Some Refinement of the Triangle Inequality in Quasi 2-normed spaces
Keywords:
triangle inequality, quasi-2-normed space, quasi-(2,p)-normed space, Dunkl-Williames inequalityAbstract
In this paper we establish a generalization of the triangle inequity and the Dunkl-Williams inequality in quasi 2-normed linear spaces.
References
Y.J. Cho, S.S. Dragomir, A. White and S.S. Kim, Some inequalities in 2-inner
product spaces, Demonstratio Math. 32(1999), 485-493.
S.S. Dragomir, Y.J. Cho, S.M. Kang, S.S. Kim and J. S. Jung, Some Gruss
type inequalities in 2-inner product Spaces and applications for determinantal
integral inequalities, Panamer. math. J. 15(2005), 79-94.
C.F. Dunkl and K.S. Williams, A simple norm inequality, Amer. Math. Monthly
(1964), 53-54.
R.W. Freese, Y.J. Cho, Geometry of linear 2-normed spaces, Nova science,
Hauppauge, NY, USA, 2001. 256-260.
Gahler, S., Linear 2-normierte Raume, Math. Nachr, 28 (1965), 1-45.
M. Kato, K.S. Saito, T. Tamura, Sharp triangle inequality and its reverse in
Banach spaces, Math. Inequal. Appl. 10(2) (2007) 451-460.
S.S. Kim, S.S. Dragomir, A. White and Y.J. Cho, On the Gruss type inequality
in 2-inner product spaces and applications, PanAmerican Math. J., 11(2001),
-97.
W.A. Kirk and M.F. Smiley, Another characterization of inner product spaces,
Amer. Math. Monthly 71 (1964), 890-891.
L. Maligranda, Simple norm inequalities, Amer. Math. Monthly 113 (2006),
-260.
L. Maligranda, Some remarks on the triangele inequality for normes, Banach
J. Math. Anal. 2 (2008), no. 2, 31-41
P.R. Mercer, The Dunkl-Williams inequality in an inner product spaces, Math.
Inequal. Appl. 10 (2007), No. 2, 447-450.
C. Park, Generalized quasi-Banach spaces and (2; p)normed spaces, J. Chung.
Math. Soc, 19,(2) (2006), 197-206.
J. Pecaric, R. Rajic, The DunklWilliams inequality with n elements in normed
linear spaces, Math. Inequal. Appl.10(2) (2007) 461-470.
C. Wu and K. Li, On the triangel inequality in quasi-Banach spaces, J. Inequal.
pure and appl. Math, 9(2)(2008) 1-9.
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Copyright (c) 2014 Majid Abrishami-Moghaddam, Tahereh Sistani
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
