On the Fekete-Szegö inequality for analytic functions via Hohlov operator on leaf-like domains
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Analytic functions, Univalent functions, Fekete-Szego inequality,Leaf like domainAbstract
This study examines the Fekete-Szegö inequality in relation to the classes of holomorphic functions, particularly starlike and convex functions of complex order. We obtain significant inequality for star-like, bounded turning, and close-to-convex functions by using the Hohlov operator and taking leaf-like domains into account. These findings improve our comprehension of function behavior in complex analysis and geometric function theory by extending traditional findings to broader contexts. We also give tight constraints on the coefficients and study certain examples of the Gaussian Hypergeometric function.
References
Alexander J. W., Function which map the interior of unit circle upon simple regions, Ann. Math., Vol. 17, (1915), 12-22.
Almalki, Y. Wanas, A.K. Shaba, T.G. Alb Lupąs, A. Abdalla, M. Coefficient Bounds and Fekete-SzegÖ Inequalities for a Two Families of Bi-Univalent Functions Related to Gegenbauer Polynomials. Axioms, 2023, 12, 1018. https://doi.org/10.3390/axioms12111018
Al-Sa’di S, Ahmad I, Shah SGA, Hussain S, Noor S. Fekete-Szegö type functionals associated with certain subclasses of bi-univalent functions. Heliyon. 2024 Mar 18;10(7):e28074. https://doi.org/10.1016/j.heliyon.2024.e28074. PMID:39668940; PMCID: PMC11636914.
Al-Shaqshi, K. and Darus, M., On the Fekete Szegö problem for certain subclass of analytic function, Appl.Math. Soc.,(Ruse)2, No. 9-12, V, 431–441.
E.A. Adegani, A. Zireh, M. Jafari, Coefficient estimates for a new subclass of analytic and bi-univalent functions by hadamard product, Bol. Soc. Paran. Mat., 39, (2021) 87–104. https://doi.org/10.5269/bspm.39164
Hari Mohan Srivastava, Timilehin Gideon Shaba, Gangadharan Murugusundaramoorthy, Abbas Kareem Wanas, Georgia Irina Oros. The Fekete-SzegÖ functional and the Hankel determinant for a certain class of analytic functions involving the Hohlov operator[J]. AIMS Mathematics, 2023, 8(1): 340–360. https://doi.org/10.3934/math.2023016
H. Tang, G. Murugusundaramoorthy, S. H. Li, L. N. Ma, Fekete-Szego and Hankel inequalities for certain class of analytic functions related to the sine function, AIMS Math., 7 (2022), 6365-6380. https://doi.org/10.3934/math.2022354
K.Thilagavathi, Certain inclusion properties of subclass of starlike and convex functions of positive order involving Hohlov operator, International Journal of Pure and Applied Mathematical Sciences, 10(1), (2017), 85–97.
Ma, W. and Minda, D. A, Unified treatment of some special classes of univalent functions, in: Proceedings of the Conference on Complex Analysis, Z. Li, F. Ren, L. Yang, and S.Zhang (Eds.), Int. Press, (1994), 157–169.
Murugusundaramoorthy, G. (2021). Fekete-Szegö inequality for certain Subclasses of analytic functions related with Crescent-Shaped domain and application of Poison distribution series. Journal of Mathematical Extension, 15.
M. Fekete, G. Szegö, Eine Bemerkung über ungerade schlichtenFunctionen, J.London Math. Soc., 8, (1933), 85–89. https://doi.org/10.1524/zkri.1933.85.1.89
M. S. Robertson, On the theory of univalent functions, Ann. Math., 37, (1936), 374–408.
Nasr, M. A., and M. K. Aouf., Starlike function of complex order, J. Natur. Sci. Math. 25.1, (1985), 1–12.
Orhan H, Cotîrlă L-I. Fekete-SzegÖ Inequalities for Some Certain Subclass of Analytic Functions Defined with Ruscheweyh Derivative Operator. Axioms. 2022; 11(10):560. https://doi.org/10.3390/axioms11100560
Pochhammer, Leo., Zur theorie der Euler’schen integrale, Mathematische Annalen, 35 (1890), 495–526.
Priya, M. H., and Sharma, R. B., On a class of bounded turning functions subordinate to a leaf-like domain, In Journal of Physics: Conference Series.IOP Publishing, Vol. 1000, No. 1, (2018), 012056.
Raina R and Sokol J., On Coefficient estimates for a certain class of starlike functions, Hacettepe Journal of Mathematics and Statistics, 44(6), (2015), 1427–1433.
Singh, Gurmeet, and Chatinder Kaur, Analytic functions subordinate to leaf-like domain, Advances in Mechanics,10.1, (2022), 1444–1448.
S. S. Miller and P. T. Mocanu, Differential Subordinations, Theory and Applications, Series of Monographs and Textbooks in Pure and Applied Mathematics, Vol. 225, Marcel Dekker Inc., New York, 2000.
Thirucheran M. and Stalin T., Fekete-Szegö inequality for the new subclasses of univalent function defined by linear operators, Journal of Computer and Mathematical Sciences, 9(8), (2018), 921–930.
Timilehin Gideon Shaba, Serkan Araci, Babatunde Olufemi Adebesin, Fekete-Szegö problem and second Hankel determinant for a subclass of bi-univalent functions associated with four leaf domain, Asia Pac. J. Math. 2023 10:21. https://doi.org/10.28924/APJM/10-21
T. Panigrahi, E. Pattnayak and R. M. El-Ashwah, Estimate on logarithmic coefficients of kamali-type starlike functions associated with four-leaf shaped domain, Surveys in Mathematics and its Applications, Volume 19 (2024), 41–55.
Yu.E. Hohlov, Hadamard convolutions,hypergeometric functions and linear operators in the class of univalent functions, Dokl.Akad.Nauk Ukrain. SSR Ser. A, 7, (1984), 25–27.
Yu. E. Hohlov, Convolution operators that preserve univalent functions, Ukrain. Mat.zh., 37, (1985), 220–226. https://doi.org/10.1007/BF01059717.
Wanas Abbas Kareem, Salagean Grigore Stefan, Pall-Szabo Agnes, Coefficient bounds and Fekete-Szegö inequality for a certain family of holomorphic and bi-univalent functions defined by (M,N)-Lucas polynomials, Filomat, 37(4) (2023),1037–1044.
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