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Sunthrayuth, Pongsakorn; Jawarneh, Yousef; Naeem, Muhammad; Iqbal, Naveed; Kafle, Jeevan

Some sharp results on coefficient estimate problems for four-leaf-type bounded turning functions. (English) Zbl 1502.30067

J. Funct. Spaces 2022, Article ID 8356125, 10 p. (2022).

MSC:

30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
30C50 Coefficient problems for univalent and multivalent functions of one complex variable

Keywords:

bounded turning functions; Fekete-Szegő problem
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References:

[1] Bieberbach, L., Über dié koeffizienten derjenigen Potenzreihen, welche eine schlichte Abbildung des Einheitskreises vermitteln, Sitzungsberichte Preussische Akademie der Wissenschaften, 138, 940-955 (1916) · JFM 46.0552.01
[2] De-Brages, L., A proof of the Bieberbach conjecture, Acta Mathematica, 154, 1-2, 137-152 (1985) · Zbl 0573.30014 · doi:10.1007/BF02392821
[3] Iqbal, N.; Niazi, A. U. K.; Khan, I. U.; Shah, R.; Botmart, T., Cauchy problem for non-autonomous fractional evolution equations with nonlocal conditions of order (1, 2), AIMS Mathematics, 7, 5, 8891-8913 (2022) · doi:10.3934/math.2022496
[4] Niazi, A. U. K.; Iqbal, N.; Wannalookkhee, F.; Nonlaopon, K., Controllability for fuzzy fractional evolution equations in credibility space, Fractal and Fractional, 5, 3, article fractalfract5030112, 112 (2021) · doi:10.3390/fractalfract5030112
[5] Naeem, M.; Azhar, O. F.; Zidan, A. M.; Nonlaopon, K.; Shah, R., Numerical analysis of fractional-order parabolic equations via Elzaki transform, Journal of Function Spaces, 2021 (2021) · Zbl 07446722 · doi:10.1155/2021/3484482
[6] Ma, W. C.; Minda, D.; Li, Z.; Ren, F.; Yang, L.; Zhang, S., A unified treatment of some special classesof univalent functions, Proceedings of the Conference on Complex Analysis. Tianjin, China, 1992. Conference Proceedings and Lecture Notes in Analysis, vol. I, 157-169 (1994), Cambridge, Massachusetts: International Press, Cambridge, Massachusetts · Zbl 0823.30007
[7] Janowski, W., Extremal problems for a family of functions with positive real part and for some related families, Ann. Polon. Math., 23, 2, 159-177 (1970) · Zbl 0199.39901 · doi:10.4064/ap-23-2-159-177
[8] Sokół, J.; Stankiewicz, J., Radius of convexity of some subclasses of strongly starlike functions, Zeszyty Naukowe Politechniki Rzeszowskiej, 19, 101-105 (1996) · Zbl 0880.30014
[9] Sharma, K.; Jain, N. K.; Ravichandran, V., Starlike functions associated with a cardioid, Afrika Matematika, 27, 5-6, article 387, 923-939 (2016) · Zbl 1352.30015 · doi:10.1007/s13370-015-0387-7
[10] Cho, N. E.; Kumar, V.; Kumar, S. S.; Ravichandran, V., Radius problems for starlike functions associated with the sine function, Bulletin of the Iranian Mathematical Society, 45, 1, article 127, 213-232 (2019) · Zbl 1409.30009 · doi:10.1007/s41980-018-0127-5
[11] Mendiratta, R.; Nagpal, S.; Ravichandran, V., On a subclass of strongly starlike functions associated with exponential function, Bulletin of the Malaysian Mathematical Sciences Society, 38, 1, article 26, 365-386 (2015) · Zbl 1312.30019 · doi:10.1007/s40840-014-0026-8
[12] Shi, L.; Srivastava, H. M.; Arif, M.; Hussain, S.; Khan, H., An investigation of the third Hankel determinant problem for certain subfamilies of univalent functions involving the exponential function, Symmetry, 11, 5, article 598 (2019) · Zbl 1425.30021 · doi:10.3390/sym11050598
