INEQUALITIES FOR THE p-ANGULAR DISTANCE IN NORMED LINEAR SPACES
نویسنده
چکیده
New upper and lower bounds for the p-angular distance in normed linear spaces are given. Some of the obtained upper bounds are better than the corresponding results due to L. Maligranda recently established in the paper [Simple norm inequalities, Amer. Math. Monthly, 113(2006), 256-260].
منابع مشابه
UPPER AND LOWER BOUNDS FOR THE p–ANGULAR DISTANCE IN NORMED SPACES WITH APPLICATIONS
For nonzero vectors x and y in the normed linear space (X ,‖·‖) we can define the p -angular distance by αp [x,y] := ∥∥‖x‖p−1 x−‖y‖p−1 y ∥∥ . In this paper we show among others that 1 2 ∣∣ ∣∣‖x‖p−1−‖y‖p−1 ∣∣‖x+ y‖− ( ‖x‖p−1 +‖y‖p−1 ) ‖x− y‖ ∣∣ αp [x,y] 1 2 ∣∣‖x‖p−1 −‖y‖p−1 ∣∣‖x+ y‖+ ( ‖x‖p−1 +‖y‖p−1 ) ‖x− y‖ ] for any p ∈ R and for any nonzero x,y ∈ X . Some reverses of the triangle and the con...
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تاریخ انتشار 2007