BI- UNIVALENT PROBLEM FOR CERTAIN GENERALIZED CLASS OF ANALYTIC FUNCTIONS INVOLVING Q-INTEGRAL OPERATOR ASSOCIATED WITH NEPHROID DOMAIN
Keywords:
Analytic, Starlike, Bounded Turning, q-Integral Operator, Nephroid Domain
Abstract
The authors in this article study a new subclass of bi-univalent functions involving q-integral operator associated with nephroid domain by using the concept of subordination and bi-linear fractional principles.We further employed our investigation to determine new coecient bounds and subsequently obtain the Fekete-Szego inequalities for functions belonging to the aforementioned subclass were obtained.
References
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[3] F. I. Akinwale and J.O. Hamzat Coefficient bounds for certain generalized class of analytic functions involving Bazil;evic type function and the Sigmoid function, J. Nig. Math. Phy. Vol. 62, Dec.,(2021), Issue, 1-8.
[4] A. Amourah, B.A. Frasin, T. Abdeijawad. Fekete-Szego Inequality for Analytic and Bi-univalent Functions Subordinate to Gegenbauer Polynomials , J. Funct. Spaces 2021, 2021, 5574673, 1-7.
[5] A. Amourah, B.A. Frasin, M. Ahmad, F. Yousef. Exploiting the Pascal Distribution Series and Gegenbauer Polynomials to Construct and Study a New Subclass of Analytic Bi-Univalent Functions , Symmetry 2022, 14, 147, 1-8.
[6] A. Arai, V. Gupta, and R. P. Agarwal. Applications of q-Calculus in Operator Theory , Springer, New York. NY, USA, (2013), 1 - 13.
[7] O.P. Ahuja, S. Kumar, Ravichandran. Applications of first order differential subordination for functions with positive real part , Stud. Univ. Babes-Bolyai Math. 63 (2018), no.3, 303-311.
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[9] A. Akgul, T. G. Shara. u; v- Lucas polynomial coefficient relations of the bi-univalent function class , Commun. Fac. Sci. Univ. Ank. Ser. AI MATH. stat. Volume 71, Number 4, (2022) pages 1121 - 1134. Doi:10.31801/cfsa.smas.1086809.
[10] S. Altinkaya, S. Yalcin. Coefficient bounds for a subclass of bi-univalent functions , 6(2015), 180 -185.
[11] S. Altinkaya, S. Yalcin. Estimates on Coefficients of a General Subclass of Bi-univalent Functions Associated with Symetric q- Derivative Operator by Means of the Chebyshev Polynomials , Asia Pac. J. Math. (2017), 8, 90 - 99.
[12] L. Bieberbach. Uber koezlenten Derjenigen Potenzreihen, Welche Eine Schlichtz Des Einheitskreises Vermitteln , Vol. 38, Sitzungsberichte der PreuBischen Akademie der Wissenschaften zu Berlin, 1916.
[13] S. Bulut. Coefficient Estimates for a Class of Analytic and Bi-univalent Functions ,Novi. Sal.J.Math. 2013, 2013,43, 59-65.
[14] R. Bucar, D. Breaz. On a new class of analytic functions with respect to symmetric points involving the q-derivative operator , In Journal of Physics: Conference Series, IOP Publishing,(2019), 1-8.
[15] T. Bulboara, P. Goswami. On some classes of bi-univalent functions , Studia Universitatis Babas-Bolyai Mathematica, 2(2015), 7 - 13.
[16] P. N. Chidera. New subclasses of the class of close - to - convex functions , Proceedings of the American Mathematical Society, ol. 62, no. 1, (1977), 37 -43.
[17] N.E. Cho, V. Kumar, S.S. Kumar, V. Ravichandran. Radius problems for starlike functions associated with sine functions , Bull. Iran, Math. Soc., 45 (2019), 213 - 232.
[18] L. De Branges. A proof of the Bieberbach conjecture , Acta.Math.154,(1985),137-152. http://dx.doi.org/10.1007/BF02392821
[19] K. Dhanalakshmi, S. Poongothai. Third Hankel determinant for a subclass of analytic univalent related to modi ed Nephroid domain ,International Journal of Mechanical Engineering,ol. 7, N0.4 April, 2022, 1-5. ISSN: 0974-5823.