[13] Srivastava, H. M.; Khan, B.; Khan, N.; Tahir, M.; Ahmad, S.; Khan, N., Upper bound of the third Hankel determinant for a subclass of \(\text{q} \)-starlike functions associated with the \(\text{q} \)-exponential function, Bulletin des Sciences Mathematiques, 167, article 102942 (2021) · Zbl 1459.05020 · doi:10.1016/j.bulsci.2020.102942
[14] Bano, K.; Raza, M., Starlike functions associated with cosine Functions, Bulletin of Iranian Mathematical Society, 47, 5, article 456, 1513-1532 (2021) · Zbl 1473.30007 · doi:10.1007/s41980-020-00456-9
[15] Alotaibi, A.; Arif, M.; Alghamdi, M. A.; Hussain, S., Starlikness associated with cosine hyperbolic function, Mathematics, 8, 7, 1118 (2020) · doi:10.3390/math8071118
[16] Al-Sawalha, M. M.; Amir, N.; Yar, M., Novel analysis of fuzzy fractional Emden-Fowler equations within new iterative transform method, Journal of Function Spaces, 2022 (2022) · Zbl 1503.34002 · doi:10.1155/2022/7731135
[17] Barukab, O.; Arif, M.; Abbas, M.; Khan, S. K., Sharp bounds of the coefficient results for the family of bounded turning functions associated with petal shaped domain, Journal of Function Spaces, 2021 (2021) · Zbl 1462.30025 · doi:10.1155/2021/5535629
[18] Pommerenke, C., On the coefficients and Hankel determinants of univalent functions, Journal of the London Mathematical Society, s1-41, 1, 111-122 (1966) · Zbl 0138.29801 · doi:10.1112/jlms/s1-41.1.111
[19] Pommerenke, C., On the Hankel determinants of univalent functions, Mathematika, 14, 1, 108-112 (1967) · Zbl 0165.09602 · doi:10.1112/S002557930000807X
[20] Hayman, W. K., On the second Hankel determinant of mean univalent functions, Proceedings of the London Mathematical Society, s3-18, 1, 77-94 (1968) · Zbl 0158.32101 · doi:10.1112/plms/s3-18.1.77
[21] Obradović, M.; Tuneski, N., Hankel determinants of second and third order for the class \(\mathcal{S}\) of univalent functions, https://arxiv.org/abs/1912.06439 · Zbl 1482.30048
[22] Janteng, A.; Halim, S. A.; Darus, M., Coefficient inequality for a function whose derivative has a positive real part, Journal of Inequalities in Pure and Applied Mathematics, 7, 2, 1-5 (2006) · Zbl 1134.30310
[23] Janteng, A.; Halim, S. A.; Darus, M., Hankel determinant for starlike and convex functions, International Journal of Mathematical Analysis, 1, 13, 619-625 (2007) · Zbl 1137.30308
[24] Lee, S. K.; Ravichandran, V.; Supramaniam, S., Bounds for the second Hankel determinant of certain univalent functions, Journal of Inequalities and Applications, 2013, 1 (2013) · Zbl 1302.30018 · doi:10.1186/1029-242X-2013-281
[25] Ebadian, A.; Bulboacă, T.; Cho, N. E.; Analouei Adegani, E., Coefficient bounds and differential subordinations for analytic functions associated with starlike functions, Revista de la Real Academia de Ciencias Exactas, Fsicasy Naturales. Series A. Matemáticas, 114, 3, article 128 (2020) · Zbl 1439.30024 · doi:10.1007/s13398-020-00871-x
[26] Altınkaya, Ş.; Yalçın, S., Upper bound of second Hankel determinant for Bi-Bazilevic̆ functions, Mediterranean Journal of Mathematics, 13, 6, article 733, 4081-4090 (2016) · Zbl 1353.30011 · doi:10.1007/s00009-016-0733-5
