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Existence Theorems for Set-valued Operators in Banach Spaces

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Abstract

In this paper, we study the problem of existence of zero points for set-valued operators in Banach spaces. We present a simple condition which can be used to verify that under some conditions, set-valued operators have zero points. Furthermore, we derive the surjectivity result and the Kakutani fixed point theorem by using this condition.

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Authors and Affiliations

  1. Department of Information Engineering, Matsue National College of Technology, Nishi-Ikuma, Matsue, Shimane, 690-8518, Japan

    Shin-ya Matsushita

  2. Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Oh-Okayama, Meguro-ku, Tokyo, 152-8552, Japan

    Wataru Takahashi

Authors
  1. Shin-ya Matsushita
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  2. Wataru Takahashi
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Correspondence to Shin-ya Matsushita.

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Matsushita, Sy., Takahashi, W. Existence Theorems for Set-valued Operators in Banach Spaces. Set-Valued Anal 15, 251–264 (2007). https://doi.org/10.1007/s11228-006-0030-8

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  • DOI: https://doi.org/10.1007/s11228-006-0030-8

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