Fixed point theorems without continuity in metric vector spaces

2022/11/06 by Li, Jinlu
#47H10 #58C30 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2211.02994

Abstract

In this oaper, we prove some fixed point theorems in metric vector spaces, in which the continuity is not required for the considered mappings to satisfy. We provide some concrete examples to demonstrate these theorems. We also give some counterexamples to show that every condition in the theorems is necessary for the considered mapping to have a fixed point.

Related

• Fixed points and completeness in metric and in generalized metric spaces
• Fixed point theorems by altering distances between the points
• A fixed point theorem for contractive mappings that characterizes metric completeness
• Continuity in Vector Metric Spaces
• Fixed point theorems for a class of mappings depending of another function and defined on cone metric spaces