Banach Fixed Point Theorem on Orthogonal Cone Metric Spaces

Abstract

In this paper, we introduce new concept of orthogonal cone metric spaces. We stablish new versions of fixed point theorems in incomplete orthogonal cone metric spaces. As an application, we show the existence and uniqueness of solution of the periodic boundry value problem.

Fixed-Point Results for Mappings Satisfying Implicit Relation in Orthogonal Fuzzy Metric Spaces

“…In 2017, Gordji et al [18] developed the conception of orthogonal sets and introduced orthogonal metric spaces as a generalisation of metric spaces. Later, in [19][20][21][22] etc., the authors added some generalisations of orthogonal metric spaces along with several fxed-point results. In 2018, Hezarjaribi [19] presented the notion of orthogonal fuzzy metric spaces, and a little work has been performed in this generalisation of a metric space [23][24][25].…”

Fixed point theorem between cone metric space and quasi-cone metric space

“…For instance, a quasi-cone metric space (QCMS) definition expands to the QMS given by Turkoglu and Abuloha [3]. Morales and Rojas have introduced the continuity of mapping between CMS (𝑋, 𝐶), 𝑃 a cone along with constant 𝐾 and 𝑇: 𝑋 ⟶ 𝑋 and it self [4]. Yaying et al introduced the continuity of mapping between QCMS (𝑋, 𝑞) and itself [5].…”

“…Also, they have proven some interesting results. For functions between (MSs), (CMSs) and (QCMSs) and themselves, many continuity ideas have been established [4], [5]. The continuity function between (QCMSs) and (CMSs) and vice versa, however, has yet to be implemented.…”