Fixed point theorems in modular vector spaces


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.


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.