[20] P.I. Duren, Univalent functions. Grundlehen der Mathematischan Wissenschaften 259: Springer: New York, Ny, USA; Berlin/Heidelberg, Germany;Tokyo,Japan, (1983).
[21] A.H. El-Qadeem, M.A. Mamon, I. S. Elshazly. Application of Einstein function on bi-univalent functions de ned on the unit disc, Symmetry, 14, 4(2022),758, 1-11.
[22] Ebrahim Analouei Adegani, Serap Bulut, Ahmad Zireh. Coefficient estimates for a subclass of analytic bi-univalent functions , Bull. Korean Math. Soc. 55 (2018), No. 2, 405 - 413.
[23] B.A. Frasin, M.K. Aouf. New subclasses of Bi-Univalent Functions, Appl. Math. lett (2011), 24, 1569 - 1573.
[24] O. Fagbemiro, J.O. Hamzat, M. T. Raji. A certain class of (j; k)- symmetric function involving sigmoid function defined by using subordination principle ,
Journal of the Nigerian Association of Mathematical Physics(2024), 39 - 46.
[25] O. Fagbemiro, M.T. Raji, J.O. Hamzat, A.T. Oladipo and B.I. Olajuwon. Coefficient
bounds for subclass of sigmoid functions involving subordination principle defined by Salagean Differential Operator, Covenant Journal of Physical and Life Sciences, Vol. 13, No. 1, June 2025, 1-16.
[26] M. Fekete, G. Szego. Eine Beemer Kung uber ungerade schlichte Functionen, Journal of the London Mathematical Sociebty, Volume 8, 85 89, 1933.
[27] A.W. Goodman. Univalent functions. Vol. 1, Mariner Publishing Co., Inc., Tampa, FL, 1983.
[28] S.P. Goyal and R. Kumar. Coefficient estimates and quasi-subordination properties associated with certain subclasses of analytic and bi-univalent functions ,
Mathematica Slovaca 65 (2015) No. 3, 533-544.
[29] Huo Tang, Gangadharan Murugusundaramoorthy, Shu-Hai Li, Li-Na Ma. Fekete-Szego and Hankel inequalities for certain class of analytic functions related to the sine function, AIS Mathematics, 7(4) (2022): 6365 - 6380.
[30] J.O. Hamzat, M. O. Oluwayemi, A. A. Lupas and A. K. Wanas. Bi-Univalent Problems Involving Generalized ultiplier Transform with Respect to Symmetric and Conjugate Points , Fractal Fract., 2022, 6 , 483, 1 - 11. https://doi.org/10.3390/fractalfract6090483
[31] J.O. Hamzat, M. O. Oluwayemi, A. T. Oladipo and A. A. Lupas. On alpha-Pseudo Spiralike Function Associated with Exponential Pareto Distribution (EPD) and Libera Integral Operator, Mathematics, 2024, 1-10. https:/doi.org/10.3390/math1010000
[32] J.O. Hamzat, G. Murugusundaramoorthy and M. O. Oluwayemi. Brief Study on a New Family of Analytic Functions, Sahand Commun. Math. Anal. vol. 21, no. 4, 109-122. Doi:1022130/scma.2024.2011065.1457
[33] J.O. Hamzat. Estimate of Second and Third Hankel Determinants for Bazilevic Function of Order Gamma, Unilag Journal of Mathematics and Applications, vol. 3, 2023, 102-112.
[34] J.O. Hamzat. Some Properties of a new subclass of m-fold symmetric bi-Bazilevic Functions Associated with Modified Sigmoid Function, Tbilisi Math. J. 14(1), 2021, 107-118. Doi:10.32513/tmj/1932200819
[35] M.Illafe, A. Amourah and H.Mohd. Inequalities for a Certain Subclass of Analytic and Bi-Univalent Functions , Axioms2022,11,147. https://doi.org//10.3390/axiom 11040147.
