Fixed point theorems in analysis

A survey of fixed point theorems in analysis is given from their initiation to the present. The many and varied operators and spaces which occur are classified into a logical arrangement. An analysis is made of certain classical as well as very recent general theorems, and a generalization of one of the modern theorems is proved. The application of fixed point theorems to the proof of existence and uniqueness of solutions to differential and integral equations is illustrated by several examples. Many conjectures and suggestions for further research are interspersed with the ordered arrangement of the fixed point theorems in analysis which appear in the literature.