Results & Lemmas (14)
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Lemma 1.1.
Lemma 1.1. Let f z A and 0 1 . Then , f T
Lemma 1.1. Let f z A and 0 1 . Then , f T
Lemma 2.1
Lemma 2.1 (see Miller and Mocanu [5]) Let be a set in the complex plane and let b be a complex number such that. Suppose that a function…
Lemma 2.1 (see Miller and Mocanu [5]) Let be a set in the complex plane and let b be a complex number such that . Suppose that a function satisfies the condition Re 0 b i , ; z
Theorem 2.2.
Theorem 2.2. Let f A , 1 2 1 and Re f z
Theorem 2.2. Let f A , 1 2 1 and Re f z
Theorem 2.3.
Theorem 2.3. Let f A 1, and Re f z z
Theorem 2.3. Let f A 1 , and Re f z z
Theorem 2.2
Theorem 2.2, we can get ,:: R p z zp z
Theorem 2.2, we can get , : : R p z zp z
Theorem 2.4.
Theorem 2.4. Let and be real numbers such that 1 2 1 and let f be a function in the class , T . Then
Theorem 2.4. Let and be real numbers such that 1 2 1 and let f be a function in the class , T . Then
Lemma 3.1.
Lemma 3.1. (see Rogosinski [6]) Let
Lemma 3.1. (see Rogosinski [6]) Let
Theorem 3.2.
Theorem 3.2. Let and be real numbers such that 0 1 1, n n n f z
Theorem 3.2. Let and be real numbers such that 0 1 1 , n n n f z
Theorem 3.2
Theorem 3.2 is completed. And now, we shall solve the Fekete-Szegö problem for , f T and we will need the following Lemma:
Theorem 3.2 is completed. And now, we shall solve the Fekete-Szegö problem for , f T and we will need the following Lemma:
Lemma 3.3.
Lemma 3.3. (see Keogh and Merkers [7]) Let 2 1 2 1 p z c z c z be a function with positive real part in
Lemma 3.3. (see Keogh and Merkers [7]) Let 2 1 2 1 p z c z c z be a function with positive real part in
Theorem 3.4.
Theorem 3.4. Let and let the function z n given by 2 n n z
Theorem 3.4. Let and let the function z n given by 2 n n z
Corollary 3.1.
Corollary 3.1. Let and let the function f, given by 2 n , n n f z a z
Corollary 3.1. Let and let the function f , given by 2 n , n n f z a z
Theorem 3.5.
Theorem 3.5. For given and such that f be given by 0 1 , let 2 n n n z
Theorem 3.5. For given and such that f be given by 0 1 , let 2 n n n z
Theorem 3.5
Theorem 3.5 is completed. 4. Acknowledgements The research was supported by Kyungsung University Re-search Grants in 2013. REFERENCES [1]…
Theorem 3.5 is completed. 4. Acknowledgements The research was supported by Kyungsung University Re-search Grants in 2013. REFERENCES [1] K. Kuroki and S. Owa, “Notes on New Class for Certain Analytic Functions,” RIMS Kokyuroku 1772, 2011, pp. 21-25. [2] H. M. Srivastava, A. K. Mishra and P. Gochhayat, “Cer- tain Subclasses of Analytic and Bi-Univalent Functions,” Applied Mathematics Letters, Vol. 23, No. 10, 2010, pp. 1188-1192. doi:10.1016/j.aml.2010.05.009 [3]
Definitions (1)
Def 1.1.
Definition 1.1. Let and be real numbers such that 0 1 . The function f A
Definition 1.1. Let and be real numbers such that 0 1 . The function f A
Function classes studied:
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