• Journal of applied mathematics & informatics
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• 제6권1호
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• pp.163-174
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• 1999

The purpose of this paper is to obtain the solution of Fredholm-Volterra integral equation with singular kernel in the space $L_2(-1, 1)\times C(0,T), 0 \leq t \leq T< \infty$, under certain conditions,. The numerical method is used to solve the Fredholm integral equation of the second kind with weak singular kernel using the Toeplitz matrices. Also the error estimate is computed and some numerical examples are computed using the MathCad package.

• 호남수학학술지
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• 제26권4호
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• pp.455-462
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• 2004

We prove that if ${\mathbb{K}}^*$ is adjoint operator on $W_2{^2}({\Omega})$, then ${\mathbb{K}}^*v(t,\;{\tau})=,\;v(x,\;y){\in}W_2{^2}({\Omega})$ ; it is also related to the decomposition of solution of Fredholm equations.

• 대한수학회논문집
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• 제36권2호
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• pp.313-325
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• 2021

In this paper, we provide a characterization of upper semi-Fredholm operators via the relative demicompactness concept. The obtained results are used to investigate the stability of various essential spectra of closed linear operators under perturbations belonging to classes involving demicompact, as well as, relative demicompact operators.

• 대한수학회보
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• 제43권3호
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• pp.653-655
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• 2006

We give a simple proof of the statement that if T is a bounded linear operator on a complex HIlbert space then T is Fredholm if and only if ${\pi}(T)$ is not a TDZ, where ${\pi}(\cdot)$ is the Catkin homomorphism.

• 대한수학회보
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• 제42권2호
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• pp.369-378
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• 2005

In this paper we will consider the weighted composition operator $W=uC_{\varphi}$ between two different $L^p(X,\;\Sigma,\;\mu)$ spaces, generated by measurable and non-singular transformations $\varphi$ from X into itself and measurable functions u on X. We characterize the functions u and transformations $\varphi$ that induce weighted composition operators between $L^p-spaces$ by using some properties of conditional expectation operator, pair $(u,\;\varphi)$ and the measure space $(X,\;\Sigma,\;\mu)$. Also, Fredholmness of these type operators will be investigated.

• 한국수학교육학회지시리즈A:수학교육
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• 제22권1호
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• pp.85-88
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• 1983

• 대한수학회지
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• 제44권2호
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• pp.275-296
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• 2007

We study the self-duality operator on conic 4-manifolds. The self-duality operator can be identified as a regular singular operator in the sense of $Br\"{u}ning$ and Seeley, based on which we construct its parametrizations and closed extensions. We also compute the indexes.

• Nonlinear Functional Analysis and Applications
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• 제26권5호
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• pp.869-885
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• 2021

In this article, we define Picard's three-step iteration process for the approximation of fixed points of Zamfirescu operators in an arbitrary Banach space. We prove a convergence result for Zamfirescu operator using the proposed iteration process. Further, we prove that Picard's three-step iteration process is almost T-stable and converges faster than all the known and leading iteration processes. To support our results, we furnish an illustrative numerical example. Finally, we apply the proposed iteration process to approximate the solution of a mixed Volterra-Fredholm functional nonlinear integral equation.

• 대한수학회논문집
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• 제13권3호
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• pp.481-487
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• 1998

Let (equation omitted) denote the closure of the set (equation omitted) of dominant operators in the norm topology. We show that the Weyl spectrum of an operator T $\in$ (equation omitted) satisfies the spectral mapping theorem for analytic functions, which is an extension of [5, Theorem 1]. Also we show that an operator approximately equivalent to an operator of class (equation omitted) is of class (equation omitted).

• 대한수학회논문집
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• 제21권1호
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• pp.53-64
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• 2006

In this paper, we are concerned with the algebraic representation of the quasi-nilpotent part for prehermitian operators on Banach spaces. The quasi-nilpotent part of an operator plays a significant role in the spectral theory and Fredholm theory of operators on Banach spaces. Properties of the quasi-nilpotent part are investigated and an application is given to totally paranormal and prehermitian operators.