Fixed Point Results in Metric space with Some Applications

Functional analysis is an important branch of mathematics. The fixed point theory has always played a central role in the problems of nonlinear functional analysis. The results discuss some common fixed point theorems for compatible and psi-compatible mappings in metric space under the more general contractive definitions like Meir-Keeler type, Boyd-Wong type and Lipschitz type contractive conditions in the presence of control function. The results obtained in this research work extend and unify some well known similar results in the literature. Also, a summary work on some applications of fixed point theory to approximation theory has been presented. This work should be useful to researchers and anyone else working in the fields of non-linear analysis and applications.