• 한국수학교육학회지시리즈B:순수및응용수학
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• 제31권3호
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• pp.299-310
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• 2024

The probabilistic metric space as one of the important generalizations of metric space, was introduced by Menger [16] in 1942. Later, Choi et al. [6] initiated the notion of bicomplex-valued metric spaces (bi-CVMS). Recently, Bhattacharyya et al. [3] linked the concept of bicomplex-valued metric spaces and menger spaces, and initiated menger space with bicomplex-valued metric. Here, in this paper, we have taken probabilistic metric space with bicomplex-valued metric, i.e., bicomplexvalued probabilistic metric space and proved some common fixed point theorems using converse commuting mappings in this space.

• 대한수학회지
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• 제32권3호
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• pp.415-425
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• 1995

• 충청수학회지
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• 제3권1호
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• pp.89-95
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• 1990

The converse of Pimsner-Popa theorem is proved, and represent the index [M : N] by finite sum of elements of M.

• Journal of applied mathematics & informatics
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• 제32권1_2호
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• pp.153-159
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• 2014

In this paper, we introduce a pair of higher-order symmetric dual models/problems. Weak, strong and converse duality theorems for this pair are established under the assumption of higher-order invexity. Moreover, self duality theorem is also discussed.

• Journal of applied mathematics & informatics
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• 제26권1_2호
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• pp.151-160
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• 2008

A pair of multiobjective fractional symmetric dual programs is formulated over arbitrary cones. Weak, strong and converse duality theorems are proved under pseudoinvexity assumptions. A self duality theorem is also discussed.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제6권1호
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• pp.67-80
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• 2002

We formulate a pair of nondifferentiable symmetric dual variational problems with a square root term. Under invexity assumptions, we establish weak, strong, converse and self duality theorems for our variational problems by using the generalized Schwarz inequality. Also, we give the static case of our nondifferentiable symmetric duality results.

• Korean Journal of Mathematics
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• 제17권3호
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• pp.237-244
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• 2009

In this paper, we define property ($C_k$) and show that Property ($C_k$) implies property ($C_{k+1}$). The converse does not hold. Moreover, we prove that property ($C_k$) implies the Banach-Saks property.

• 대한수학회논문집
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• 제21권4호
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• pp.759-769
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• 2006

Let L : $C\;\rightarrow\;C$ be a hyperbolic automorphism. Then the hyperbolic toral automorphism $L_A\;T^2\;\rightarrow\;T^2$, induced by L, is a chaotic map ([2] pg.192). We characterize hyperbolic toral automorphisms by proving the converse of the above statement.

• Journal of applied mathematics & informatics
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• 제5권3호
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• pp.797-804
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• 1998

A pair of multiobjective generalized symmetric dual non-linear programming problems and weak strong and converse dual-ity theorems for these problems are established under generalized $\rho-(\eta,0)$-invexity assumptions. Several known results are obtained as special cases.

• 기술사
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• 제38권4호
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• pp.1-3
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• 2005

In these days, managing city's garbage is one of important environmental policy to be solved. Accordingly, I try to suggest to manage garbage and apply an energy source with conversing city's garbage into alternative energy.