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Results & Lemmas (6)
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Theorem 1.
Theorem 1. Let the function ݂ሺݖሻ defined by Eq. (14) be in the class ߑ∗. Then the function ݂ሺݖሻ belongs to the class ( ) k, s,a l m…
Theorem 1. Let the function ݂ሺݖሻ defined by Eq. (14) be in the class ߑ∗. Then the function ݂ሺݖሻ belongs to the class ( ) k, s,a l m L , ;A,B,b if and only if:
Corollary 1.
Corollary 1. Let the function ݂ሺݖሻ defined by Eq. (14) be in the class ( ) k, s,a l m L,; A,B,b. Then:
Corollary 1. Let the function ݂ሺݖሻ defined by Eq. (14) be in the class ( ) k , s,a l m L , ; A,B,b . Then:
Theorem 2.
Theorem 2. If a function ݂ሺݖሻ defined by Eq. (14) is in the class ( ) k, s,a l m L,; A,B,b, then for |ݖ| ൌݎ൏1, we have:
Theorem 2. If a function ݂ሺݖሻ defined by Eq. (14) is in the class ( ) k , s,a l m L , ; A,B,b , then for |ݖ| ൌݎ൏1, we have:
Theorem 3.
Theorem 3. Let the function ݂ሺݖሻ defined by Eq. (14) be in the class Ls,a k,(l,m;A,B,b). Then we have: (i) ݂ሺݖሻ is meromorphically…
Theorem 3. Let the function ݂ሺݖሻ defined by Eq. (14) be in the class Ls,a k ,(l ,m;A,B,b). Then we have: (i) ݂ሺݖሻ is meromorphically starlike of order φ in the disc |ݖ| ൏ݎଵ, that is:
Theorem 4.
Theorem 4. The class ( ) k, s,a l m L,;A,B,b is closed under convex linear combinations.
Theorem 4. The class ( ) k, s,a l m L , ;A,B,b is closed under convex linear combinations.
Theorem 5.
Theorem 5. Let 0 1 ( ) f z z and 1 ( ) nf z z
Theorem 5. Let 0 1 ( ) f z z and 1 ( ) nf z z
Function classes studied:
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