@article{Tariq2022, 
author = {Muhammad Tariq and Mujahid Abbas and Aftab Hussain and Muhammad Arshad and Amjad Ali and Hamid Al-Sulami},
title = {Fixed points of non-linear set-valued        (                  α                  ∗                    ,              ϕ                  M                      )  -contraction mappings and related applications},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {5},
pages = {8861-8878},
keywords = {(α∗, ϕM)-contractions, M-metric space, homotopy fixed point results, functional equation},
url = {https://www.sciopen.com/article/10.3934/math.2022494},
doi = {10.3934/math.2022494},
abstract = {The aim of this manuscript is to prove some fixed point results for non-linear set-valued maps with new approach of        (                  α                  ∗                    ,              ϕ                  M                      )  -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.}
}