Reconciliation of Elementary Order and Metric Fixpoint Theorems
نویسنده
چکیده
We prove two new fixed point theorems for generalized metric spaces and show that various fundamental fixed point principles, including: Banach Contraction Principle, Caristi fixed point theorem for metric spaces, Knaster-Tarski fixed point theorem for complete lattices, and the Bourbaki-Witt fixed point theorem for directed-complete orders, follow as corollaries of our results.
منابع مشابه
SOME FIXED POINT THEOREMS FOR SINGLE AND MULTI VALUED MAPPINGS ON ORDERED NON-ARCHIMEDEAN FUZZY METRIC SPACES
In the present paper, a partial order on a non- Archimedean fuzzymetric space under the Lukasiewicz t-norm is introduced and fixed point theoremsfor single and multivalued mappings are proved.
متن کاملOn Fixed Point Theorems for Contractive-type Mappings in Fuzzy Metric Spaces
In this paper, we provide two different kinds of fixed pointtheorems in fuzzy metric spaces. The first kind is for the fuzzy$varepsilon$-contractive type mappings and the second kind is forthe fuzzy order $psi$-contractive type mappings. They improve thecorresponding conclusions in the literature.
متن کاملRational Geraghty Contractive Mappings and Fixed Point Theorems in Ordered $b_2$-metric Spaces
In 2014, Zead Mustafa introduced $b_2$-metric spaces, as a generalization of both $2$-metric and $b$-metric spaces. Then new fixed point results for the classes of rational Geraghty contractive mappings of type I,II and III in the setup of $b_2$-metric spaces are investigated. Then, we prove some fixed point theorems under various contractive conditions in partially ordered $b_2$-metric spaces...
متن کاملFixed point theorems under weakly contractive conditions via auxiliary functions in ordered $G$-metric spaces
We present some fixed point results for a single mapping and a pair of compatible mappings via auxiliary functions which satisfy a generalized weakly contractive condition in partially ordered complete $G$-metric spaces. Some examples are furnished to illustrate the useability of our main results. At the end, an application is presented to the study of exi...
متن کاملNon-Archimedean fuzzy metric spaces and Best proximity point theorems
In this paper, we introduce some new classes of proximal contraction mappings and establish best proximity point theorems for such kinds of mappings in a non-Archimedean fuzzy metric space. As consequences of these results, we deduce certain new best proximity and fixed point theorems in partially ordered non-Archimedean fuzzy metric spaces. Moreover, we present an example to illustrate the us...
متن کامل