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The existence of a fixed point for the sum of two monotone operators

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Abstract

Let A and H be two operators defined in an ordered Banach space such that

$$H(tx)\, \geq\, tHx\, \quad \,{\text for\, all}\, t\,\in\, (0,1)$$

, and

$$A(tx)\, \geq\, t^{\alpha}\, Ax\, \quad\, {\text for\, all} \,t\,\in\, (0,1),$$

, where \(\alpha\,\in\,(0,1)\). This paper discusses the conditions which will guarantee the existence of an asymptotically attractive fixed point for T = A + H.

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Authors and Affiliations

  1. Department of Mathematics, University of Pittsburgh at Bradford, Bradford, PA, 16701, UK

    Yong-Zhuo Chen

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  1. Yong-Zhuo Chen
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Correspondence to Yong-Zhuo Chen.

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Chen, YZ. The existence of a fixed point for the sum of two monotone operators. Positivity 12, 643–652 (2008). https://doi.org/10.1007/s11117-008-2154-6

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  • DOI: https://doi.org/10.1007/s11117-008-2154-6

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