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

Muhammad Tariq; Mujahid Abbas; Aftab Hussain; Muhammad Arshad; Amjad Ali; Hamid Al-Sulami; Muhammad Tariq; Mujahid Abbas; Aftab Hussain; Muhammad Arshad; Amjad Ali; Hamid Al-Sulami

doi:10.3934/math.2022494

AIMS Mathematics

2022, Volume 7, Issue 5: 8861-8878. doi: 10.3934/math.2022494

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

1.
Department of Mathematics and Statistics, Internatioal Islamic University, Islamabad, Pakistan
2.
Department of Mathematics GC University Lahore, Pakistan
3.
Department of Mathematics, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia

Received: 12 December 2021 Revised: 02 February 2022 Accepted: 11 February 2022 Published: 04 March 2022
MSC : 47H10, 54H25

The aim of this manuscript is to prove some fixed point results for non-linear set-valued maps with new approach of $ \left(\alpha _{\ast }, \phi _{M}\right) $-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.
- $ \left(\alpha _{\ast }, \phi _{M}\right) $-contractions,
- $ M $ -metric space,
- homotopy fixed point results,
- functional equation
Citation: Muhammad Tariq, Mujahid Abbas, Aftab Hussain, Muhammad Arshad, Amjad Ali, Hamid Al-Sulami. Fixed points of non-linear set-valued $ \left(\alpha _{\ast }, \phi _{M}\right) $-contraction mappings and related applications[J]. AIMS Mathematics, 2022, 7(5): 8861-8878. doi: 10.3934/math.2022494

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Abstract

The aim of this manuscript is to prove some fixed point results for non-linear set-valued maps with new approach of $ \left(\alpha _{\ast }, \phi _{M}\right) $-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.

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