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Results & Lemmas (9)
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Lemma 1.1.
Lemma 1.1. [33] If p ∈P is of the form (1.2) with c1 ≥0, then c1 = 2d1, c2 = 2d2 1 + 2 1 −d2 1 d2, c3 = 2d3 1 + 4 1 −d2 1 d1d2 −2 1…
Lemma 1.1. [33] If p ∈P is of the form (1.2) with c1 ≥0, then c1 = 2d1, c2 = 2d2 1 + 2 1 −d2 1 d2, c3 = 2d3 1 + 4 1 −d2 1 d1d2 −2 1 −d2
Lemma 1.2.
Lemma 1.2. If p ∈P is of the form (1.2) then the following inequalities hold |cn| ≤2 for n ≥1, (1.13) |cn+k −µcnck| < 2 for 0 ≤µ ≤1, (1.14)…
Lemma 1.2. If p ∈P is of the form (1.2) then the following inequalities hold |cn| ≤2 for n ≥1, (1.13) |cn+k −µcnck| < 2 for 0 ≤µ ≤1, (1.14) |cmcn −ckcl| ≤4 for m + n = k + l, (1.15) |cn+2k −µcnc2 k| ≤2(1 + 2µ)
Lemma 1.3.
Lemma 1.3. [36] Let p ∈P and has the form (1.2), then |Kc3 1 −Lc1c2 + Mc3| ≤2|K| + 2|L −2K| + 2|K −L + M|.
Lemma 1.3. [36] Let p ∈P and has the form (1.2), then |Kc3 1 −Lc1c2 + Mc3| ≤2|K| + 2|L −2K| + 2|K −L + M|.
Lemma 1.4.
Lemma 1.4. [37] Given real numbers A, B, C, let Y (A, B, C):= max A + Bz + Cz2 + 1 −|z|2: z ∈U
Lemma 1.4. [37] Given real numbers A, B, C, let Y (A, B, C) := max A + Bz + Cz2 + 1 −|z|2 : z ∈U
Theorem 2.1.
Theorem 2.1. If f ∈RL and it has the form given in (1.1), then γ1 ≤1 4, γ2 ≤1 6, γ3 ≤1 8, (2.1) γ4 ≤607 2304, (2.2)
Theorem 2.1. If f ∈RL and it has the form given in (1.1), then γ1 ≤1 4, γ2 ≤1 6, γ3 ≤1 8, (2.1) γ4 ≤607 2304, (2.2)
Theorem 3.1.
Theorem 3.1. If f ∈RL, then |H2,1(Ff/2)| ≤1 36. (3.1) The inequality in (3.1) is sharp.
Theorem 3.1. If f ∈RL, then |H2,1(Ff/2)| ≤1 36. (3.1) The inequality in (3.1) is sharp.
Theorem 4.1.
Theorem 4.1. If f ∈RL, then γ2γ4 −γ2 3 ≤4247 69120. (4.1)
Theorem 4.1. If f ∈RL, then γ2γ4 −γ2 3 ≤4247 69120. (4.1)
Theorem 4.2.
Theorem 4.2. If f ∈RL, then γ1γ4 −γ2γ3 < 103 1920. (4.2)
Theorem 4.2. If f ∈RL, then γ1γ4 −γ2γ3 < 103 1920. (4.2)
Theorem 4.3.
Theorem 4.3. If f ∈RL, then H3,1(f) ≤ 415763 13271040.
Theorem 4.3. If f ∈RL, then H3,1(f) ≤ 415763 13271040.
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