• Journal of the Chungcheong Mathematical Society
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• v.21 no.2
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• pp.231-246
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• 2008

In this paper, we use a generalized Brownian motion process to define a generalized analytic Feynman integral. We then establish several integration formulas for generalized analytic Feynman integrals generalized analytic Fourier-Feynman transforms and generalized integral transforms of functionals in the class of functionals ${\mathbb{E}}_0$. Finally, we use these integration formulas to obtain several generalized Feynman integrals involving the generalized analytic Fourier-Feynman transform and the generalized integral transform of functionals in ${\mathbb{E}}_0$.

• Bulletin of the Korean Mathematical Society
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• v.41 no.1
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• pp.73-93
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• 2004

In [10], Chang and Skoug used a generalized Brownian motion process to define a generalized analytic Feynman integral and a generalized analytic Fourier-Feynman transform. In this paper we define the conditional generalized Fourier-Feynman transform and conditional generalized convolution product on function space. We then establish some relationships between the conditional generalized Fourier-Feynman transform and conditional generalized convolution product for functionals on function space that belonging to a Banach algebra.

• Journal of the Korean Mathematical Society
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• v.40 no.5
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• pp.883-899
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• 2003

In this paper, we will introduce the general concepts of generalized multiobjective game, generalized weight Nash equilibria and generalized Pareto equilibria. Next using the fixed point theorems due to Idzik [5] and Kim-Tan [6] , we shall prove the existence theorems of generalized weight Nash equilibria under general hypotheses. And as applications of generalized weight Nash equilibria, we shall prove the existence of generalized Pareto equilibria in non-compact generalized multiobjective game.

• Korean Journal of Mathematics
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• v.31 no.4
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• pp.521-536
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• 2023

This paper is a further development of the recent results by the author and coworker on the generalized sequential Fourier-Feynman transform for functionals in a Banach algebra Ŝ and some related functionals. We establish existence of the generalized first variation of these functionals. Also we investigate various relationships between the generalized sequential Fourier-Feynman transform, the generalized sequential convolution product and the generalized first variation of the functionals.

• Communications of the Korean Mathematical Society
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• v.19 no.1
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• pp.93-111
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• 2004

In this paper, we use a generalized Brownian motion process to define a generalized Feynman integral and a generalized Fourier-Feynman transform. We also define the concepts of the multiple Lp analytic generalized Fourier-Feynman transform and the generalized convolution product of functional on function space $C_{a,\;b}[0,\;T]$. We then verify the existence of the multiple $L_{p}$ analytic generalized Fourier-Feynman transform for functional on function space that belong to a Banach algebra $S({L_{a,\;b}}^{2}[0, T])$. Finally we establish some relationships between the multiple $L_{p}$ analytic generalized Fourier-Feynman transform and the generalized convolution product for functionals in $S({L_{a,\;b}}^{2}[0, T])$.

• Journal of the Korean Institute of Intelligent Systems
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• v.20 no.2
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• pp.257-261
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• 2010

In this paper, we introduce the concept of fuzzy r-generalized almost continuous mapping and obtain some characterizations of such a mapping. In particular, we investigate characterizations for the fuzzy r-generalized almost continuity by using the concept of fuzzy r-generalized regular open sets.

• Korean Journal of Mathematics
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• v.29 no.2
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• pp.321-332
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• 2021

This paper is a further development of the recent results by the authors on the generalized sequential Fourier-Feynman transform for functionals in a Banach algebra Ŝ and some related functionals. We investigate various relationships between the generalized sequential Fourier-Feynman transform and the generalized sequential convolution product of functionals. Parseval's relation for the generalized sequential Fourier-Feynman transform is also given.

• Structural Engineering and Mechanics
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• v.83 no.2
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• pp.135-151
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• 2022

The generalized displacement method is a nonlinear solution scheme that follows the equilibrium path of the structure based on the development of the generalized displacement. This method traces the path uniformly with a constant amount of generalized displacement. In this article, we first develop higher-order generalized displacement methods based on multi-point techniques. According to the concept of generalized stiffness, a relation is proposed to adjust the generalized displacement during the path-following. This formulation provides the possibility to change the amount of generalized displacement along the path due to changes in generalized stiffness. We, then, introduce higher-order algorithms of variable generalized displacement method using multi-point methods. Finally, we demonstrate with numerical examples that the presented algorithms, including multi-point generalized displacement methods and multi-point variable generalized displacement methods, are capable of following the equilibrium path. A comparison with the arc length method, generalized displacement method, and multi-point arc-length methods illustrates that the adjustment of generalized displacement significantly reduces the number of steps during the path-following. We also demonstrate that the application of multi-point methods reduces the number of iterations.

• Communications of the Korean Mathematical Society
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• v.35 no.3
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• pp.733-744
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• 2020

Let 𝕽 be a commutative ring with unity, A and B be 𝕽-algebras, M be a (A, B)-bimodule and N be a (B, A)-bimodule. The 𝕽-algebra 𝕾 = 𝕾(A, M, N, B) is a generalized matrix algebra defined by the Morita context (A, B, M, N, 𝝃_MN, Ω_NM). In this article, we study generalized derivation and generalized Jordan derivation on generalized matrix algebras and prove that every generalized Jordan derivation can be written as the sum of a generalized derivation and antiderivation with some limitations. Also, we show that every generalized Jordan derivation is a generalized derivation on trivial generalized matrix algebra over a field.

• Korean Journal of Mathematics
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• v.15 no.1
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• pp.27-37
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• 2007

In this paper, we introduce the concepts of r-semi-generalized fuzzy closed sets, r-semi-generalized fuzzy open sets, r-semi-generalized fuzzy continuous maps in fuzzy topological spaces and investigate some of their properties.