A graphical version of Reichs fixed point theorem
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Authors
Monther R. Alfuraidan
- Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia.
Mostafa Bachar
- Department of Mathematics, College of Sciences, King Saud University, Riyadh, Saudi Arabia.
Mohamed A. Khamsi
- Department of Mathematical Sciences, University of Texas at El Paso, El Paso, TX 79968, U. S. A..
Abstract
In this paper, we discuss the definition of the Reich multivalued monotone contraction mappings defined
in a metric space endowed with a graph. In our investigation, we prove the existence of fixed point results
for these mappings. We also introduce a vector valued Bernstein operator on the space C([0; 1];X), where
X is a Banach space endowed with a partial order. Then we give an analogue to the Kelisky-Rivlin theorem.
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ISRP Style
Monther R. Alfuraidan, Mostafa Bachar, Mohamed A. Khamsi, A graphical version of Reichs fixed point theorem, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 6, 3931--3938
AMA Style
Alfuraidan Monther R., Bachar Mostafa, Khamsi Mohamed A., A graphical version of Reichs fixed point theorem. J. Nonlinear Sci. Appl. (2016); 9(6):3931--3938
Chicago/Turabian Style
Alfuraidan, Monther R., Bachar, Mostafa, Khamsi, Mohamed A.. "A graphical version of Reichs fixed point theorem." Journal of Nonlinear Sciences and Applications, 9, no. 6 (2016): 3931--3938
Keywords
- Multivalued monotone contraction
- graph theory
- fixed point theory
- partial order.
MSC
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