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Math Help - The name of the refrence!!(help)

  1. #1
    Junior Member miss_lolitta's Avatar
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    Angry prove these inequalities???

    hi, Can any of you help me to give me proof of these inequlities:

    (1)

    <br /> <br />
(a+b)^{\alpha}\leq 2^{\alpha-1}(a^{\alpha}+b^{\alpha})\quad\text{for }a,b\geq 0 \quad\text{and<br />
}\alpha\geq1<br /> <br />

    and

    (2)

    <br /> <br />
|x|^{\alpha}\leq1+|x|\quad\text{for } x\in\mathbb{R}\quad\text{and } \alpha\in[0,1].<br /> <br />




    thanx for all,,
    Last edited by miss_lolitta; March 11th 2010 at 12:50 PM.
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  2. #2
    Junior Member miss_lolitta's Avatar
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    So sorry my brothers members of the forum ..

    I tried to prove 2 inequalities above and we get that:

    The second inequality I can not prove when x is a negative, while others i use mathematical induction to prove it but i'm not sure ??!

    Please help me in finding the correct proof ..

    Thankful your help,,

    Your sister,,

    Lolitta
    Last edited by miss_lolitta; March 11th 2010 at 12:57 PM.
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  3. #3
    Junior Member miss_lolitta's Avatar
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    hi,,

    Plz,,Can anyone guide me in any book or reference I can find written proof of the above inequlities??!!
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