• East Asian mathematical journal
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• v.25 no.1
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• pp.11-26
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• 2009

In this paper, the concepts of compatible mappings of types (A) and (P) are introduced in an induced metric space, two common xed point theorems for two pairs of compatible mappings of types (A) and (P) in an induced complete metric space are established. As their applications, the existence and uniqueness results of common solution for a system of functional equations arising in dynamic programming are discussed.

• The Pure and Applied Mathematics
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• v.15 no.1
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• pp.1-17
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• 2008

Here, we consider the existence and uniqueness solution of nonlinear integral equation of the second kind of type Volterra-Hammerstein. Also, the normality and continuity of the integral operator are discussed. A numerical method is used to obtain a system of nonlinear integral equations in position. The solution is obtained, and many applications in one, two and three dimensionals are considered.

• Journal of applied mathematics & informatics
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• v.26 no.1_2
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• pp.61-73
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• 2008

In this paper common fixed point theorems dealing with compatible mappings of type (P) are established. As a application, the existence and uniqueness of common solution for a system of functional equations arising in dynamic programming is given. The results presented in this paper improve, generalize and unify the corresponding results in this field.

• Journal of applied mathematics & informatics
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• v.9 no.2
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• pp.695-703
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• 2002

The fractional order evolutionary integral equations have been considered by first author in [6], the existence, uniqueness and some other properties of the solution have been proved. Here we study the continuation of the solution and its fractional order derivative. Also we study the generality of this problem and prove that the fractional order diffusion problem, the fractional order wave problem and the initial value problem of the equation of evolution are special cases of it. The abstract diffusion-wave problem will be given also as an application.

• Kyungpook Mathematical Journal
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• v.59 no.4
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• pp.735-769
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• 2019

In this paper, we consider the Robin-Dirichlet problem for a nonlinear wave equation of Kirchhoff-Carrier type with a viscoelastic term. Using the Faedo-Galerkin method and the linearization method for nonlinear terms, the existence and uniqueness of a weak solution are proved. An asymptotic expansion of high order in a small parameter of a weak solution is also discussed.

• Journal of applied mathematics & informatics
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• v.31 no.5_6
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• pp.609-621
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• 2013

At present, research on providing new methods to solve nonlinear integral equations for minimizing the error in the numerical calculations is in progress. In this paper, necessary conditions for existence and uniqueness of solution for nonlinear 2D Fredholm integral equations are given. Then, two different numerical solutions are presented for this kind of equations using 2D shifted Legendre polynomials. Moreover, some results concerning the error analysis of the best approximation are obtained. Finally, illustrative examples are included to demonstrate the validity and applicability of the new techniques.

• Bulletin of the Korean Mathematical Society
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• v.47 no.2
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• pp.263-274
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• 2010

In this paper, a new class of general nonlinear variational inclusions involving H-monotone is introduced and studied in Hilbert spaces. By applying the resolvent operator associated with H-monotone, we prove the existence and uniqueness theorems of solution for the general nonlinear variational inclusion, construct an iterative algorithm for computing approximation solution of the general nonlinear variational inclusion and discuss the convergence of the iterative sequence generated by the algorithm. The results presented in this paper improve and extend many known results in recent literatures.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.381-394
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• 2011

In this paper, a Naveir-Stokes equation is solved by using the Adomian's decomposition method (ADM), modified Adomian's decomposition method (MADM), variational iteration method (VIM), modified variational iteration method (MVIM), modified homotopy perturbation method (MHPM) and homotopy analysis method (HAM). The approximate solution of this equation is calculated in the form of series which its components are computed by applying a recursive relation. The existence and uniqueness of the solution and the convergence of the proposed methods are proved. A numerical example is studied to demonstrate the accuracy of the presented methods.

• Journal of the Korean Mathematical Society
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• v.54 no.1
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• pp.193-213
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• 2017

We investigate an efficient approximation of solution to stochastic Burgers equation driven by an additive space-time noise. We discuss existence and uniqueness of a solution through the Orstein-Uhlenbeck (OU) process. To approximate the OU process, we introduce the Karhunen-$Lo{\grave{e}}ve$ expansion, and sparse grid stochastic collocation method. About spatial discretization of Burgers equation, two separate finite element approximations are presented: the conventional Galerkin method and Galerkin-conservation method. Numerical experiments are provided to demonstrate the efficacy of schemes mentioned above.

• Nonlinear Functional Analysis and Applications
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• v.27 no.3
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• pp.471-497
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• 2022

In this paper, we study a system of nonlinear wave equations associated with the helical flows of Maxwell fluid. By constructing a N-order iterative scheme, we prove the local existence and uniqueness of a weak solution. Furthermore, we show that the sequence associated with N-order iterative scheme converges to the unique weak solution at a rate of N-order.