[36] F.H. Jackson. On q-functions and a certain difference operator, Trans. R. Soc. Ediah, 1908,46, 253-281.
[37] F.H. Jackson. On q-definte integrals, Q.J. Pure Appl. Math.1910, 41, 193-203.
[38] K.A. Karthikeyan, G. Murugusundaramoorthy, S.D. Purohit and D.I. Suthar. Certain class of Analytic Functions with respect to the Symmetric Points defined by Q-Calculus ,Journal of Mathematics, volume 2021,Article 105298848, 9 pages.
[39] F.R. Keogh, E.P. Merkes. A coefficient inequality for certain classes of analytic functions , Proceedings of the American Mathematical Society, Vol, 20, 969, 8 - 12.
[40] S. Kumar, V. Ravichandran. Subordination for functions with positive real part, Complex Anal. Open Theory 12 (2018), no.5, 1179 - 1191.
[41] M. Lewin. On a Coefficient Problem for Bi-Univalent Functions ,Proc. Math. Soc. 1967, 18, 63 -68.
[42] A.Y. Lashin. On certain subclasses of analytic and bi-univalent functions, Journal of the Egyptian Mathematical Society 24 (2016), no. 2, 220 - 225.
[43] A. M. Lashin, A. Badghaish and B. Algethami. Certain subclasses of analytic functions and bi-univalent functions defined on the unite disc, Research Square, 2023, 1 - 12. Doi:https:https://doi.org/10.21203/rs.3.rs-2800195/v1
[44] K. L _ o wner. UntersuchungenU ber schlichte Konforme Abbildungen des Einheitskreises, I, Mathematische Annalen,V ol. 89, no. 1-2, (1923), 103 -121.
[45] Mamoun Harayzeh Al-Abbadi, Maslina Darus. The Fekete-Szego Theorem for certain class of analytic functions, General Mathematics Vol. 19, No. 3 (2011), 41 -51.
[46] B.S. Mehrok, G. Singh. Fekete-Szego coecient functional for Certain subclasses of close-to-star functions , Hindawi Publishing Corporation, Germany, Volume 2013, Article ID 642142, 6 pages.
[47] G. Murugusundaramoorthy, N. Magesh, V. Prameela. Coefficient Bounds for Certain Subclasses of Bi-univalent Function , Abstr. Appl. (2013), 2013, 573017, 1-3.
[48] C. Pommerenke. Univalent Functions , Vandenhoeck and Rupercht: Go_ttingen, Germany,1975.
[49] B.Seker, V. Mehmetogia. Coecient bounds for bi-univalent functions , New Trends in Mathematical Sciences, 4(2016), 197 -203.
[50] H.M. Srivastava, A.K. Mistra, P. Gochhayat. Certain Subclasses of Analytic and Bi-Univalent Functions , Appl. Math. Lett. 2010,23,1188 - 1192.
[51] L.A. Wani, A. Swaminathan. Starlike and Convex functions associated with a Nephroid domain having CUSPS on the real axis, arxiv: 1912.05767v1[math.V] 12 Dec 2019, pp 1-23.
[52] T. Yavuz, S. Altinkaya. Notes on some classes of spiralike functions associated with the q-integral operator ,Hacet.J.Math.Stat. Volume 53 (1) 2024, 53 - 61.
[53] F. Yousef, S. Alroud, M. IIIafe. New Subclasses of Analytic and Bi-univalent Functions Endowed with Coefficient Estimate Problems , Anal. Math. Phys. 2021, 11: 58, 1-12.
[54] F. Yousef, T. Al-Hawary, G. Murugusundarmoorthy. Fekete-Szego Functional Problems for some Subclasses of Bi-univalent Functions Defined by Frasin Differential Operator,Afr. Mat. 2019, 30, 495 - 503.
Operators, Facta Universitatis(NIS) SER. MATH. INFORM. vol. 32, No 2 (2017), 255 -267.
[2] E. A. Adegani, S. Bulut and A. Zireh. Cofficient estimates for a subclass of analytics bi-univalent functions, Bull. Korean Math. Soc. 55 (2018); No 2, 405 - 413. https://doi.org/10.4134/BKMS.6170061.
