BI-G-STARLIKE FUNCTION ASSOCIATED WITH NORMALIZED ONE VARIABLE GEGENBAUER AND BELL-SHEFFER POLYNOMIALS INVOLVING GREGORY COEFFICIENTS
Keywords:
Analytic function, Combinaterial Analysis, Coefficient Estimate, FeketeSzego functional, Toeplitz determinant
Abstract
In this enquiry, applying normalized one variable Gegenbauer and Bell-Sheffer Polynomials, the authors introduce a new class of bi-G-starlike functions defined by Gregory and Caratheodory coefficients. Coefficient bounds for the new class were obtained and were consequently used to investigate the concept of Fekete-Szego functional and Toeplitz determinant in this direction.
References
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[30] S. O. Olatunji, H. Dutta. Subclasses of multivalent functions of complex order associated with sigmoid function and Bernoulli lemniscate. TWMS J. App. Eng. Math. 2020, 10, 360369.
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[32] P. E. Ricci, P. Natalini, G. Bretti. Sheffer and Brenke polynomials associated with generalized Bell numbers. Jnanabha Vijnana Parishad India (2017), 337-352.
[33] H.M. Srivastava, A.K. Mishira, P. Gochhayat. Certain subclasses of analytic and biunivalent functions. Appl. Math. Lett. 23 (2010), no. 10, 11881192
[34] E. C. Titmarsh. The theory functions (1939) E.d. Oxford Uni. Press. Amen.House London
[2] A.Amourah, B.A. Frasin, T. Abdeljawad. Fekete-Szeg inequality for analytic and bi-univalent functions subordinate to Gegenbauer polynomials. J. Funct. Spaces 2021, 2021, 5574673.
[3] A. Amourah, M. Alomari, F. Yousef, A.Alsoboh. Consolidation of a Certain Discrete Probability Distribution with a Subclass of Bi-Univalent Functions Involving Gegenbauer Polynomials. Math. Probl. Eng. 2022, 2022, 6354994.
[4] J.A Antonino. Strong differential subordination and applications to univalency conditions. J. Korean Math. Soc. 2006, 43, 311322.
[5] J.A. Antonino, and S. Romaguera. Strong differential subordination to Briot-Bouquet differential equations. J. Diff. Equ. 1994, 114, 101105.
[6] I.T Awolere. Hankel determinant for bi-Bazelevic function involing error and Sigmoid function defined by derivative calculus via Chebyshev polynomials. Journal of Fractional Calcu- lus and Applications, Vol. 11(2) July 2020, PP-208-217.
[7] I.T. Awolere, S. Ibrahim-Tiamiyu. New classes of bi-univalent pseudo Starlike function using Alhindi-Darus generalized hypergeometric function. J. Nigerian Assoc. Math. Phys. (2017) 40 65(72).
[8] I. T. Awolere and A.T.Oladipo. Determinant for bi-univalent of pseudo starlikeness for certain class of analytic univalent functions. Libertas Mathematica (new series), Volume 39, (2019) No. 2, 27-43.
[9] I.T. Awolere and A.T.Oladipo. Coefficients of bi-univalent functions involving psedo- starlikeness associated with Chebyshev polynomials. Khayyam J.Math.5, (2019) no 1, 140- 149.
[10] I.T. Awolere, A.T. Oladipo and S. Altinkaya. Application of Gegenbauer Polynomials with two variables to bi-unvalency of generalized discrete probability distribution via zero-truncated Poisson distribution series. Sahand Communicationin Mathematical Anal- ysis(SCMA), (2024) Vol. 21 No. 3, 65-88.
[11] K.O. Babalola. On pseudo-starlike functions. J. Class. Anal. 2013, 3,137147.
[12] H. Bavinck,G. Hooghiemstra, E. De Waard, An application of Gegenbauer polynomials in queueing theory. Int. J. Comput. Appl. Math. 1993, 49, 110.
[13] E. D. Belokolos, A. I Bobenko, V.Z, Enolskii and A.R. Algebro Geometric Approach to non-linear integrable equations New York Springer.
[14] L. De Branges. A proof of the Bieberbach conjecture. Acta Math. 1985, 154, 137152.
[15] Alexander, J.W. Functions which map the interior of the unit circle upon simple region. Ann. Math. 1915, 17, 1222.
[16] D.A. Brannan and S.T. Taha. On some classes of bi-univalent functions. Studia Univ.
