Fixed points of non-linear set-valued (α∗, φM)-contraction mappings and related applications

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

doi:10.3934/math.2022494

Fixed points of non-linear set-valued (α_∗, φ_M)-contraction mappings and related applications

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

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

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.

Original language	English
Pages (from-to)	8861-8878
Number of pages	18
Journal	AIMS Mathematics
Volume	7
Issue number	5
DOIs	https://doi.org/10.3934/math.2022494
Publication status	Published - 2022
Externally published	Yes

Keywords

(α, φ )-contractions
Functional equation
Homotopy fixed point results
M-metric space

ASJC Scopus subject areas

General Mathematics

Access to Document

10.3934/math.2022494

Cite this

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title = "Fixed points of non-linear set-valued (α∗, φM)-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.",

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AU - Tariq, Muhammad

AU - Abbas, Mujahid

AU - Hussain, Aftab

AU - Arshad, Muhammad

AU - Ali, Amjad

AU - Al-Sulami, Hamid

PY - 2022

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AB - 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.

KW - (α, φ )-contractions

KW - Functional equation

KW - Homotopy fixed point results

KW - M-metric space

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