• 대한수학회보
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• 제54권6호
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• pp.2013-2027
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• 2017

We compute explicitly the matrices represented by Toeplitz operators on the Hardy space over the unit circle with respect to a special orthonormal basis constructed by author in terms of their symbols. And we also find a necessary condition for the matrix generated by the product of two Toeplitz operators with respect to the basis to be a Toeplitz matrix by a direct calculation and we finally solve commuting problems of two Toeplitz operators in terms of symbols. This is a generalization of the classical results obtained regarding to the orthonormal basis consisting of the monomials.

• 대한수학회보
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• 제51권2호
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• pp.303-315
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• 2014

In this work, we construct Kantorovich type generalization of a class of linear positive operators via Riemann type q-integral. We obtain estimations for the rate of convergence by means of modulus of continuity and the elements of Lipschitz class and also investigate weighted approximation properties.

• 대한수학회보
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• 제50권6호
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• pp.1973-1979
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• 2013

The main purpose of this paper is to give the Wintner theorem in unital complete random normed algebras which is a random generalization of the classical Wintner theorem in Banach algebras. As an application of the Wintner theorem in unital complete random normed algebras, we also obtain that the identity operator on a complete random normed module is not a commutator.

• 대한수학회지
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• 제47권1호
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• pp.29-40
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• 2010

In this paper, we study a generalization of the Banach space B($l_2$) of all bounded linear operators on $l_2$. Over this space, we present some reasonable ways to define Schatten-type classes which are generalizations of the classical Schatten classes of compact operators on $l_2$.

• 대한수학회보
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• 제29권2호
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• pp.215-220
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• 1992

Using a matrix method, pp. Antosik and C. Swartz have obtained a series of nice properties of bounded multiplier convergent (BMC) series on metric linear spaces ([1],[8],[9]). In this paper, we establish a basic property of BMC series on topological vector spaces which is a generalization of a result due to J. Batt([2], Th.2). From this, we have obtained a kind of inclusion theorem of operator spaces. This theorem yields a nice result on infinite systems of linear equations.

• Kyungpook Mathematical Journal
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• 제56권3호
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• pp.877-897
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• 2016

In the present article, we study some approximation properties of the Kantorovich type generalization of $Sz{\acute{a}}sz$ type operators involving Charlier polynomials introduced by S. Varma and F. Taşdelen (Math. Comput. Modelling, 56 (5-6) (2012) 108-112). First, we establish approximation in a Lipschitz type space, weighted approximation theorems and A-statistical convergence properties for these operators. Then, we obtain the rate of approximation of functions having derivatives of bounded variation.

• 충청수학회지
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• 제25권1호
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• pp.35-42
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• 2012

In this paper we first introduce a Carleson inequality and study the generalized form of Carleson inequality in the context of spaces of homogeneous type. The previous inequality is known to play important roles in harmonic analysis.

• Journal of Applied and Pure Mathematics
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• 제6권3_4호
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• pp.191-200
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• 2024

Motivated by the previously reported results, this work attempts to provide fresh refinements to both vector and numerical radius inequalities by providing a refinement to the well known Buzano's inequality which as a consequence yielded another refinement of the Cauchy-Schwartz (CS) inequality. Utilizing the new refinements of the Buzano's and Cauchy-Schwartz inequalities, we proceed to obtain various vector and numerical radius type inequalities. Methods used in the paper are standard for the operator theory inequality topics.

• 정보처리학회논문지:소프트웨어 및 데이터공학
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• 제6권12호
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• pp.573-580
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• 2017

심층 신경망은 많은 노드의 층을 쌓아 만든 거대한 신경망이다. 심층 신경망으로 대표되는 딥 러닝은 오늘날 많은 응용 분야에서 괄목할만한 성과를 거두고 있다. 하지만 다년간의 연구를 통해 심층 신경망에 대한 다양한 문제점이 식별되고 있다. 이 중 일반화는 가장 널리 알려진 문제점들 중 하나이며, 최근 연구 결과인 드롭아웃은 이러한 문제를 어느 정도 성공적으로 해결하였다. 드롭아웃은 노이즈와 같은 역할을 하여 신경망이 노이즈에 강건한 데이터 표현형을 학습할 수 있도록 하는데, 오토인코더와 관련된 연구에서 이러한 효과가 입증되었다. 하지만 드롭아웃은 빈번한 난수 연산과 확률연산으로 인해 신경망의 학습 시간이 길어지고, 신경망 각 계층의 데이터 분포가 크게 변화하여 작은 학습율을 사용해야하는 단점이 있다. 본 논문에서는 돌연변이 연산을 사용하여 비교적 적은 횟수의 연산으로 드롭아웃과 동등 이상의 성능을 나타내는 모델을 제시하고, 실험을 통하여 논문에서 제시한 방법이 드롭아웃 방식과 동등한 성능을 보임과 동시에 학습 시간 문제를 개선함을 보인다.

• 충청수학회지
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• 제25권4호
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• pp.703-709
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• 2012

Recently, Kazmi and Khan [7] introduced a kind of equilibrium problem called generalized system (GS) with a single-valued bi-operator F. Next, in [10], the first author considered a generalization of (GS) into a multi-valued circumstance called the multi-valued quasi-generalized system (in short, MQGS). In the current work, we provide an extension of (MQGS) into a system of (MQGS) in general settings. This system is called the generalized multi-valued quasi-generalized system (in short, GMQGS). Using the existence theorem for abstract economy by Kim [8], we prove the existence of solutions for (GMQGS) in the framework of Hausdorff topological vector spaces. As an application, an existence result of a system of generalized vector quasi-variational inequalities is derived.