Babes-Bolyai Math. 31(2) (1986), 70-77
[17] L. Bieberbach. ber die koeffizienten derjenigen Potenzreihen, welche eine schlichte Abbildung des Einheitskreises vermitteln. Sitzungsber. Preuss. Akad. Wiss. Phys.-Math. Kl. 1916, 138, 940955.
[18] G. Bretti, P. Natalini, P.F. Ricci, A new set of Sheffer-Bell polynomials and logarithm numbers. Georgian Math. J. 2018, in print
[19] P. L. Duren. Univalent functions. Volume 259 of Grundlehren der mathematischen Wissenschaften. Springer Verlag, New York, NY.
[20] B. A. Frasin. Suubodination results for certain class of analytic functions defined by a linear operator. Journal of Inequalities Pure Applied Mathematics, Volume 7, Issue 4 (2006), Article 134, 1-7.
[21] A.M. Gbolagade and I.T. Awolere. Coefficient Estimates of Certain Subclasses of bi- Bazilevic Functions Associated with Chebyshev Polynomials and Mittag-Leffler Function. Earthline Journal of Mathematical Sciences, (2021) Vol. 5, No. 2: 365 376.
[22] A. M. Gbolagade and I. T. Awolere. Generalized distribution for bi-univalent functions defined by error and Poisson distribution via Bell number. COAST Journal of the School of Science, (2024) Vol. 6(2): 1120-1128
[23] A. M. Gbolagade, T. M. Asiru, and I. T. Awolere. Coefficient bounds of bi-univalent function involving pseudo-starlikeness associated with Sigmoid function defined by Salagean operator via Chebyshev polynomial. International Journal of Mathematics and Computer Research. Vol. 12(1): 3955-3965
[24] P. Koebe. ber die Uniformisierung beliebiger analytischer Kurven. Nachr. Kgl. Ges. Wiss. Gtt. Math-Phys. Kl. 1907, 1907,191210.
[25] M. Lewin. On the coefficient problem for bi-univalent functions. Proc. Amer. Math. Soc. 18 (1967), no. 1, 63(68).
[26] G. Murugusundaramoorthy , K. Vijaya and T. Bulboac. ”Initial Coefficient Bounds for Bi-Univalent Functions Related to Gregory Coefficients”. Mathematics, MDPI, vol. 11(13), pages 1-16, June 2023.
[27] P. Natalini,P.E. Ricci. Remarks on Bell and higher order Bell polynomials and numbers. Cogent Math. (2016), 3, 1-15
[28] P. Natalini, P. E. Ricci. Higher order Bell polynomials and the relevant integer sequences. Appl. Anal. Discret. Math. (2017), 11, 327-339.
[29] P. Natalini, and P.E.Ricci, New Bell-Sheffer polynomial sets. Axioms 2018, 7,71; doi: 10.3390/axioms7040071, 1-10
[30] S. O. Olatunji, H. Dutta. Subclasses of multivalent functions of complex order associated with sigmoid function and Bernoulli lemniscate. TWMS J. App. Eng. Math. 2020, 10, 360369.
[31] S. O. Olatunji, M. O. Oluwayemi, Oros, G.I. Coefficient Results concerning a New Class of Functions Associated Gegenbauer Polynomials and Convolution in Terms of Subordination. Axioms 2023, 12, 360
[32] P. E. Ricci, P. Natalini, G. Bretti. Sheffer and Brenke polynomials associated with generalized Bell numbers. Jnanabha Vijnana Parishad India (2017), 337-352.
[33] H.M. Srivastava, A.K. Mishira, P. Gochhayat. Certain subclasses of analytic and biunivalent functions. Appl. Math. Lett. 23 (2010), no. 10, 11881192
[34] E. C. Titmarsh. The theory functions (1939) E.d. Oxford Uni. Press. Amen.House London
Published
2025-12-29
How to Cite
AWOLERE, I. T., & GBOLAGADE, A. M. (2025). BI-G-STARLIKE FUNCTION ASSOCIATED WITH NORMALIZED ONE VARIABLE GEGENBAUER AND BELL-SHEFFER POLYNOMIALS INVOLVING GREGORY COEFFICIENTS. Unilag Journal of Mathematics and Applications, 5(2), 65 - 79. Retrieved from https://lagjma.unilag.edu.ng/article/view/2787
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Articles
Copyright (c) 2025 IBRAHIM TUNJI AWOLERE, ADENIYI MUSIBAU GBOLAGADE
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