[3] F. I. Akinwale and J.O. Hamzat Coefficient bounds for certain generalized class of analytic functions involving Bazil;evic type function and the Sigmoid function, J. Nig. Math. Phy. Vol. 62, Dec.,(2021), Issue, 1-8.
[4] A. Amourah, B.A. Frasin, T. Abdeijawad. Fekete-Szego Inequality for Analytic and Bi-univalent Functions Subordinate to Gegenbauer Polynomials , J. Funct. Spaces 2021, 2021, 5574673, 1-7.
[5] A. Amourah, B.A. Frasin, M. Ahmad, F. Yousef. Exploiting the Pascal Distribution Series and Gegenbauer Polynomials to Construct and Study a New Subclass of Analytic Bi-Univalent Functions , Symmetry 2022, 14, 147, 1-8.
[6] A. Arai, V. Gupta, and R. P. Agarwal. Applications of q-Calculus in Operator Theory , Springer, New York. NY, USA, (2013), 1 - 13.
[7] O.P. Ahuja, S. Kumar, Ravichandran. Applications of first order differential subordination for functions with positive real part , Stud. Univ. Babes-Bolyai Math. 63 (2018), no.3, 303-311.
[8] R.M. Ali, S.K. Lee, V. Ravichandran, and S. Subramaniam. Coefficient estimates for bi-univalent Ma-Minda starlike and convex functions , Appl. Math. Latt.25 (2012), no. 3, 344 351.
[9] A. Akgul, T. G. Shara. u; v- Lucas polynomial coefficient relations of the bi-univalent function class , Commun. Fac. Sci. Univ. Ank. Ser. AI MATH. stat. Volume 71, Number 4, (2022) pages 1121 - 1134. Doi:10.31801/cfsa.smas.1086809.
[10] S. Altinkaya, S. Yalcin. Coefficient bounds for a subclass of bi-univalent functions , 6(2015), 180 -185.
[11] S. Altinkaya, S. Yalcin. Estimates on Coefficients of a General Subclass of Bi-univalent Functions Associated with Symetric q- Derivative Operator by Means of the Chebyshev Polynomials , Asia Pac. J. Math. (2017), 8, 90 - 99.
[12] L. Bieberbach. Uber koezlenten Derjenigen Potenzreihen, Welche Eine Schlichtz Des Einheitskreises Vermitteln , Vol. 38, Sitzungsberichte der PreuBischen Akademie der Wissenschaften zu Berlin, 1916.
[13] S. Bulut. Coefficient Estimates for a Class of Analytic and Bi-univalent Functions ,Novi. Sal.J.Math. 2013, 2013,43, 59-65.
[14] R. Bucar, D. Breaz. On a new class of analytic functions with respect to symmetric points involving the q-derivative operator , In Journal of Physics: Conference Series, IOP Publishing,(2019), 1-8.
[15] T. Bulboara, P. Goswami. On some classes of bi-univalent functions , Studia Universitatis Babas-Bolyai Mathematica, 2(2015), 7 - 13.
[16] P. N. Chidera. New subclasses of the class of close - to - convex functions , Proceedings of the American Mathematical Society, ol. 62, no. 1, (1977), 37 -43.
[17] N.E. Cho, V. Kumar, S.S. Kumar, V. Ravichandran. Radius problems for starlike functions associated with sine functions , Bull. Iran, Math. Soc., 45 (2019), 213 - 232.
[18] L. De Branges. A proof of the Bieberbach conjecture , Acta.Math.154,(1985),137-152. http://dx.doi.org/10.1007/BF02392821
[19] K. Dhanalakshmi, S. Poongothai. Third Hankel determinant for a subclass of analytic univalent related to modi ed Nephroid domain ,International Journal of Mechanical Engineering,ol. 7, N0.4 April, 2022, 1-5. ISSN: 0974-5823.
[20] P.I. Duren, Univalent functions. Grundlehen der Mathematischan Wissenschaften 259: Springer: New York, Ny, USA; Berlin/Heidelberg, Germany;Tokyo,Japan, (1983).
