c Functions, Proc. Amer. Math. Soc., 38, pp. 261-271.
  • Srivastava, H. M., Mishra, A. K. and Gochhayat, P., (2010), Certain subclasses of analytic and bi- univalent functions, Appl. Math. Lett., 23, pp. 1188-1192.
  • Srivastava, H. M. and Bansal, D., (2015), Coefficient estimates for a subclass of analytic and bi- univalent functions, J. Egyptian Math. Soc., 23, pp. 242-246.
  • Srivastava, H. M., Bulut, S., C¸ a˘glar, M. and Ya˘gmur, N., (2013), Coefficient estimates for a general subclass of analytic and bi-univalent functions, Filomat, 27, pp. 831-842.
  • Srivastava, H. M., Joshi, S. B., Joshi, S. S. and Pawar, H., (2016), Coefficient estimates for certain subclasses of meromorphically bi-univalent functions, Palest. J. Math., 5, pp. 250-258.
  • Srivastava, H. M., Gaboury, S. and Ghanim, F., (2016), Initial coefficient estimates for some subclasses of m-fold symmetric bi-univalent functions, Acta Math. Sci. Ser. B Engl. Ed., 36, pp. 863–871.
  • Srivastava, H. M., Gaboury, S. and Ghanim, F., (2017), Coefficient estimates for some general sub- classes of analytic and bi-univalent functions, Afrika Matematika, 28, pp. 693-706.
  • Srivastava, H. M., Mishra, A. K. and Das, M. K., (2001), The Fekete-Szeg¨o problem for a subclass of close-to-convex functions, Complex Var. Theory Appl., 44, pp. 145-163.
  • Srivastava, H. M., Murugusundaramoorthy, G. and Vijaya, K., (2013), Coefficient estimates for some families of bi-Bazileviˇc functions of the Ma-Minda type involving the Hohlov operator, J. Class. Anal., 2, pp. 167-181.
  • Srivastava, H. M., S¨umer Eker, S. and Ali, R. M., (2015), Coefficient bounds for a certain class of analytic and bi-univalent functions, Filomat, 29, pp. 1839-1845.
  • Srivastava, H. M., Sivasubramanian, S. and Sivakumar, R., (2014), Initial coefficient bounds for a subclass of m-fold symmetric bi-univalent functions, Tbilisi Math. J., 7, pp. 1-10.
  • Tang, H., Srivastava, H. M., Sivasubramanian, S. and Gurusamy, P., (2016), The Fekete-Szeg¨o func- tional problems for some subclasses of m-fold symmetric bi-univalent functions, Journal of Mathe- matical Inequalities, 10, pp. 1063-1092.
  • Xu, Q.-H., Gui, Y.-C. and Srivastava, H. M., (2012), Coefficient estimates for a certain subclass of analytic and bi-univalent functions, Appl. Math. Lett., 25, pp. 990-994.
  • Xu, Q.-H., Xiao, H.-G. and Srivastava, H. M., (2012), A certain general subclass of analytic and bi-univalent functions and associated coefficient estimates problems, Appl. Math. Comput., 218, pp. 11461-11465.
  • Zaprawa, P., (2014), On Fekete-Szeg problem for classes of bi-univalent functions, Bull. Belg. Math. Soc. Simon Stevin, 21, pp. 169-178.
  • Zireh, A., Hajiparvaneh, S. and Bulut, S., (2016), Faber polynomial coefficient estimates for a com- prehensive subclass of analytic bi-univalent functions defined by subordination, Bull. Belg. Math. Soc. Simon Stevin, 23, pp. 487-504.
  • S¸ahsene Altınkaya for the photography and short autobiography, see TWMS J. App. Eng. Math.V.8, N.1a, 2018.
Toplam 36 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

Ş. Altınkaya Bu kişi benim

S. Yalçin

Yayımlanma Tarihi 1 Ocak 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 10 Sayı: 1

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