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Ma-Minda φ-classes studied in this paper:
Results & Lemmas (10)
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Lemma 3.1
Lemma 3.1 30 Let p ∈P, is given in (4). Then,
Lemma 3.1 30 Let p ∈P, is given in (4). Then,
Lemma 3.2
Lemma 3.2 30 Let p ∈P, is given in (4). Then,
Lemma 3.2 30 Let p ∈P, is given in (4). Then,
Lemma 3.3
Lemma 3.3 31,32 Let p ∈P, is given in (4). Then, if S ∈[0, 1] with S(2S −1) ≤T ≤S, we have
Lemma 3.3 31,32 Let p ∈P, is given in (4). Then, if S ∈[0, 1] with S(2S −1) ≤T ≤S, we have
Lemma 3.4
Lemma 3.4 Let p ∈P, is in the form (4). Then, for x, y ∈U, we have
Lemma 3.4 Let p ∈P, is in the form (4). Then, for x, y ∈U, we have
Lemma 3.5
Lemma 3.5 35 Let σ, η, ϕ and u satisfy u, σ ∈(0, 1) and
Lemma 3.5 35 Let σ, η, ϕ and u satisfy u, σ ∈(0, 1) and
Theorem 4.1
Theorem 4.1 Let f ∈A be given by (1). If f ∈SS∗cre, then
Theorem 4.1 Let f ∈A be given by (1). If f ∈SS∗cre, then
Theorem 4.2
Theorem 4.2 Let f ∈A and is given in (1). If f ∈SS∗cre, then
Theorem 4.2 Let f ∈A and is given in (1). If f ∈SS∗cre, then
Theorem 4.3
Theorem 4.3 Let f ∈A and is given in (1). If f ∈SS∗cre, then
Theorem 4.3 Let f ∈A and is given in (1). If f ∈SS∗cre, then
Theorem 4.4
Theorem 4.4 Let f ∈A and is given in (1). If f ∈SS∗cre, then
Theorem 4.4 Let f ∈A and is given in (1). If f ∈SS∗cre, then
Theorem 4.5
Theorem 4.5 Let f ∈A and is given in (1). If f ∈SS∗cre, then
Theorem 4.5 Let f ∈A and is given in (1). If f ∈SS∗cre, then
Definitions (1)
Def 1.1
Definition 1.1 If φ(z) = z + √ 1 + z2 was introduced by Raina and Sokol17, φ(z) maps U to the cres cent-shaped region z ∈C: |z2 −1| < 2z,…
Definition 1.1 If φ(z) = z + √ 1 + z2 was introduced by Raina and Sokol17, φ(z) maps U to the cres cent-shaped region {z ∈C : |z2 −1| < 2z, Rez > 0}, we will define S∗s (φ(z)) = SS∗cre, is the class of sym metric star-like functions linked with Cresent-shaped domain. Literature review Recent developments in geometric function theory seem to have a special focus on the exploration of Hankel determinants, particularly within various subclasses of analytic and starlike functions.These determinan
Function classes studied:
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