• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제16권1호
• /
• pp.47-57
• /
• 2009

In this paper, we give some results which are in connection to the parallelogram law in G-inner product spaces and also prove some results related to Bohr's inequality in G-inner product spaces.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제16권4호
• /
• pp.359-367
• /
• 2009

The graph of the parallelogram law is well known, which gives rise to the characterization of an inner product space among normed linear spaces [6]. In this paper we will sketch graphs of its deformations according to our previous paper [7, Theorem 3.1 and 3.2]; each one of which characterizes an inner product space among normed linear spaces. Consequently, the graphs of some classical characterizations of an inner product space follow easily.

• 대한수학회논문집
• /
• 제17권4호
• /
• pp.583-592
• /
• 2002

In this paper, we give Hlawka's type inequalities and related results in n-inner product spaces.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제14권2호
• /
• pp.127-137
• /
• 2007

The classical Bohr's inequality states that $|z+w|^2{\leq}p|z|^2+q|w|^2$ for all $z,\;w{\in}\mathbb{C}$ and all p, q>1 with $\frac{1}{p}+\frac{1}{q}=1$. In this paper, Bohr's inequality is generalized to the setting of n-inner product spaces for all positive conjugate exponents $p,\;q{\in}\mathbb{R}$. In. In particular, the parallelogram law is recovered and an interesting operator inequality is obtained.