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The existence of a fixed point for the sum of two monotone operators
Authors:Yong-Zhuo Chen
Affiliation:(1) Department of Mathematics, University of Pittsburgh at Bradford, Bradford, PA, 16701, UK
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 TA + H.
Keywords:Cone  convex metric space  fixed point  monotone operator  ordered Banach space  Thompson’  s metric
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