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Theorem of Existence and Uniqueness of Fixed Points of Monotone Operators

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Genetic and Evolutionary Computing

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 329))

Abstract

Operator equation and the fixed point problem are an important component of nonlinear functional analysis theory. They are playing important role in solving nature and uniqueness problems about all kinds of differential equations and integral equations. Generally, the monotone operator has been defined with compactness, continuity and concavity and convexity in partially ordered Banach space. In this paper, without compactness and continuity, concavity and convexity of functions, a new fixed point theorem of increasing and decreasing operator and mixed monotone operator has obtained through introducing order-difference in the cone.

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Author information

Authors and Affiliations

  1. Faculty of Science, Nanchang Institute of Technology, Nanchang, China, 330099

    Hui Luan

  2. Business Administration College, Nanchang Institute of Technology, Nanchang, China, 330099

    Zhihong Xia

Authors
  1. Hui Luan
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  2. Zhihong Xia
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Editor information

Editors and Affiliations

  1. HIGH-TECH Industry Development Zone, Nanchang Institute of Technology, Jiangxi Province, China

    Hui Sun

  2. Department of Computer Science and Information Engineering, National Penghu University of Science and Technology, Magong City, Taiwan

    Chin-Yu Yang

  3. Innovative Information Industry Research Center, Shenzhen University Harbin Institute of Technology, Shenzhen, China

    Chun-Wei Lin

  4. Harbin Institute of Technology Innovative Info. Industry Res. Center, Shenzhen University, Shenzhen, China

    Jeng-Shyang Pan

  5. Department of Computer Science Faculty of Elec. Eng. & Comp. Sci., VSB-Technical University of Ostrava, Ostrava, Czech Republic

    Vaclav Snasel

  6. Scientific Network for Innovation and Research Excellence, Machine Intelligence Research Labs (MIR Labs), Auburn, Washington, USA

    Ajith Abraham

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© 2015 Springer International Publishing Switzerland

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Luan, H., Xia, Z. (2015). Theorem of Existence and Uniqueness of Fixed Points of Monotone Operators. In: Sun, H., Yang, CY., Lin, CW., Pan, JS., Snasel, V., Abraham, A. (eds) Genetic and Evolutionary Computing. Advances in Intelligent Systems and Computing, vol 329. Springer, Cham. https://doi.org/10.1007/978-3-319-12286-1_2

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  • DOI: https://doi.org/10.1007/978-3-319-12286-1_2

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-12285-4

  • Online ISBN: 978-3-319-12286-1

  • eBook Packages: EngineeringEngineering (R0)

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