On Weak Contraction Mappings

• Main Authors: Chao-Hung Chen, 陳昭宏
• Other Authors: Jin-Chirng Lee
• Format: Others
• Language: en_US
• Published: 2013
• Online Access: http://ndltd.ncl.edu.tw/handle/31149229348136983324

博士 === 中原大學 === 應用數學研究所 === 101 === The thesis is organized into four parts. The first part that we introduce the notions weak contraction mappings and weak contraction mappings in complete generalized metric spaces and prove two theorems which assure the existence of a periodic point for these two types of weak contraction. The second part that we study fixed point theorems for a mapping satisfying the generalized Meir –Keeler -type contractions in complete partial metric spaces. The third part that we prove two new fixed point theorems in the framework of partially ordered metric spaces. The final part that by using the stronger Meir-Keeler mapping, we introduce the concepts of the sMK-G-cyclic mappings, sMK-K-cyclic mappings and sMK-C-cyclic mappings, and then we prove some best proximity point theorems for these various types of contractions. The results of this thesis generalize and improve many recent best proximity point theorems and fixed point theorems in the literature