Results & Lemmas (9)
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Lemma 1
Lemma 1:[1] If P be a class of all analytic functions p(z) of the form:
Lemma 1 :[1] If P be a class of all analytic functions p(z) of the form:
Lemma 2
Lemma 2: [22] If p∈P, then
Lemma 2: [22] If p∈P, then
Theorem 1
Theorem 1: If f is given by (1) belongs to the subclass ℛ(𝑡, 𝛾, 𝜆), 𝑡∈( 1 2, 1), then
Theorem 1: If f is given by (1) belongs to the subclass ℛ(𝑡, 𝛾, 𝜆), 𝑡∈( 1 2 , 1), then
Theorem 2
Theorem 2: If f is given by (1) belongs to the subclass ℛ(𝑡, 𝛾, 𝜆), 𝑡∈( 1 2, 1), then
Theorem 2: If f is given by (1) belongs to the subclass ℛ(𝑡, 𝛾, 𝜆), 𝑡∈( 1 2 , 1), then
Theorem 3
Theorem 3: If f is given by (1) belongs to the subclass ℛ(𝑡, 𝛾, 𝜆), 𝑡∈( 1 2, 1), then
Theorem 3: If f is given by (1) belongs to the subclass ℛ(𝑡, 𝛾, 𝜆), 𝑡∈( 1 2 , 1), then
Theorem 4
Theorem 4: If f is given by (1) belongs to the subclass ℛ(𝑡, 𝛾, 𝜆), 𝑡∈( 1 2, 1), then
Theorem 4: If f is given by (1) belongs to the subclass ℛ(𝑡, 𝛾, 𝜆), 𝑡∈( 1 2 , 1), then
Lemma 1
Lemma 1, we get (45).
Lemma 1, we get (45).
Theorem 5
Theorem 5: If f is given by (1) belongs to the subclass ℛ(𝑡, 𝛾, 𝜆), 𝑡∈( 1 2, 1), 𝛾∈ℂ∖ 0 and 𝜆≥1, then we have
Theorem 5: If f is given by (1) belongs to the subclass ℛ(𝑡, 𝛾, 𝜆), 𝑡∈( 1 2 , 1) , 𝛾∈ℂ∖{0} and 𝜆≥1, then we have
Corollary 1
Corollary 1: If f is given by (1) belongs to the subclass ℛ(𝑡, 𝛾, 1), 𝑡∈( 1 2, 1) and 𝛾∈ℂ∖ 0, then we have
Corollary 1: If f is given by (1) belongs to the subclass ℛ(𝑡, 𝛾, 1), 𝑡∈( 1 2 , 1) and 𝛾∈ℂ∖{0} , then we have
Definitions (1)
Def 1
Definition 1: A function f∈Σ, given by (1) is said to be in the class ℛ(𝑡, 𝛾, 𝜆), if the following conditions are satisfied holds:
Definition 1: A function f∈Σ, given by (1) is said to be in the class ℛ(𝑡, 𝛾, 𝜆), if the following conditions are satisfied holds:
Function classes studied:
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