Fixed point theory for multivalued φ-contractions

被引：0
作者：
Vasile L Lazăr
机构：
[1] Babeş-Bolyai University Cluj-Napoca,Department of Applied Mathematics
[2] Satu-Mare Branch,Vasile Goldiş Western University Arad
来源：
Fixed Point Theory and Applications | / 2011卷
关键词：
successive approximations; multivalued operator; Picard operator; weakly Picard operator; fixed point; strict fixed point; periodic point; strict periodic point; multivalued weakly Picard operator; multivalued Picard operator; data dependence; fractal operator; limit shadowing; set-to-set operator; Ulam-Hyers stability; sequence of operators;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
The purpose of this paper is to present a fixed point theory for multivalued φ-contractions using the following concepts: fixed points, strict fixed points, periodic points, strict periodic points, multivalued Picard and weakly Picard operators; data dependence of the fixed point set, sequence of multivalued operators and fixed points, Ulam-Hyers stability of a multivalued fixed point equation, well-posedness of the fixed point problem, limit shadowing property of a multivalued operator, set-to-set operatorial equations and fractal operators. Our results generalize some recent theorems given in Petruşel and Rus (The theory of a metric fixed point theorem for multivalued operators, Proc. Ninth International Conference on Fixed Point Theory and its Applications, Changhua, Taiwan, July 16-22, 2009, 161-175, 2010).
引用
收藏
相关论文
共 54 条
[1]  
Nadler SB(2003)Periodic points of multi-valued Topol Methods Nonlinear Anal 22 399-409
[2]  
Covitz H(1970)-contractive maps Israel J Math 8 5-11
[3]  
Nadler SB(2007)Multivalued contraction mappings in generalized metric spaces Banach Center Publ 77 89-114
[4]  
Frigon M(2008)Fixed point and continuation results for contractions in metric and gauge spaces Bull Korean Math Soc 45 67-73
[5]  
Lazăr T(2009)Fixed points and homotopy results for Ćirić-type multivalued operators on a set with two metrics Nonlinear Anal 70 117-125
[6]  
O'Regan D(1969)Fixed points for non-self operators and domain invariance theorems J Math Anal Appl 28 326-329
[7]  
Petruşel A(1989)A theorem on contraction mappings J Math Anal Appl 141 177-188
[8]  
Lazăr TA(2001)Fixed point theorems for multivalued mappings on complete metric spaces Nonlinear Anal 47 649-659
[9]  
Petruşel A(2007)Generalized multivalued contractions Fixed Point Theory 8 97-104
[10]  
Shahzad N(2001)Fixed point theory for multivalued operators on a set with two metrics Nonlinear Anal 47 2683-2693
123456