[27] Çaglar, M.; Deniz, E.; Srivastava, H. M., Second Hankel determinant for certain subclasses of bi-univalent functions, Turkish Journal of Mathematics, 41, 3, 694-706 (2017) · Zbl 1424.30034 · doi:10.3906/mat-1602-25
[28] Kanas, S.; Adegani, E. A.; Zireh, A., An unified approach to second Hankel determinant of bi-subordinate functions, Mediterranean Journal of Mathematics, 14, 6, 233 (2017) · Zbl 1381.30010 · doi:10.1007/s00009-017-1031-6
[29] Babalola, K. O., On \(H_3\left( 1\right)\) Hankel determinant for some classes of univalent functions, Inequality Theory and Applications, 6, 1-7 (2010)
[30] Altınkaya, Ş.; Yalçın, S., Third Hankel determinant for Bazilevi \(\breve{\text{c}}\) functions, Advances in Mathematics, 5, 2, 91-96 (2016) · Zbl 1377.30007
[31] Bansal, D.; Maharana, S.; Prajapat, J. K., Third order Hankel determinant for certain univalent functions, Journal of Korean Mathematical Society, 52, 6, 1139-1148 (2015) · Zbl 1328.30005 · doi:10.4134/JKMS.2015.52.6.1139
[32] Krishna, D. V.; Venkateswarlu, B.; Ram Reddy, T., Third Hankel determinant for bounded turning functions of order alpha, Society, 34, 2, 121-127 (2015) · Zbl 1353.30013 · doi:10.1016/j.jnnms.2015.03.001
[33] Raza, M.; Malik, S. N., Upper bound of third Hankel determinant for a class of analytic functions related with lemniscate of Bernoulli, Journal Inequalities and Applications, 2013, 1, article 412 (2013) · Zbl 1291.30106 · doi:10.1186/1029-242X-2013-412
[34] Shanmugam, G.; Stephen, B. A.; Babalola, K. O., Third Hankel determinant for \(\alpha \)-starlike functions, Gulf Journal of Mathematics, 2, 2, 107-113 (2014) · Zbl 1389.30083
[35] Zaprawa, P., Third Hankel determinants for subclasses of univalent functions, Mediterranean Journal of Mathematics, 14, 1, 19 (2017) · Zbl 1362.30027 · doi:10.1007/s00009-016-0829-y
[36] Kwon, O. S.; Lecko, A.; Sim, Y. J., The bound of the Hankel determinant of the third kind for starlike functions, Bulletin of the Malaysian Mathematical Sciences Society, 42, 2, 767-780 (2019) · Zbl 1419.30007 · doi:10.1007/s40840-018-0683-0
[37] Zaprawa, P.; Obradović, M.; Tuneski, N., Third Hankel determinant for univalent starlike functions, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 115, 2, article 49 (2021) · Zbl 1461.30048 · doi:10.1007/s13398-020-00977-2
[38] Kowalczyk, B.; Lecko, A.; Sim, Y. J., The sharp bound FOR the Hankel determinant of the third kind for convex functions, Bulletin of the Australian Mathematical Society, 97, 3, article S0004972717001125, 435-445 (2018) · Zbl 1394.30007 · doi:10.1017/S0004972717001125
[39] Lecko, A.; Sim, Y. J.; Śmiarowska, B., The sharp bound of the Hankel determinant of the third kind for starlike functions of order 1/2, Complex Analysis and Operator Theory, 13, 5, 2231-2238 (2019) · Zbl 1422.30022 · doi:10.1007/s11785-018-0819-0
[40] Shi, L.; Shutaywi, M.; Alreshidi, N.; Arif, M.; Ghufran, M. S., The sharp bounds of the third-order Hankel determinant for certain analytic functions associated with an eight-shaped domain, Fractal and Fractional, 6, 4, article fractalfract6040223, 223 (2022) · doi:10.3390/fractalfract6040223
[41] Mahmood, S.; Srivastava, H. M.; Khan, N.; Ahmad, Q. Z.; Khan, B.; Ali, I., Upper bound of the third Hankel determinant for a subclass of \(\text{q} \)-starlike functions, Symmetry, 11, 3, article 347 (2019) · Zbl 1423.05030 · doi:10.3390/sym11030347
