Common fixed points of monotone Lipschitzian semigroups in Banach spaces

Volume 11, Issue 1, pp 73--79 http://dx.doi.org/10.22436/jnsa.011.01.06

Publication Date: December 24, 2017 Submission Date: October 14, 2017 Revision Date: November 17, 2017 Accteptance Date: November 20, 2017

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Authors

M. Bachar - Department of Mathematics, College of Science, King Saud University, Saudi Arabia. Mohamed A. Khamsi - Department of Mathematical Sciences, The University of Texas at El Paso, El Paso, TX 79968, U. S. A.. - Department of Mathematics & Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia. W. M. Kozlowski - School of Mathematics and Statistics, University of New South Wales, Australia. M. Bounkhel - Department of Mathematics, College of Science, King Saud University, Saudi Arabia.

Abstract

In this paper, we investigate the existence of common fixed points of monotone Lipschitzian semigroup in Banach spaces under the natural condition that the images under the action of the semigroup at certain point are comparable to the point. In particular, we prove that if one map in the semigroup is a monotone contraction mapping, then such common fixed point exists. In the case of monotone nonexpansive semigroup we prove the existence of common fixed points if the Banach space is uniformly convex in every direction. This assumption is weaker than uniform convexity.

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Keywords

• Common fixed point
• fixed point
• monotone contraction mappings
• monotone nonexpansive mappings
• monotone Lipschitzian semigroup

MSC

•  47H10
•  47H09

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