Fixed Point Theorems In Neutrosophic Metric Spaces

In this paper, we introduce the neutrosophic cantractive and neutrosophic mapping. We establish some results on fixed points of a neutrosophic mapping.

In this manuscript, we obtain common fixed point theorems in the neutrosophic cone metric space. Also, notion of (Φ,Ψ)-weak contraction is defined in the neutrosophic cone metric space by using the idea of altering distance function. Finally, we review many examples of cone metric spaces to verify some properties.

In this article, we present fixed and common fixed point results for Banach and Edelstein contraction theorems in neutrosophic metric spaces. Then some properties and examples are given for neutrosophic metric spaces. Thus, we added a new path in neutrosophic theory to obtain fixed point results. We investigate and prove some contraction theorems that are extended to neutrosophic metric space with the assistance of Grabiec.

The intention of this paper is to give the general de nition of cone metric space in the context of the neutrosophic theory. In this relation, we obtain some fundamental results concerting xed points for weakly compatible mapping.

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.

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.

The main aim of this paper is to premise bipolar neutrosophic soft metric space (BNSMS) in terms of bipolar neutrosophic soft points. In addition, we define convergence of sequence, Cauchy sequence and completeness in BNSMS with appropriate examples. Further, we represent bipolar neutrosophic soft mappings using a Cartesian product with relations on bipolar neutrosophic soft sets and developed a fixed point theorem for self maps with contractive conditions using BNS mappings.

This book presents fixed point theory, one of the crucial tools in applied mathematics, functional analysis, and topology, which has been used to solve distinct real-world problems in computer science, engineering, and physics. The authors begin with an overview of the extension of metric spaces. Readers are introduced to general fixed-point theorems while comparing and contrasting important and insignificant metric spaces. The book is intended to be self-contained and serves as a unique resource for researchers in various disciplines.