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

The existence of a fixed point for the sum of two monotone operators 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

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

, Volume 12 (4) – May 1, 2008
10 pages

/lp/springer_journal/the-existence-of-a-fixed-point-for-the-sum-of-two-monotone-operators-nDvYv3QcOl
Publisher
Springer Journals
Subject
Mathematics; Econometrics; Calculus of Variations and Optimal Control; Optimization; Potential Theory; Operator Theory; Fourier Analysis
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-008-2154-6
Publisher site
See Article on Publisher Site

### 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.

### Journal

PositivitySpringer Journals

Published: May 1, 2008

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