• Kyungpook Mathematical Journal
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• v.56 no.1
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• pp.221-233
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• 2016

The present paper proposes a new monotone iteration method for existence as well as approximation of the coupled solutions for a coupled periodic boundary value problem of first order ordinary nonlinear differential equations. A new hybrid coupled fixed point theorem involving the Dhage iteration principle is proved in a partially ordered normed linear space and applied to the coupled periodic boundary value problems for proving the main existence and approximation results of this paper. An algorithm for the coupled solutions is developed and it is shown that the sequences of successive approximations defined in a certain way converge monotonically to the coupled solutions of the related differential equations under some suitable mixed hybrid conditions. A numerical example is also indicated to illustrate the abstract theory developed in the paper.

• Nonlinear Functional Analysis and Applications
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• v.29 no.2
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• pp.527-543
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• 2024

In the realm of differential games and bioeconomic modeling, where intricate systems and multifaceted interactions abound, we explore the precision and efficiency of the Chebyshev Tau method (CTM). We begin with the Weierstrass Approximation Theorem, employing Chebyshev polynomials to pave the way for solving intricate bioeconomic differential games. Our case study revolves around a three-player bioeconomic differential game, unveiling a unique open-loop Nash equilibrium using Hamiltonians and the FilippovCesari existence theorem. We then transition to numerical implementation, employing CTM to resolve a Three-Point Boundary Value Problem (TPBVP) with varying degrees of approximation.

• Journal of the Korean Mathematical Society
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• v.32 no.3
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• pp.415-425
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• 1995

• Bulletin of the Korean Mathematical Society
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• v.33 no.3
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• pp.367-376
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• 1996

We characterize best simultaneous approximations from a finite-dimensional subspace of a normed linear space. In the characterization we reveal usefulness of a minimax theorem presented in [2,4].

• Journal of The Korean Astronomical Society
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• v.2 no.1
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• pp.1-9
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• 1969

On the instantaneous tidal relaxation approximation, formulae are derived for the ellipticities and virial theorem of a slightly flattened homogeneous rotating cluster (the largest axis of the cluster is directed towards the Galactic center), in terms of the Galactic tidal force and the characteristic intrinsic plus orbital angular velocity. The expression for a purely tidally-determined ellipticity is identical to that for an incompressible fluid body of uniform density. Orbital motion generally contributes significantly to the shape of the cluster. The virial theorem is identical to that for an isolated cluster except that the gravitational potential energy is multiplied by (1-${\chi}$), where ${\chi}$ is a positive tidal correction term. To obtain the actual mass of a cluster, the virial theorem mass based on an isolated cluster should be multiplied by the factor 1/(1-${\chi}$). The formulae are applied to open star clusters, the globular cluster ${\omega}$ Centauri, and dwarf elliptical galaxies in the Local Group.

• Journal of applied mathematics & informatics
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• v.9 no.2
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• pp.531-542
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• 2002

In this paper we deal with a sequence of positive linear operators ${{R_n}}^{[$\beta$]}$ approximating functions on the unbounded interval [0, $\infty$] which were firstly used by K. balazs and J. Szabados. We give pointwise estimates in the framework of polynomial weighted function spaces. Also we establish a Voronovskaja type theorem in the same weighted spaces for ${{K_n}}^{[$\beta$]}$ operators, representing the integral generalization in Kantorovich sense of the ${{R_n}}^{[$\beta$]}$.

• Nonlinear Functional Analysis and Applications
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• v.26 no.1
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• pp.83-92
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• 2021

This paper studies approximate solutions for a class of nonlinear diffusion population models. Our methods are to use the fundamental solution of heat equations to construct integral forms of the models and the well-known Banach compression map theorem to prove the existence of positive solutions of integral equations. Non-steady-state local approximate solutions for suitable harvest functions are obtained by utilizing the approximation theorem of multivariate continuous functions.

• Korean Journal of Mathematics
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• v.30 no.4
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• pp.571-592
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• 2022

By established a Banach space with the Hausdorff distance, we introduce the alternative fixed-point theorem to explore the existence and uniqueness of a fixed subset of Y and investigate the stability of set-valued Euler-Lagrange functional equations in this space. Some properties of the Hausdorff distance are furthermore explored by a short and simple way.

• Bulletin of the Korean Mathematical Society
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• v.39 no.1
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• pp.43-51
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• 2002

The aim of this paper is to prove a convergence theorem of a generalized Ishikawa iteration sequence for two multi-valued strongly pseudo-contractive mappings by using an approximation method in real uniformly smooth Banach spaces. We generalize and extend the results of Chang and Chang, Cho, Lee, Jung, and Kang.

• Bulletin of the Korean Mathematical Society
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• v.40 no.4
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• pp.603-611
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• 2003

In this paper we extend the definition of K-positive definite operators from linear to Frechet differentiable operators. Under this setting, we derive from the inverse function theorem a local existence and approximation results corresponding to those of Theorems land 2 of the authors [8], in an arbitrary real Banach space. Furthermore, an asymptotically K-positive definite operator is introduced and a simplified iteration sequence which converges to the unique solution of an asymptotically K-positive definite operator equation is constructed.