Fixed Point Theorem for Neutrosophic Triplet Partial Metric Space

Memet Şahin,Abdullah Kargın,Mehmet Ali Çoban

doi:10.3390/sym10070240

Abstract

Neutrosphic triplet is a new theory in neutrosophy. In a neutrosophic triplet set, there is a neutral element and antielement for each element. In this study, the concept of neutrosophic triplet partial metric space (NTPMS) is given and the properties of NTPMS are studied. We show that both classical metric and neutrosophic triplet metric (NTM) are different from NTPM. Also, we show that NTPMS can be defined with each NTMS. Furthermore, we define a contraction for NTPMS and we give a fixed point theory (FPT) for NTPMS. The FPT has been revealed as a very powerful tool in the study of nonlinear phenomena. This study is also part of the “Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets” which is a special issue.

Highlights

Neutrosophy was first studied by Smarandache in [1]
We obtained a new structure for developing NT theory
It was shown that both the classical metric and neutrosophic triplet metric (NTM) are different from the NTPM, and neutrosophic triplet partial metric space (NTPMS) can be defineddefined with each

Summary

Introduction

Neutrosophy was first studied by Smarandache in [1]. Neutrosophy consists of neutrosophic logic, probability, and sets. Smarandache and Ali studied NT theory in [10] and NT groups (NTG) in [11,12]. Smarandache, Şahin, and Kargın studied neutrosophic triplet G-module in [17], and Bal, Shalla, and Olgun introduced neutrosophic triplet cosets and quotient groups in [18]. Matthew introduced the concept of partial metric spaces (PMS) in [19]. Shukla introduced FPT for ordered contractions in partial b-metric space in [24]. Okeke, and Lim introduced common coupled FPT for w-compatible mappings in PMS in [25]. Lim introduced common coupled FPT for w-compatible mappings in PMS in [25]. Researchers can arrive at nonlinear partial differential equations problem solutions in NT theory.

Preliminaries

Neutrosophic Triplet Partial Metric Space

Preliminaries eliminaries

Preliminaries some basic definitions for NTPM and NTM i

Neutrosophic

Conclusions