On Reich fixed point theorem of \(G\)-contraction mappings on modular function spaces

Volume 9, Issue 6, pp 4600--4606 http://dx.doi.org/10.22436/jnsa.009.06.98

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Authors

Monther Rashed Alfuraidan - Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia.

Abstract

We define the multivalued Reich (\(G; \rho\))-contraction mappings on a modular function space. Then we obtain sufficient conditions for the existence of fixed points for such mappings. As an application, we introduce a \(\rho\)-valued Bernstein operator on the set of functions \(f : [0; 1] \rightarrow L_\rho\) and then give the modular analogue to Kelisky-Rivlin theorem.

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Keywords

• Bernstein polynomial
• directed graph
• Reich fixed point theorem
• monotone mapping
• multivalued mapping
• modular function spaces.

MSC

•  47H09
•  46B20
•  47H10

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