Fixed Points of Kannan Maps in the Variable Exponent Sequence Spaces <i>ℓ</i>_<i>p</i>(·)

Abstract

Kannan maps have inspired a branch of metric fixed point theory devoted to the extension of the classical Banach contraction principle. The study of these maps in modular vector spaces was attempted timidly and was not successful. In this work, we look at this problem in the variable exponent sequence spaces ℓ p ( · ) . We prove the modular version of most of the known facts about these maps in metric and Banach spaces. In particular, our results for Kannan nonexpansive maps in the modular sense were never attempted before.

Keywords

• electrorheological fluids
• fixed point
• kannan contraction mapping
• kannan nonexpansive mapping
• modular vector spaces
• nakano