Fixed Point of Modified <i>F</i>-Contraction with an Application

Abstract

In this paper, we prove the existence of fixed points for every 2-rotative continuous mapping in Banach spaces to answer an open question raised by Goebel and Koter. Further, we modify F-contraction by developing F-rotative mapping and establish some fixed-point theorems. Finally, we apply our results to prove the existence of a solution of a non-linear fractional differential equation.

Keywords

• mean non-expansive mapping
• <i>F</i>-contraction
• rotative mapping
• fixed point