Fixed point theorems in modular vector spaces

Volume 10, Issue 8, pp 4046--4057 http://dx.doi.org/10.22436/jnsa.010.08.01

Publication Date: August 06, 2017 Submission Date: April 24, 2017

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Authors

Afrah A. N. Abdou - Department of Mathematics, Faculty of Sciences, King Abdulaziz University, Jeddah 21593, 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.

Abstract

In this work, we initiate the metric fixed point theory in modular vector spaces under Nakano formulation. In particular, we establish an analogue to Banach contraction principle, Browder and G¨ohde fixed point theorems for nonexpansive mappings in the modular sense. Then we finish by proving a common fixed point result of a commutative family of nonexpansive mappings in the modular sense.

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Keywords

• Best approximant
• electrorheological fluids
• fixed point
• modular vector spaces
• Nakano
• nonexpansive
• uniformly convex.

MSC

•  47H09
•  46B20
•  47H10

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