Geodesic
Common fixed points of monotone Lipschitzian semigroups in Banach spaces
Bachar, M. 1 ; Khamsi, Mohamed A. 2 ; Kozlowski, W. M. 3 ; Bounkhel, M. 1
1 Department of Mathematics, College of Science, King Saud University, Saudi Arabia
2 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
3 School of Mathematics and Statistics, University of New South Wales, Australia
Journal of nonlinear sciences and its applications, Tome 11 (2018) no. 1, p. 73-79.

Voir la notice de l'article provenant de la source International Scientific Research Publications

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.
DOI : 10.22436/jnsa.011.01.06
Classification : 47H10, 47H09
Keywords: Common fixed point, fixed point, monotone contraction mappings, monotone nonexpansive mappings, monotone Lipschitzian semigroup

Bachar, M.  1 ; Khamsi, Mohamed A.  2 ; Kozlowski, W. M.  3 ; Bounkhel, M.  1

1 Department of Mathematics, College of Science, King Saud University, Saudi Arabia
2 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
3 School of Mathematics and Statistics, University of New South Wales, Australia 
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     title = {Common fixed points of monotone {Lipschitzian} semigroups in {Banach} spaces},
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Bachar, M. ; Khamsi, Mohamed A. ; Kozlowski, W. M. ; Bounkhel, M. . Common fixed points of monotone Lipschitzian semigroups in Banach spaces. Journal of nonlinear sciences and its applications, Tome 11 (2018) no. 1, p. 73-79. doi : 10.22436/jnsa.011.01.06. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.011.01.06/

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