[21] A.H. El-Qadeem, M.A. Mamon, I. S. Elshazly. Application of Einstein function on bi-univalent functions de ned on the unit disc, Symmetry, 14, 4(2022),758, 1-11.
[22] Ebrahim Analouei Adegani, Serap Bulut, Ahmad Zireh. Coefficient estimates for a subclass of analytic bi-univalent functions , Bull. Korean Math. Soc. 55 (2018), No. 2, 405 - 413.
[23] B.A. Frasin, M.K. Aouf. New subclasses of Bi-Univalent Functions, Appl. Math. lett (2011), 24, 1569 - 1573.
[24] O. Fagbemiro, J.O. Hamzat, M. T. Raji. A certain class of (j; k)- symmetric function involving sigmoid function defined by using subordination principle ,
Journal of the Nigerian Association of Mathematical Physics(2024), 39 - 46.
[25] O. Fagbemiro, M.T. Raji, J.O. Hamzat, A.T. Oladipo and B.I. Olajuwon. Coefficient
bounds for subclass of sigmoid functions involving subordination principle defined by Salagean Differential Operator, Covenant Journal of Physical and Life Sciences, Vol. 13, No. 1, June 2025, 1-16.
[26] M. Fekete, G. Szego. Eine Beemer Kung uber ungerade schlichte Functionen, Journal of the London Mathematical Sociebty, Volume 8, 85 89, 1933.
[27] A.W. Goodman. Univalent functions. Vol. 1, Mariner Publishing Co., Inc., Tampa, FL, 1983.
[28] S.P. Goyal and R. Kumar. Coefficient estimates and quasi-subordination properties associated with certain subclasses of analytic and bi-univalent functions ,
Mathematica Slovaca 65 (2015) No. 3, 533-544.
[29] Huo Tang, Gangadharan Murugusundaramoorthy, Shu-Hai Li, Li-Na Ma. Fekete-Szego and Hankel inequalities for certain class of analytic functions related to the sine function, AIS Mathematics, 7(4) (2022): 6365 - 6380.
[30] J.O. Hamzat, M. O. Oluwayemi, A. A. Lupas and A. K. Wanas. Bi-Univalent Problems Involving Generalized ultiplier Transform with Respect to Symmetric and Conjugate Points , Fractal Fract., 2022, 6 , 483, 1 - 11. https://doi.org/10.3390/fractalfract6090483
[31] J.O. Hamzat, M. O. Oluwayemi, A. T. Oladipo and A. A. Lupas. On alpha-Pseudo Spiralike Function Associated with Exponential Pareto Distribution (EPD) and Libera Integral Operator, Mathematics, 2024, 1-10. https:/doi.org/10.3390/math1010000
[32] J.O. Hamzat, G. Murugusundaramoorthy and M. O. Oluwayemi. Brief Study on a New Family of Analytic Functions, Sahand Commun. Math. Anal. vol. 21, no. 4, 109-122. Doi:1022130/scma.2024.2011065.1457
[33] J.O. Hamzat. Estimate of Second and Third Hankel Determinants for Bazilevic Function of Order Gamma, Unilag Journal of Mathematics and Applications, vol. 3, 2023, 102-112.
[34] J.O. Hamzat. Some Properties of a new subclass of m-fold symmetric bi-Bazilevic Functions Associated with Modified Sigmoid Function, Tbilisi Math. J. 14(1), 2021, 107-118. Doi:10.32513/tmj/1932200819
[35] M.Illafe, A. Amourah and H.Mohd. Inequalities for a Certain Subclass of Analytic and Bi-Univalent Functions , Axioms2022,11,147. https://doi.org//10.3390/axiom 11040147.
[36] F.H. Jackson. On q-functions and a certain difference operator, Trans. R. Soc. Ediah, 1908,46, 253-281.
[37] F.H. Jackson. On q-definte integrals, Q.J. Pure Appl. Math.1910, 41, 193-203.
[38] K.A. Karthikeyan, G. Murugusundaramoorthy, S.D. Purohit and D.I. Suthar. Certain class of Analytic Functions with respect to the Symmetric Points defined by Q-Calculus ,Journal of Mathematics, volume 2021,Article 105298848, 9 pages.
