Fixed points of non-linear set-valued $ \left(\alpha _{\ast }, \phi _{M}\right) $-contraction mappings and related applications

Abstract

The aim of this manuscript is to prove some fixed point results for non-linear set-valued maps with new approach of (α∗,ϕM)-contraction in complete M-metric space. Also, we prove some fixed point results in ordered M-metric space. As an presented work which are the extension and improves the current study of set-valued mappings. Finally, we also give an non-trivial extensive examples and application to homotopy theory and the existence solution of functional equations to show that our concepts are meaningful and to support our results.

Keywords

• (α∗
• ϕm)-contractions
• m -metric space
• homotopy fixed point results
• functional equation