[42] Arif, M.; Raza, M.; Tang, H.; Hussain, S.; Khan, H., Hankel determinant of order three for familiar subsets of analytic functions related with sine function, Open Mathematics., 17, 1, 1615-1630 (2019) · Zbl 1441.30019 · doi:10.1515/math-2019-0132
[43] Shi, L.; Ali, I.; Arif, M.; Cho, N. E.; Hussain, S.; Khan, H., A study of third Hankel determinant problem for certain subfamilies of analytic functions involving cardioid domain, Mathematics, 7, 5, article 418 (2019) · doi:10.3390/math7050418
[44] Raza, M.; Srivastava, H. M.; Arif, M.; Ahmad, K., Coefficient estimates for a certain family of analytic functions involving a q-derivative operator, The Ramanujan Journal, 55, 1, article 338, 53-71 (2021) · Zbl 1462.30039 · doi:10.1007/s11139-020-00338-y
[45] Wang, Z. G.; Raza, M.; Arif, M.; Ahmad, K., On the third and fourth Hankel determinants for a subclass of analytic functions, Bulletin of the Malaysian Mathematical Sciences Society, 45, 1, article 1195, 323-359 (2022) · Zbl 1483.30052 · doi:10.1007/s40840-021-01195-8
[46] Gandhi, S.; Deo, N.; Gupta, V.; Agrawal, P., Radius estimates for three leaf function and convex combination of starlike functions, mathematical Analysis 1: Approximation Theory. ICRAPAM, 306 (2018), Singapore: Spinger, Singapore
[47] Libera, R. J.; Zlotkiewicz, E. J., Coefficient bounds for the inverse of a function with derivative in \(P\), Proceedings of the American Mathematical Society, 87, 2, 251-257 (1983) · Zbl 0488.30010 · doi:10.2307/2043698
[48] Pommerenke, C., Univalent Function (1975), Göttingen, Germany: Vanderhoeck & Ruprecht, Göttingen, Germany · Zbl 0298.30014
[49] Libera, R. J.; Złotkiewicz, E. J., Early coefficients of the inverse of a regular convex function, Proceedings of the American Mathematical Society, 85, 2, 225-230 (1982) · Zbl 0464.30019 · doi:10.1090/S0002-9939-1982-0652447-5
[50] Kwon, O. S.; Lecko, A.; Sim, Y. J., On the fourth coefficient of functions in the Carathéodory class, Computational Methods and Function Theory, 18, 2, article 229, 307-314 (2018) · Zbl 1395.30019 · doi:10.1007/s40315-017-0229-8
[51] Ravichandran, V.; Verma, S., Borne pour le cinquieme coefficient des fonctions etoilees, Comptes Rendus Mathematique, 353, 6, article S1631073X1500076X, 505-510 (2015) · Zbl 1317.30022 · doi:10.1016/j.crma.2015.03.003
[52] Krushkal, S. K., A Short Geometric Proof of the Zalcman and Bieberbach Conjectures
[53] Tang, H.; Arif, M.; Haq, M.; Khan, N.; Khan, M.; Ahmad, K.; Khan, B., Fourth Hankel determinant problem based on certain analytic functions, Symmetry, 14, 4, article sym14040663, 663 (2022) · doi:10.3390/sym14040663
[54] Arif, M.; Rani, L.; Raza, M.; Zaprawa, P., Fourth Hankel determinant for the family of functions with bounded turning, Bulletin of the Korean Mathematical Society, 55, 6, 1703-1711 (2018) · Zbl 1411.30009
[55] Arif, M.; Rani, L.; Raza, M.; Zaprawa, P., Fourth Hankel determinant for the set of star-like functions, Mathematical Problems in Engineering, 2021 (2021) · Zbl 1512.30003 · doi:10.1155/2021/6674010
[56] Arif, M.; Ullah, I.; Raza, M.; Zaprawa, P., Investigation of the fifth Hankel determinant for a family of functions with bounded turnings, Mathematica Slovaca, 70, 2, 319-328 (2020) · Zbl 1505.30008 · doi:10.1515/ms-2017-0354
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