[39] F.R. Keogh, E.P. Merkes. A coefficient inequality for certain classes of analytic functions , Proceedings of the American Mathematical Society, Vol, 20, 969, 8 - 12.
[40] S. Kumar, V. Ravichandran. Subordination for functions with positive real part, Complex Anal. Open Theory 12 (2018), no.5, 1179 - 1191.
[41] M. Lewin. On a Coefficient Problem for Bi-Univalent Functions ,Proc. Math. Soc. 1967, 18, 63 -68.
[42] A.Y. Lashin. On certain subclasses of analytic and bi-univalent functions, Journal of the Egyptian Mathematical Society 24 (2016), no. 2, 220 - 225.
[43] A. M. Lashin, A. Badghaish and B. Algethami. Certain subclasses of analytic functions and bi-univalent functions defined on the unite disc, Research Square, 2023, 1 - 12. Doi:https:https://doi.org/10.21203/rs.3.rs-2800195/v1
[44] K. L _ o wner. UntersuchungenU ber schlichte Konforme Abbildungen des Einheitskreises, I, Mathematische Annalen,V ol. 89, no. 1-2, (1923), 103 -121.
[45] Mamoun Harayzeh Al-Abbadi, Maslina Darus. The Fekete-Szego Theorem for certain class of analytic functions, General Mathematics Vol. 19, No. 3 (2011), 41 -51.
[46] B.S. Mehrok, G. Singh. Fekete-Szego coecient functional for Certain subclasses of close-to-star functions , Hindawi Publishing Corporation, Germany, Volume 2013, Article ID 642142, 6 pages.
[47] G. Murugusundaramoorthy, N. Magesh, V. Prameela. Coefficient Bounds for Certain Subclasses of Bi-univalent Function , Abstr. Appl. (2013), 2013, 573017, 1-3.
[48] C. Pommerenke. Univalent Functions , Vandenhoeck and Rupercht: Go_ttingen, Germany,1975.
[49] B.Seker, V. Mehmetogia. Coecient bounds for bi-univalent functions , New Trends in Mathematical Sciences, 4(2016), 197 -203.
[50] H.M. Srivastava, A.K. Mistra, P. Gochhayat. Certain Subclasses of Analytic and Bi-Univalent Functions , Appl. Math. Lett. 2010,23,1188 - 1192.
[51] L.A. Wani, A. Swaminathan. Starlike and Convex functions associated with a Nephroid domain having CUSPS on the real axis, arxiv: 1912.05767v1[math.V] 12 Dec 2019, pp 1-23.
[52] T. Yavuz, S. Altinkaya. Notes on some classes of spiralike functions associated with the q-integral operator ,Hacet.J.Math.Stat. Volume 53 (1) 2024, 53 - 61.
[53] F. Yousef, S. Alroud, M. IIIafe. New Subclasses of Analytic and Bi-univalent Functions Endowed with Coefficient Estimate Problems , Anal. Math. Phys. 2021, 11: 58, 1-12.
[54] F. Yousef, T. Al-Hawary, G. Murugusundarmoorthy. Fekete-Szego Functional Problems for some Subclasses of Bi-univalent Functions Defined by Frasin Differential Operator,Afr. Mat. 2019, 30, 495 - 503.
Published
2025-06-24
How to Cite
Fagbemiro , O., Sangoniyi , S. O., Raji , M. T., & Olajuwon , B. I. (2025). BI- UNIVALENT PROBLEM FOR CERTAIN GENERALIZED CLASS OF ANALYTIC FUNCTIONS INVOLVING Q-INTEGRAL OPERATOR ASSOCIATED WITH NEPHROID DOMAIN. Unilag Journal of Mathematics and Applications, 4(2), 106-125. Retrieved from https://lagjma.unilag.edu.ng/article/view/2633
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Copyright (c) 2024 Olalekan Fagbemiro , Sunday Oloruntoyin Sangoniyi , Musiliu Tayo Raji , Bakai Ishola Olajuwon
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