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|Title: ||The Proofs of product inequalities in a generalized vector space|
|Authors: ||t Barnes, Benedic|
Owusu-Ansah, E. D. J.
Amponsah, S. K.
|Keywords: ||Product inequality|
, first product inequality
second product inequality
generalized vector space
|Issue Date: ||2018|
|Publisher: ||EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS|
|Citation: ||EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS, Vol. 11, No. 2, 2018, 375-389|
|Abstract: ||In this paper, we introduce the proofs of product inequalities:
kukkvk ≤ kuk+kvk, for all u, v ∈ [0, 2], and kuk+kvk ≤ kukkvk, for all u, v ∈ [2, ∞). By applying
the first product inequality to the L
spaces, we observed that if f : Ω → [0, 1], and g : Ω → R,
then kfkpkgkp ≤ kfkp + kgkp. Also, if f, g : Ω → R, then kfkp + kgkp ≤ kfkpkgkp.
2010 Mathematics Subject Classifications: 4B45, 44B46|
|Description: ||This article is published in EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS|
|Appears in Collections:||College of Science|
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