Fixed point theorems for nonexpansive mappings and Suzuki-generalized nonexpansive mappings on a Banach lattice |
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Authors: | S Dhompongsa A Kaewcharoen |
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Institution: | aDepartment of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand;bDepartment of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand |
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Abstract: | We prove the existence of fixed points for multivalued nonexpansive nonself-mappings on a weakly orthogonal reflexive Banach lattice with uniformly monotone norm. Moreover, for single-valued mappings, we extend Betiuk-Pilarska and Prus’s result A. Betiuk-Pilarska, S. Prus, Banach lattices which are order uniformly noncreasy, J. Math. Anal. Appl. 342 (2008) 1271–1279] on the weak fixed point property to continuous mappings satisfying condition (C) on a w-weakly orthogonal OUNC Banach lattice. |
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Keywords: | Multivalued nonexpansive mapping Suzuki-generalized nonexpansive mapping Banach lattice Weak orthogonality Uniformly monotone norm color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6V0Y-4W32KK1-2&_mathId=mml2&_user=10&_cdi=5659&_rdoc=27&_acct=C000069468&_version=1&_userid=6189383&md5=dae315d3b8c165dced8d39ac3f2a3cca" title="Click to view the MathML source" r-order uniform noncrease" target="_blank">alt="Click to view the MathML source">r-order uniform noncrease |
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