• 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.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제2권2호
• /
• pp.163-172
• /
• 1995

G.Lumer [8] introduced the concept of semi-product space. H.M.El-Hamouly [7] introduced the concept of fuzzy inner product spaces. In this paper, we defined fuzzy semi-inner-product space and investigated some properties of fuzzy semi product space.

• 대한수학회지
• /
• 제38권6호
• /
• pp.1125-1156
• /
• 2001

An analogue of Grams inequality for 2-inner product spaces is given. Further, a number of inequalities involving Grams determinant are stated and proved in terms of 2-inner products.

• 대한수학회보
• /
• 제44권3호
• /
• pp.447-459
• /
• 2007

The purpose of this paper is to introduce the notion of fuzzy n-inner product space. Ascending family of quasi ${\alpha}$-n-norms corresponding to fuzzy quasi n-norm is introduced and we provide some results on it.

• Journal of applied mathematics & informatics
• /
• 제19권1_2호
• /
• pp.297-310
• /
• 2005

The concept of the Moore-Penrose inverse in an indefinite inner product space is introduced. Extensions of some of the formulae in the Euclidean space to an indefinite inner product space are studied. In particular range-hermitianness is completely characterized. Equivalence of a weighted generalized inverse and the Moore-Penrose inverse is proved. Finally, methods of computing the Moore-Penrose inverse are presented.

• 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.

• Nonlinear Functional Analysis and Applications
• /
• 제29권2호
• /
• pp.487-499
• /
• 2024

The main motivation for this paper is to investigate the fixed point property for nonlinear contraction defined on b-Menger inner product spaces. First, we introduce a b-Menger inner product spaces, then the topological structure is discussed and the probabilistic Pythagorean theorem is given and established. Also we prove the existence and uniqueness of fixed point in these spaces. This result generalizes and improves many previously known results.

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

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

• 대한수학회보
• /
• 제43권2호
• /
• pp.377-387
• /
• 2006

In this paper, some characterizations of representation for continuous linear functionals on $2{\kappa}$-inner product spaces in terms of best approximations and orthogonalities are given.

• 대한수학회보
• /
• 제43권1호
• /
• pp.27-41
• /
• 2006

A counterpart of the famous Bessel's inequality for orthornormal families in real or complex inner product spaces is given. Applications for some Gruss type inequalities are also provided.