Fu-Gui Shi | Searcharxiv

arXiv2022

Existence and uniqueness of fixed point on closed ball in multiplicative $\mathbf{G}_\mathcal{M}-$metric space

In this article, we investigate some fixed point results satisfying a new generalized $Δ$-implicit contractive condition in ordered complete multiplicative $\mathbf{G}_\mathcal{M}-$metric space. Also, some new definitions and fixed point theorems are presented in ordered complete multiplicative $\mathbf{G}_\mathcal{M}-$metric space. Furthermore, some nontrivial and illustrative examples are given to validate our obtained results.

math.FA↗

arXiv2017

$(L,M)$-fuzzy convex structures

In this paper, the notion of $(L,M)$-fuzzy convex structures is introduced. It is a generalization of $L$-convex structures and $M$-fuzzifying convex structures. In our definition of $(L,M)$-fuzzy convex structures, each $L$-fuzzy subset can be regarded as an $L$-convex set to some degree. The notion of convexity preserving functions is also generalized to lattice-valued case. Moreover, under the framework of $(L,M)$-fuzzy convex structures, the concepts of quotient structures, substructures and products are presented and their fundamental properties are discussed. Finally, we create a functor $ω$ from $\mathbf{MYCS}$ to $\mathbf{LMCS}$ and show that there exists an adjunction between $\mathbf{MYCS}$ and $\mathbf{LMCS}$, where $\mathbf{MYCS}$ and $\mathbf{LMCS}$ denote the category of $M$-fuzzifying convex structures, and the category of $(L,M)$-fuzzy convex structures, respectively.

math.GN↗