Keywords
Nadler’s fixed point theorem
Banach contraction principle
Simultaneous generalization
Kannan’s fixed point theorem
Chatterjea’s fixed point theorem
Berinde-Berinde’s fixed point theorem
Mizoguchi-Takahashi’s fixed point theorem
How to Cite
Abstract
The primary goal of this work is to establish some new fixed point theorems and new simultaneous generalizations of Berinde-Berinde’s fixed point theorem, Mizoguchi-Takahashi’s fixed point theorem, Nadler’s fixed point theorem, Banach contraction principle, Kannan’s fixed point theorem and Chatterjea’s fixed point theorem.
References
Banach S. Sur les opérations dans les ensembles abstraits et leurs applications aux équations intégrales. Fund Math 1922; 3: 133-181.
Berinde M, Berinde V. On a general class of multi-valued weakly Picard mappings. J Math Anal Appl 2007; 326: 772-782.
Chatterjea SK. Fixed-point theorems. C.R. Acad. Bulgare Sci 1972; 25: 727-730.
Du W-S. Some new results and generalizations in metric fixed point theory. Nonlinear Anal 2010; 73: 1439-1446.
Du W-S. On coincidence point and fixed point theorems for nonlinear multivalued maps. Topology and its Applications 2012; 159: 49-56.
Du W-S. New existence results of best proximity points and fixed points for MT(λ) -functions with applications to differential equations. Linear and Nonlinear Analysis 2016; 2(2): 199-213.
Du W-S. Simultaneous generalizations of fixed point theorems of Mizoguchi-Takahashi type, Nadler type Banach type, Kannan type and Chatterjea type. Nonlinear Analysis and Differential Equations 2017; 5(4): 171-180.
Kannan R. Some results on fixed point- II. Amer Math Monthly 1969; 76: 405-408.
Mizoguchi N, Takahashi W. Fixed point theorems for multivalued mappings on complete metric spaces. J Math Anal Appl 1989; 141: 177-188.
Nadler SB. Jr. Multi-valued contraction mappings. Pacific J Math 1969; 30: 475-488.
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.