• Bulletin of the Korean Mathematical Society
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• v.36 no.1
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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

• Communications of the Korean Mathematical Society
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• v.12 no.4
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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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• v.6 no.2
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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.

• Journal of the Korean Mathematical Society
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• v.45 no.1
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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.

• Communications of the Korean Mathematical Society
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• v.19 no.2
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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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• v.60 no.1
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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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• v.17 no.1
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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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• v.29 no.1
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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.

• Journal of the Chungcheong Mathematical Society
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• v.19 no.3
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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 $$x(n)=f(n)+\sum_{j=0}^{n}B(n,j)x(j)$$, $n{\geq}0$.

• Journal of the Korean Mathematical Society
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• v.56 no.2
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• pp.523-537
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• 2019

We estimate the essential norms of Volterra-type integral operators $V_g$ and $I_g$, and multiplication operators $M_g$ with holomorphic symbols g on a large class of generalized Fock spaces on the complex plane ${\mathbb{C}}$. The weights defining these spaces are radial and subjected to a mild smoothness conditions. In addition, we assume that the weights decay faster than the classical Gaussian weight. Our main result estimates the essential norms of $V_g$ in terms of an asymptotic upper bound of a quantity involving the inducing symbol g and the weight function, while the essential norms of $M_g$ and $I_g$ are shown to be comparable to their operator norms. As a means to prove our main results, we first characterized the compact composition operators acting on the spaces which is interest of its own.