A Common Generalization of Metric and Ultrametric Fixed Point Theorems
نویسنده
چکیده
We present a general fixed point theorem which can be seen as the quintessence of the principles of proof for Banach’s Fixed Point Theorem and ultrametric fixed point theorems. It works in a minimal setting, not involving any metrics, only based on the notion of “ball” and the property of “spherical completeness”. We demonstrate its applications to the metric and the ultrametric cases, and (in two possible ways) to ordered abelian groups and fields.
منابع مشابه
A generalization of Kannan and Chatterjea fixed point theorems on complete $b$-metric spaces
In this paper, we give some results on the common fixed point of self-mappings defined on complete $b$-metric spaces. Our results generalize Kannan and Chatterjea fixed point theorems on complete $b$-metric spaces. In particular, we show that two self-mappings satisfying a contraction type inequality have a unique common fixed point. We also give some examples to illustrate the given results.
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 کاملA Common Generalization of Metric, Ultrametric and Topological Fixed Point Theorems
We present a general fixed point theorem which can be seen as the quintessence of the principles of proof for Banach’s Fixed Point Theorem, ultrametric and certain topological fixed point theorems. It works in a minimal setting, not involving any metrics. We demonstrate its applications to the metric, ultrametric and topological cases, and to ordered abelian groups and fields.
متن کاملCommon fixed point results on vector metric spaces
In this paper we consider the so called a vector metric space, which is a generalization of metric space, where the metric is Riesz space valued. We prove some common fixed point theorems for three mappings in this space. Obtained results extend and generalize well-known comparable results in the literature.
متن کاملTwo common fixed Point theorems for compatible mappings
Recently, Zhang and Song [Q. Zhang, Y. Song, Fixed point theory forgeneralized $varphi$-weak contractions,Appl. Math. Lett. 22(2009) 75-78] proved a common fixed point theorem for two mapssatisfying generalized $varphi$-weak contractions. In this paper, we prove a common fixed point theorem fora family of compatible maps. In fact, a new generalization of Zhangand Song's theorem is given.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2011