Volume 18, Issue 2 (10-2023)
IJMSI 2023, 18(2): 199-210 |
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Mahzoon H, Sokól J. New Subclass of Close-to-convex Functions Associated with the Vertical Strip Domains. IJMSI 2023; 18 (2) :199-210
URL: http://ijmsi.ir/article-1-1618-en.html
URL: http://ijmsi.ir/article-1-1618-en.html
Abstract:
In the present paper, we introduce the class Βθ(α,β) consisting of functions f, analytic in the unit disc ∆, normalized by the condition f(0)=0=f'(0)-1 and satisfying the following two-sided inequality
α< Re{f'(z)+(1+eiθ)/2 zf''(z)}<β (z∈∆),
where θ∊(-π,π], 0<α<1 and β>1. Integral representation, differential subordination results, coefficient estimates and Fekete-Szegö coefficient functional associated with the k-th (k≥1) root transform [f(zk)]1/k for functions in the class Βθ(α,β), are determined.
α< Re{f'(z)+(1+eiθ)/2 zf''(z)}<β (z∈∆),
where θ∊(-π,π], 0<α<1 and β>1. Integral representation, differential subordination results, coefficient estimates and Fekete-Szegö coefficient functional associated with the k-th (k≥1) root transform [f(zk)]1/k for functions in the class Βθ(α,β), are determined.
Keywords: Univalent, Close-to-convex, Differential subordination, Coefficient estimates, Fekete-Szegö problem.
Type of Study: Research paper |
Subject:
General
References
1. R. M. Ali, S. K. Lee, V. Ravichandran, S. Supramanian, The Fekete-Szegö Coefficient Functional for Transforms of Analytic Functions, Bull. Iran. Math. Soc., 35, (2009), 119-142.
2. P. L. Duren, Univalent Functions, Springer-Verlag, New York, 1983.
3. P. N. Chichra, New Subclasses of the Class of Close-to-convex Functions, Proc. Amer. Math. Soc., 62, (1977), 37-43. [DOI:10.1090/S0002-9939-1977-0425097-1]
4. D. J. Hallenbeck, St. Ruscheweyh, Subordination by Convex Functions, Proc. Amer. Math. Soc., 52, (1975), 191-195. [DOI:10.1090/S0002-9939-1975-0374403-3]
5. W. Kaplan, Close-to-convex Schlicht Functions, Michigan Math. J., 1, (1952), 169-185. [DOI:10.1307/mmj/1028988895]
6. R. Kargar, A. Ebadian, J. Sokó l, On Booth Lemniscate and Starlike Functions, Anal. Math. Phys., 9, (2019), 143-154. [DOI:10.1007/s13324-017-0187-3]
7. R. Kargar, A. Ebadian, J. Sokó l, On Subordination of Some Analytic Functions, Sib. Math. J., 57, (2016), 599-605. [DOI:10.1134/S0037446616040042]
8. R. Kargar, A. Ebadian, J. Sokó l, Radius Problems for Some Subclasses of Analytic Functions, Complex Anal. Oper. Theory, 11, (2017), 1639-1649. [DOI:10.1007/s11785-016-0584-x]
9. F. R. Keogh, E. P. Merkes, A Coefficient Inequality for Certain Classes of Analytic Functions, Proc. Amer. Math. Soc., 20, (1969), 8-12. [DOI:10.1090/S0002-9939-1969-0232926-9]
10. K. Kuroki, S. Owa, Notes on New Class for Certain Analytic Functions, RIMS Kokyuroku Kyoto Univ., 1772, (2011), 21-25.
11. H. Mahzoon, Coefficient and Fekete-Szegö Problem Estimates for Certain Subclass of Analytic and Bi-univalent Functions, Filomat, (accepted). arXiv preprint arXiv:1905.08600.
12. H. Mahzoon, R. Kargar, Further Results for Two Certain Subclasses of Close-to-convex Functions, Asian-Eur. J. Math., (2020). [DOI:10.1142/S1793557121500455]
13. K. Noshiro, On the Theory of Schlicht Functions, J. Fac. Sci. Hokkaido Univ. Jap. Ser. 1, 2, (1934), 129-155. [DOI:10.14492/hokmj/1531209828]
14. St. Ruscheweyh, New Criteria for Univalent Functions, Proc. Amer. Math. Soc., 49, (1975), 109-115. [DOI:10.1090/S0002-9939-1975-0367176-1]
15. St. Ruscheweyh, T. Sheil-Small, Hadamard Products of Schlicht Functions and the Pòlya-Schoenberg Conjecture, Comment. Math. Helv., 48, (1973), 119-135. [DOI:10.1007/BF02566116]
16. W. Rogosinski, On the Coefficients of Subordinate Functions, Proc. London Math. Soc., 48, (1943), 48-82. [DOI:10.1112/plms/s2-48.1.48]
17. H. Silverman, A Class of Bounded Starlike Functions, Internat. J. Math. Math. Sci., 17, (1994), 249-252. [DOI:10.1155/S0161171294000360]
18. H. Silverman, E. M. Silvia, Characterizations for Subclasses of Univalent Functions, Math. Japan. 50, (1999), 103-109.
19. R. Singh, S. Singh, Convolutions Properties of a Class of Starlike Functions, Proc. Amer. Math. Soc., 106, (1989), 145-152. [DOI:10.1090/S0002-9939-1989-0994388-6]
20. S. E. Warschawski, On the Higher Derivatives at the Boundary in Conformal Mapping, Trans. Amer. Math. Soc., 38, (1935) 310-340. [DOI:10.1090/S0002-9947-1935-1501813-X]
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