Some fixed point results for <i>ξ</i>-chainable neutrosophic and generalized neutrosophic cone metric spaces with application

Muhammad Riaz; Umar Ishtiaq; Choonkil Park; Khaleel Ahmad; Fahim Uddin; Muhammad Riaz; Umar Ishtiaq; Choonkil Park; Khaleel Ahmad; Fahim Uddin

doi:10.3934/math.2022811

AIMS Mathematics

2022, Volume 7, Issue 8: 14756-14784. doi: 10.3934/math.2022811

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Some fixed point results for ξ-chainable neutrosophic and generalized neutrosophic cone metric spaces with application

1.
Department of Mathematics, University of the Punjab, Lahore 54590, Pakistan
2.
Office of Research, Innovation and Commercialization, University of Management and Technology Lahore, Pakistan
3.
Research Institute for Natural Sciences, Hanyang University, Seoul 04763, Korea
4.
Department of Math & Stats, International Islamic University Islamabad, Pakistan
5.
Abdus Salam School of Mathematical Sciences, Government College University, Lahore, Pakistan

Received: 04 April 2022 Revised: 20 May 2022 Accepted: 20 May 2022 Published: 08 June 2022
MSC : 47H10, 54H25

This manuscript is concerned for introducing novel concepts of ξ-chainable neutrosophic metric space and generalized neutrosophic cone metric spaces. We use four self-mappings to establish common fixed point theorem in the sense of ξ-chainable neutrosophic metric space and three self-mappings to establish common fixed point results in the sense of generalized neutrosophic metric spaces. Certain properties of ξ-chainable neutrosophic metric space and generalized neutrosophic metric spaces are defined and their examples are presented. An application to fuzzy Fredholm integral equation of second kind is developed to verify the validity of proposed results. These results boost the approaches of existing literature of fuzzy metric spaces and fuzzy fixed theory.
Citation: Muhammad Riaz, Umar Ishtiaq, Choonkil Park, Khaleel Ahmad, Fahim Uddin. Some fixed point results for ξ-chainable neutrosophic and generalized neutrosophic cone metric spaces with application[J]. AIMS Mathematics, 2022, 7(8): 14756-14784. doi: 10.3934/math.2022811

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Abstract

This manuscript is concerned for introducing novel concepts of ξ-chainable neutrosophic metric space and generalized neutrosophic cone metric spaces. We use four self-mappings to establish common fixed point theorem in the sense of ξ-chainable neutrosophic metric space and three self-mappings to establish common fixed point results in the sense of generalized neutrosophic metric spaces. Certain properties of ξ-chainable neutrosophic metric space and generalized neutrosophic metric spaces are defined and their examples are presented. An application to fuzzy Fredholm integral equation of second kind is developed to verify the validity of proposed results. These results boost the approaches of existing literature of fuzzy metric spaces and fuzzy fixed theory.

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