• 대한수학회보
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• 제36권1호
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• pp.171-181
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• 1999

In this note, we will prove that the operator-valued function space integral as an operator from $L_p\;to\;L_{p'}$ (1

• 대한수학회논문집
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• 제12권4호
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• pp.1039-1064
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• 1997

Existence and Uniqueness for Volterra equations (VE) with a weak regularity assumption on A, the relative closedness of A are investigaed by means of the Laplace transform theory. Also, (VE) are studied by means of the method of convoluted solution operator families.

• Journal of applied mathematics & informatics
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• 제6권2호
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• pp.407-416
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• 1999

In this paper we give some sufficient conditions for the existence and uniqueness of a continuous for the existence and uniqueness of a continuous slution of the system of Urysohn-Volterra equation with hysteresis.

• 대한수학회지
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• 제45권1호
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• pp.229-248
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• 2008

The boundedness and compactness of the Volterra composition operators between weighted Bergman spaces and Bloch type spaces are discussed in this paper.

• 대한수학회논문집
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• 제19권2호
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• pp.293-305
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• 2004

Trotter-Kato type approximations of the convoluted solution operator families for the Volterra integral equations (V $E_n$): v(t)=$A_{n} \int_0^t v(t-s) d\mu_n(s) + f_n(t), t \geq 0$ and the convergence of the solutions to the equations (V $E_n$) are studied.

• Kyungpook Mathematical Journal
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• 제60권1호
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• pp.163-175
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• 2020

The stability of a class of Volterra-type difference equations that include a generalized difference operator ∆_a is investigated using Krasnoselskii's fixed point theorem and some results are obtained. In addition, some examples are given to illustrate our theoretical results.

• East Asian mathematical journal
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• 제17권1호
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• pp.71-85
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• 2001

The strong convergences of solutions to a nonlinear Volterra equation are studied in Banach space. As an application, a nonlinear heat flow in a homogeneous bar of unit length of a material with memory is investigated.

• East Asian mathematical journal
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• 제29권1호
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• pp.69-82
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• 2013

In this paper we consider a doubly nonlinear Volterra equation related to the Leray-Lions with a nonsmooth kernel. By exploiting a suitable implicit time-discretization technique we obtain the existence of global strong solution.

• 대한수학회보
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• 제61권4호
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• pp.949-957
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• 2024

Let Y_p be the multiplication operator M_p plus the Volterra operator V_p induced by p(z), where p is a polynomial. Under a mild condition, we prove that Y_p acting on the Dirichlet space 𝔇 is similar to multiplication operator M_p acting on a subspace S(𝔻) of 𝔇. Furthermore, it shows that T_zⁿ (n ≥ 2) has exactly 2ⁿ reducing subspaces on 𝔇.

• 충청수학회지
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• 제19권3호
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• pp.237-244
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• 2006

In this paper, we examine the existence and bounded- ness of the solutions of discrete Volterra equations $$x(n)=f(n)+\sum_{j=0}^{n}g(n,j,x(j))$$, $n{\geq}0$ and $$x(n)=f(n)+\sum_{j=0}^{n}B(n,j)x(j)$$, $n{\geq}0$.