• Journal of the Korean Mathematical Society
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• v.53 no.5
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• pp.1037-1056
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• 2016

In this paper, we define the concepts of commute proximally, dominate proximally, weakly dominate proximally, proximal generalized ${\varphi}$-contraction and common best proximity point in probabilistic Menger space. We prove some common best proximity point and common fixed point theorems for dominate proximally and weakly dominate proximally mappings in probabilistic Menger space under certain conditions. Finally we show that proximal generalized ${\varphi}$-contractions have best proximity point in probabilistic Menger space. Our results generalize many known results in metric space.

• The Pure and Applied Mathematics
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• v.30 no.4
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• pp.417-427
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• 2023

The purpose of this paper is establish the existence of proximity point for the cyclic B-contraction mapping on metric spaces and uniformly convex Banach spaces. Also, we prove the common proximity point for the S-weakly cyclic B-contraction mapping. In addition, a few examples are provided to demonstrate our findings.

• Bulletin of the Korean Mathematical Society
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• v.53 no.5
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• pp.1363-1371
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• 2016

This paper is concerned with best proximity points for multimaps in normed spaces and in hyperconvex metric spaces. Using the generalized KKM theorem, we deduce new best proximity pair theorems for a family of multimaps with unionly open fibers in normed spaces. And we prove a new best proximity point theorem for quasi-lower semicontinuous multimaps in hyperconvex metric spaces.

• Nonlinear Functional Analysis and Applications
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• v.27 no.2
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• pp.261-269
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• 2022

The purpose of this paper is to introduce a new generalization class of cyclic mappings, called cyclic generalized 𝜑-weak contraction and obtain a corresponding best proximity point theorem for this cyclic mapping under certain conditions.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.119-133
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• 2011

This paper proposes an infeasible interior-point algorithm with full-Newton step for linear programming. We introduce a special self-regular proximity to induce the feasibility step and also to measure proximity to the central path. The result of polynomial complexity coincides with the best-known iteration bound for infeasible interior-point methods, namely, O(n log n/${\varepsilon}$).

• The Pure and Applied Mathematics
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• v.29 no.4
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• pp.335-352
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• 2022

In this paper, we give an extended version of fixed point results for 𝜃-contraction and 𝜃-𝜙-contraction and define a new type of contraction, namely, cyclic 𝜃-contraction and cyclic 𝜃-𝜙-contraction in a complete metric space. Moreover, we prove the existence of best proximity point for cyclic 𝜃-contraction and cyclic 𝜃-𝜙-contraction. Also, we establish best proximity result in the setting of uniformly convex Banach space.

• Korean Journal of Mathematics
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• v.12 no.1
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• pp.41-47
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• 2004

We introduce the $K_0$-proximity space as a generalization of the Efremovi$\check{c}$-proximity space. We try to show every ultrafilter in $K_0$-proximity space generates a cluster and every Cauchy cluster is a point cluster.

• Journal of the Chungcheong Mathematical Society
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• v.19 no.1
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• pp.19-26
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• 2006

In this paper, using the fixed point theorem for acyclic factorizable multifunctions, we shall prove an existence theorem of general best proximity pairs and equilibrium pairs for free generalized games.

• Journal of Korea Multimedia Society
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• v.15 no.6
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• pp.794-804
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• 2012

For the geometric computations on the protein molecules, the proximity queries, such as computing the minimum distance from an arbitrary point to the molecule or detecting the collision between a point and the molecule, are essential. For the proximity queries, the efficiency of the computation time can be different according to the data structure used for the molecule. In this paper, we present the data structures and algorithms for applying proximity queries to a molecule with GPU acceleration. We present two data structures, a voxel map and a sphere tree, where the molecule is represented as a set of spheres, and corresponding algorithms. Moreover, we show that the performance of presented data structures are improved from 3 to 633 times compared to the previous data structure for the molecules containing 1,000~15,000 atoms.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.14 no.2
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• pp.93-111
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• 2010

The purpose of this paper is to obtain new complexity results for a second-order cone optimization (SOCO) problem. We define a proximity function for the SOCO by a kernel function. Furthermore we formulate an algorithm for a large-update primal-dual interior-point method (IPM) for the SOCO by using the proximity function and give its complexity analysis, and then we show that the new worst-case iteration bound for the IPM is $O(q\sqrt{N}(logN)^{\frac{q+1}{q}}log{\frac{N}{\epsilon})$, where $q{\geqq}1$.