Contributions to the fixed point theory of diagonal operators

Fixexd point theory and applications

erban¹  el¹  Ioan A Rus²  Adrian Petruş³  Marcel-Adrian ޳ 

[1] -Bolyai University Cluj-Napoca, Cluj-Napoca, Romania;Academy of Romanian Scientists, Bucharest, Romania;Faculty of Mathematics and Computer Science, Babeş

关键词: diagonal operator;    fixed point;    fixed point structure;    coupled fixed point;    weakly Picard operator;    difference equation;    multi-valued operator;    differential equation;    integral equation;    research direction;    47H10;    54H25;    47J25;    65J15;    47H09;   

DOI  :  10.1186/s13663-016-0589-1

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we introduce the notion of diagonal operator, we present the historical roots of diagonal operators and we give some fixed point theorems for this class of operators. Our approaches are based on the weakly Picard operator technique, difference equation techniques, and some fixed point theorems for multi-valued operators. Some applications to differential and integral equations are given. We also present some research directions.

【 授权许可】

CC BY