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Results & Lemmas (9)
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Theorem 1
Theorem 1: Let f∈Σp,α A sufficient condition for a function of the form (1) to be in Sp,α(µ,ν) is that:
Theorem 1: Let f∈Σp,α A sufficient condition for a function of the form (1) to be in Sp,α(µ,ν) is that:
Corollary 1
Corollary 1: Let the assumptions of Theorem 1 hold. Then:
Corollary 1: Let the assumptions of Theorem 1 hold. Then:
Corollary 2
Corollary 2: Let the assumptions of Theorem 1 hold. Then:
Corollary 2: Let the assumptions of Theorem 1 hold. Then:
Corollary 3
Corollary 3: Let the assumptions of Theorem 1 hold. Then:
Corollary 3: Let the assumptions of Theorem 1 hold. Then:
Corollary 4
Corollary 4: Let the assumptions of Theorem 1 hold. Then:
Corollary 4: Let the assumptions of Theorem 1 hold. Then:
Theorem 2
Theorem 2: A necessary and sufficient condition for f of the form (2) namely:
Theorem 2: A necessary and sufficient condition for f of the form (2) namely:
Theorem 3
Theorem 3: The extreme points of TSp,α (µ,ν) are the functions given by:
Theorem 3: The extreme points of TSp,α (µ,ν) are the functions given by:
Theorem 4
Theorem 4: Let F∈Σp. A sufficient condition for a function of the form (11) to be in Sp,α (µ,ν) is (6).
Theorem 4: Let F∈Σp. A sufficient condition for a function of the form (11) to be in Sp,α (µ,ν) is (6).
Theorem 5
Theorem 5: Let F∈Tp, A necessary and sufficient condition for a function of the form (12) to be in TSp,α(µ,ν) is (8).
Theorem 5: Let F∈Tp, A necessary and sufficient condition for a function of the form (12) to be in TSp,α(µ,ν) is (8).
Definitions (1)
Def 1
Definition 1: The fractional integral of order α is defined, for a function f Srivastava and Owa (1989):
Definition 1: The fractional integral of order α is defined, for a function f Srivastava and Owa (1989):
Function classes studied:
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