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Abstract
In this paper, it is attempted to introduce and
investigate new subclasses of Sakaguchi kind of functions
related to shell – likes curves connected with Fibonacci numbers.
Furthermore, the estimates of first two coefficients of functions
in these classes are obtained. Fekete – Szego inequalities for
these function classes are also determined.
Results & Lemmas (8)
Each result is auto-extracted from the paper via OCR - the math is shown verbatim and may carry occasional transcription artifacts. Click to expand the full statement.
Theorem 1.3.
Theorem 1.3. [5] The function 2 2 2 2 1 1 ~ z z z z p
Theorem 1.3. [5] The function 2 2 2 2 1 1 ~ z z z z p
Theorem 2.2.
Theorem 2.2. Let f be given by (1) be in the class z p SLM t ~,, . Then
Theorem 2.2. Let f be given by (1) be in the class z p SLM t ~ , , . Then
Corollary 2.3.
Corollary 2.3. Let f given by (1) be in the class z p KSL ~ . Then
Corollary 2.3. Let f given by (1) be in the class z p KSL ~ . Then
Corollary 2.4.
Corollary 2.4. Let f given by (1) be in the class z p KSL ~ . Then
Corollary 2.4. Let f given by (1) be in the class z p KSL ~ . Then
Theorem 3.1.
Theorem 3.1. let f given by (1) be in the class z p SLM t ~,, and
Theorem 3.1. let f given by (1) be in the class z p SLM t ~ , , and
Corollary 3.2.
Corollary 3.2. If z p SLM f t ~,, , then
Corollary 3.2. If z p SLM f t ~ , , , then
Corollary 3.3.
Corollary 3.3. Let f given by (1) be in the class z p KSL ~ and
Corollary 3.3. Let f given by (1) be in the class z p KSL ~ and
Corollary 3.4.
Corollary 3.4. Let f given by (1) be in the class z p KSL ~ and . Then we have
Corollary 3.4. Let f given by (1) be in the class z p KSL ~ and . Then we have
Definitions (3)
Def 1.1.
Definition 1.1. The function A f belongs to the class SL if it satisfies the condition that z p z
Definition 1.1. The function A f belongs to the class SL if it satisfies the condition that z p z
Def 1.2.
Definition 1.2. The function A f belongs to the class KSL of convex shell – like functions if it satisfies the condition that
Definition 1.2. The function A f belongs to the class KSL of convex shell – like functions if it satisfies the condition that
Def 2.1.
Definition 2.1. For 1,1 0 t but
Definition 2.1. For 1 ,1 0 t but
Function classes studied:
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