Fixed point theorems and the Krein-S̆mulian property in locally convex spaces

Fixexd point theory and applications

Hua Zhou¹  Fuli Wang¹ 

[1] School of Mathematics and Physics, Changzhou University, Changzhou, China

关键词: fixed point theorem;    locally convex space;    Krein-S̆mulian property;    family of measures of weak noncompactness;    47H10;    47H08;    47H30;   

DOI  :  10.1186/s13663-015-0400-8

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

The aim of this paper is to establish some new fixed point theorems for the superposition operators in locally convex spaces which satisfy the Krein-S̆mulian property. We employ a family of measures of noncompactness in conjunction with the Schauder-Tychonoff fixed point theorem. As an application, the existence of solutions to a quite general nonlinear Volterra type integral equation is considered in locally integrable spaces.

【 授权许可】

CC BY