• Korean Journal of Mathematics
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• v.28 no.4
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• pp.973-984
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• 2020

This paper is devoted to study the reproducing property on 2-inner product Hilbert spaces. We focus on a new structure to produce reproducing kernel Hilbert and Banach spaces. According to multi variable computing, this structures play the key role in probability, mathematical finance and machine learning.

• Journal of the Korean Mathematical Society
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• v.38 no.6
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• pp.1125-1156
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• 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.

• Nonlinear Functional Analysis and Applications
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• v.29 no.2
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• pp.487-499
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• 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.

• Bulletin of the Korean Mathematical Society
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• v.43 no.2
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• pp.377-387
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• 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.

• Kyungpook Mathematical Journal
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• v.48 no.2
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• pp.207-222
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• 2008

A new counterpart of Bessel's inequality for orthonormal families in real or complex 2-inner product spaces is obtained. Applications for some Gr$\"{u}$ss inequality for determinantal integral inequalities are also provided.

• The Pure and Applied Mathematics
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• v.16 no.4
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• pp.359-367
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• 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.

• Bulletin of the Korean Mathematical Society
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• v.42 no.3
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• pp.591-608
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• 2005

Some new reverses of Bessel's inequality for orthonormal families in real or complex 2-inner product spaces are pointed out. Applications for some Gruss type inequalities and for determinantal integral inequalities are given as well.

• Bulletin of the Korean Mathematical Society
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• v.41 no.4
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• pp.739-777
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• 2004

An analogue of the Gram's inequality for n-inner product spaces is given. Further, a number of inequalities involving Gram's determinant are stated and proved in terms of n-inner products.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.279-292
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• 2006

A reverse of Bessel's inequality in 2-inner product spaces and companions of $Gr\ddot{u}ss$ inequality with applications for determinantal integral inequalities are given.

• Journal of the Korean Mathematical Society
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• v.34 no.2
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• pp.265-277
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• 1997

Let E be a real, non-degenerate, indefinite inner product space with dim $E \geq 3$. It is shown that any bijection of E which preserves the light cones is an affine map.