tailieunhanh - Dissertation summary: On the existence of fixed point for some mapping classes in spaces with uniform structure and application

Research objective: The thesis is devoted to extend some results on the existence of fixed points in metric spaces to spaces with uniform structure. We also considered the existence of solutions of some classes of integral equations with unbounded deviation, which we can not apply fixed point theorems in metric spaces. The thesis can be a reference for under graduated students, master students and students in analysis major in general, and the fixed point theory and applications in particular. | MINISTRY OF EDUCATION AND TRAINING VINH UNIVERSITY LE KHANH HUNG ON THE EXISTENCE OF FIXED POINT FOR SOME MAPPING CLASSES IN SPACES WITH UNIFORM STRUCTURE AND APPLICATIONS Speciality Mathematical Analysis Code 62 46 01 02 A SUMMARY OF MATHEMATICS DOCTORAL THESIS NGHE AN - 2015 Work is completed at Vinh University Supervisors 1. Assoc. Prof. Dr. Tran Van An 2. Dr. Kieu Phuong Chi Reviewer 1 Reviewer 2 Reviewer 3 Thesis will be presented and defended at school - level thesis evaluating Council at Vinh University at . h. date. month. year . Thesis can be found at 1. Nguyen Thuc Hao Library and Information Center 2. Vietnam National Library 1 PREFACE 1 Rationale . The first result on fixed points of mappings was obtained in 1911. At that time L. Brouwer proved that Every continuous mapping from a compact convex set in a finite-dimensional space into itself has at least one fixed point. In 1922 S. Banach introduced a class of contractive mappings in metric spaces and proved the famous contraction mapping principle Each contractive mapping from a complete metric space X d into itself has a unique fixed point. The birth of the Banach contraction mapping principle and its application to study the existence of solutions of differential equations marks a new development of the study of fixed point theory. After that many mathematicians have studied to extend the Banach contraction mapping principle for classes of maps and different spaces. Expanding only contractive mappings till 1977 was summarized and compared with 25 typical formats by . Rhoades. . The Banach contraction mapping principle associates with the class of contractive mappings T X X in complete metric space X d with the contractive condition B d TX Ty kd X y for all x y 2 X where 0 k 1. There have been many mathematicians seeking to extend the Banach contraction mapping principle for classes of mappings and different spaces. The first extending was obtained by E. Rakotch by mitigating a contractive .