• Title, Summary, Keyword: fixed point

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NOTE FOR THE TRIPLED AND QUADRUPLE FIXED POINTS OF THE MIXED MONOTONE MAPPINGS

  • Wu, Jun;Liu, Yicheng
    • Bulletin of the Korean Mathematical Society
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    • v.50 no.3
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    • pp.993-1005
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    • 2013
  • In this paper, to include more generalized cases, the authors present a modified concept for the tripled and quadruple fixed point of the mixed monotone mappings. Also, they investigate the existence and uniqueness of fixed point of the ordered monotone operator with the Matkowski contractive conditions in the partial ordered metric spaces. As the direct consequences, the existence of coupled fixed point, tripled fixed point and quadruple fixed point are explored at the common framework and some previous results in [T. G. Bhaskar and V. Lakshmikan-tham, Fixed point theory in partially ordered metric spaces and applications, Nonlinear Anal. 65 (2006), 1379-1393; V. Berinde and M. Borcut, Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces, Nonlinear Anal. 74 (2011), no. 15, 4889-4897; E. Karapinar and N. V. Luong, Quadruple fixed point theorems for nonlinear contractions, Computers and Mathematics with Applications (2012), doi:10.1016/j.camwa.2012.02061] are improved. Finally, some fixed point theorems are proved.

FIXED POINTS OF WEAKLY INWARD 1-SET-CONTRACTION MAPPINGS

  • Duan, Huagui;Xu, Shaoyuan;Li, Guozhen
    • Journal of the Korean Mathematical Society
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    • v.45 no.6
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    • pp.1725-1740
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    • 2008
  • In this paper, we introduce a fixed point index of weakly inward 1-set-contraction mappings. With the aid of the new index, we obtain some new fixed point theorems, nonzero fixed point theorems and multiple positive fixed points for this class of mappings. As an application of nonzero fixed point theorems, we discuss an eigenvalue problem.

SOME FIXED POINT THEOREMS IN GENERALIZED DARBO FIXED POINT THEOREM AND THE EXISTENCE OF SOLUTIONS FOR SYSTEM OF INTEGRAL EQUATIONS

  • Arab, Reza
    • Journal of the Korean Mathematical Society
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    • v.52 no.1
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    • pp.125-139
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    • 2015
  • In this paper we introduce the notion of the generalized Darbo fixed point theorem and prove some fixed and coupled fixed point theorems in Banach space via the measure of non-compactness, which generalize the result of Aghajani et al. [6]. Our results generalize, extend, and unify several well-known comparable results in the literature. One of the applications of our main result is to prove the existence of solutions for the system of integral equations.

COMMON FIXED POINT RESULTS FOR NON-COMPATIBLE R-WEAKLY COMMUTING MAPPINGS IN PROBABILISTIC SEMIMETRIC SPACES USING CONTROL FUNCTIONS

  • Das, Krishnapada
    • Korean Journal of Mathematics
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    • v.27 no.3
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    • pp.629-643
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    • 2019
  • In common fixed point problems in metric spaces several versions of weak commutativity have been considered. Mappings which are not compatible have also been discussed in common fixed point problems. Here we consider common fixed point problems of non-compatible and R-weakly commuting mappings in probabilistic semimetric spaces with the help of a control function. This work is in line with research in probabilistic fixed point theory using control functions. Further we support our results by examples.

Fixed Point Theorems in Product Spaces

  • Bae, Jong Sook;Park, Myoung Sook
    • Journal of the Chungcheong Mathematical Society
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    • v.6 no.1
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    • pp.53-57
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    • 1993
  • Let E and F be Banach spaces with $X{\subset}E$ and $Y{\subset}F$. Suppose that X is weakly compact, convex and has the fixed point property for a nonexpansive mapping, and Y has the fixed point property for a multivalued nonexpansive mapping. Then $(X{\oplus}Y)_p$, $1{\leq}$ P < ${\infty}$ has the fixed point property for a multi valued nonexpansive mapping. Furthermore, if X has the generic fixed point property for a nonexpansive mapping, then $(X{\oplus}Y)_{\infty}$ has the fixed point property for a multi valued nonexpansive mapping.

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Fixed-point optimization utility for digital signal processing programs (디지탈 신호처리용 고정 소수점 최적화 유틸리티)

  • 김시현;성원용
    • Journal of the Korean Institute of Telematics and Electronics C
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    • v.34C no.9
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    • pp.33-42
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    • 1997
  • Fixed-point optimization utility software that can aid scaling and wordlength determination of digital signal processign algorithms written in C or C$\^$++/ language is developed. This utility consists of two programs: the range estimator and the fixed-point simulator. The former estimates the ranges of floating-point variables for automatic scaling purpose, and the latter translates floating-point programs into fixed-point equivalents for evaluating te fixed-point performance by simulation. By exploiting the operator overloading characteristics of C$\^$++/ language, the range estimation and the fixed-point simulation can be conducted just by modifying the variable declaration of the original program. This utility is easily applicable to nearly all types of digital signal processing programs including non-linear, time-varying, multi-rate, and multi-dimensional signal processing algorithms. In addition, this software can be used for comparing the fixed-point characteristics of different implementation architectures.

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FIXED POINT THEOREMS ON GENERALIZED CONVEX SPACES

  • Kim, Hoon-Joo
    • 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.

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C++ Template-based Fixed-Point Arithmetic Library (C++ 템플릿 기반의 Fixed-Point 연산 라이브러리)

  • Hwang, Seon Joong;Kim, Seon Wook;Min, Byung Gueon
    • Proceedings of the Korea Information Processing Society Conference
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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.

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