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Results & Lemmas (6)
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Lemma 1.1
Lemma 1.1 ([5]) If p ∈P, then |ci −µcjci−j| ≤2, satisfies for the values i, j ∈N, with i > j and µ ∈[0, 1], which is same as |cn+k −µcnck|…
Lemma 1.1 ([5]) If p ∈P, then |ci −µcjci−j| ≤2, satisfies for the values i, j ∈N, with i > j and µ ∈[0, 1], which is same as |cn+k −µcnck| ≤2, for n, k ∈N, with µ ∈[0, 1].
Lemma 1.2
Lemma 1.2 ([11]) For p ∈P, then |ct| ≤2, for t ∈N, equality occurs for the function po = 1+z 1−z, z ∈D.
Lemma 1.2 ([11]) For p ∈P, then |ct| ≤2, for t ∈N, equality occurs for the function po = 1+z 1−z, z ∈D.
Lemma 1.3
Lemma 1.3 ([15]) If p ∈P, is of the form (1.7) with c1 ≥0, then 2c2 = c2 1 + tζ, 4c3 = c3 1 + 2c1tζ −c1tζ2 + 2t 1 −|ζ|2 η, and 8c4 = c4 1…
Lemma 1.3 ([15]) If p ∈P, is of the form (1.7) with c1 ≥0, then 2c2 = c2 1 + tζ, 4c3 = c3 1 + 2c1tζ −c1tζ2 + 2t 1 −|ζ|2 η, and 8c4 = c4 1 + 3c2 1tζ + 4 −3c2 1 tζ2 + c2
Theorem 2.1
Theorem 2.1 If f ∈Ks then H2,1(f −1) ≤1 3, and the result is sharp for fo = log p (1 + z)/(1 −z).
Theorem 2.1 If f ∈Ks then H2,1(f −1) ≤1 3, and the result is sharp for fo = log{ p (1 + z)/(1 −z)}.
Theorem 2.2
Theorem 2.2 If f ∈Ks then H2,2(f −1) ≤1 9, and the result is sharp for the same function mentioned in Theorem 2.1.
Theorem 2.2 If f ∈Ks then H2,2(f −1) ≤1 9, and the result is sharp for the same function mentioned in Theorem 2.1.
Theorem 2.3
Theorem 2.3 If f ∈Ks then H2,3(f −1) ≤2 45, and the result is sharp for the same function mentioned in Theorem 2.1.
Theorem 2.3 If f ∈Ks then H2,3(f −1) ≤2 45, and the result is sharp for the same function mentioned in Theorem 2.1.
Function classes studied:
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