• Journal of the Korean Institute of Telematics and Electronics A
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• v.29A no.3
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• pp.96-105
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• 1992

The use of fixed-point digital signal processors, such as the TMS 320C25, requires scaling of data at each arithmetic step to prevent overflows while keeping the accuracy. A software which automatizes this process is developed for TMS 320C25. The programmers use a model of a hypothetical floating-point digital signal processor and a floating-point format for data representation. However, the program and data are automatically translated to a fixed-point version by this software. Thus, the execution speed is not sacrificed. A fixed-point variable has a unique binary-point location, which is dependent on the range of the variable. The range is estimated from the floating-point simulation. The number of shifts needed for arithmetic or data transfer step is determined by the binary-points of the variables associated with the operation. A fixed-point code generator is also developed by using the proposed automatic scaling software. This code generator produces floating-point assembly programs from the specifiations of FIR, IIR, and adaptive transversal filters, then floating-point programs are transformed to fixed-point versions by the automatic scaling software.

• East Asian mathematical journal
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• v.36 no.5
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• pp.593-604
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• 2020

Let the circle act on a compact oriented manifold with a discrete fixed point set. At each fixed point, there are positive integers called weights, which describe the local action of S¹ near the fixed point. In this paper, we provide the author's original proof that only uses the Atiyah-Singer index formula for the classification of the weights at the fixed points if the dimension of the manifold is 4 and there are at most 4 fixed points, which made the author possible to give a classification for any finite number of fixed points.

• Journal of applied mathematics & informatics
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• v.9 no.1
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• pp.433-440
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• 2002

In this paper, we first prove the existence of fixed points for fuzzy mappings that satisfy a certain contractive condition. Also, we give a fixed point theorem for generalized contractive fuzzy mapping by using Caristi's by fixed point theorem.

• Journal of the Korean Mathematical Society
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• v.35 no.2
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• pp.491-502
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• 1998

We obtain new fixed point theorems on maps defined on "locally G-convex" subsets of a generalized convex spaces. Our first theorem is a Schauder-Tychonoff type generalization of the Brouwer fixed point theorem for a G-convex space, and the second main result is a fixed point theorem for the Kakutani maps. Our results extend many known generalizations of the Brouwer theorem, and are based on the Knaster-Kuratowski-Mazurkiewicz theorem. From these results, we deduce new results on collectively fixed points, intersection theorems for sets with convex sections and quasi-equilibrium theorems.

• Journal of the Chungcheong Mathematical Society
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• v.37 no.1
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• pp.1-17
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• 2024

The boundary conditions $\tilde{P}_0$ and $\tilde{P}_1$ were introduced in [5] by using the Hodge decomposition on the de Rham complex. In [6] the Atiyah-Bott-Lefschetz type fixed point formulas were proved on a compact Riemannian manifold with boundary for some special type of smooth functions by using these two boundary conditions. In this paper we slightly extend the result of [6] and give two examples showing these fixed point theorems.

• Kyungpook Mathematical Journal
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• v.56 no.3
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• pp.807-817
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• 2016

The aim of this paper is to introduce the notion of ${\epsilon}$-compatible maps and obtain some common fixed point theorems. Also, our results generalize some well known fixed point theorems.

• Proceedings of the Korea Information Processing Society Conference
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• 2010.04a
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• pp.49-52
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• 2010

디지털 신호처리 알고리즘들은 실제 시스템에 적용할 때 임베디드 시스템 등 하드웨어의 성능과 소비전력 및 비용에 제약이 있을 경우 연산 정밀도가 높은 floating-point 연산 대신 제한된 정밀도와 적은 연산 비용을 요구하는 fixed-point 연산을 사용하여 구현한다. 시스템의 개발단계에서는 적용할 알고리즘을 floating-point 연산을 이용한 코드를 먼저 작성한 후 이를 fixed-point 연산으로 대체하는 과정을 거치게 되는데, 이는 숙련된 개발자와 상당한 양의 개발기간을 요하는 까다로운 작업이다. 이에 본 연구에는 코드작성 편의를 높이고 개발기간을 단축하기 위해 C++ template 기반의 fixed-point 연산 라이브러리를 개발하였다. 이는 floating-point 연산 코드와 fixed-point 연산 코드를 별도로 개발할 필요 없이 하나의 코드를 이용하여 자유로이 연산 정밀도를 지정할 수 있으며 개발자는 기존의 floating-point 연산을 이용하는 코드를 작성하는 것처럼 쉽게 코드를 작성할 수 있도록 한다. 또한, template 기반으로 작성되어 기존의 연구들과 달리 추가적인 작업도구 없이도 범용 C++ 컴파일러가 최적화된 코드를 생성할 수 있도록 되어있는 것이 특징이다.

• Communications of the Korean Mathematical Society
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• v.33 no.3
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• pp.943-960
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• 2018

Our aim is to introduce the notion of a parametric $N_b-metric$ and study some basic properties of parametric $N_b-metric$ spaces. We give some fixed-point results on a complete parametric $N_b-metric$ space. Some illustrative examples are given to show that our results are valid as the generalizations of some known fixed-point results. As an application of this new theory, we prove a fixed-circle theorem on a parametric $N_b-metric$ space.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.425-434
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• 2007

We iteratively generate a sequence of measurable mappings and study necessary conditions for its convergence to a random fixed point of random nonexpansive operator. A random fixed point theorem for random nonexpansive operator, relaxing the convexity condition on the underlying space, is also proved. As an application, we obtained random fixed point theorems for Caristi type random operators.

• The Pure and Applied Mathematics
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• v.10 no.4
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• pp.245-254
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• 2003

In this paper we prove common fixed point theorems for four mappings, under the condition of weakly compatible mappings in Menger spaces, without taking any function continuous. We improve results of [A common fixed point theorem for three mappings on Menger spaces. Math. Japan. 34 (1989), no. 6, 919-923], [On common fixed point theorems of compatible mappings in Menger spaces. Demonstratio Math. 31 (1998), no. 3, 537-546].