On Fixed Point Theorems for Contraction Mappings of Integral Type

Fixed point theory is a branch of mathematics having a wide spectrum of applications is not only areas of mathematics, but also is many practical fields such as Physics, Economics, Game and Computer theory. For example, in Economics, the proofs of the existence of equilibrium for various economic problems are based on fixed point theorems. Although a significant proportion of the theory lies in the branch of Functional Analysis, fixed point theory also resides in areas such as Algebraic topology and degree theory. Theorems concerning the existence and uniqueness of fixed points are known as fixed point theorems. Fixed point theory has a very fruitful application in eigenvalue problems as in boundary value problems. In recent times the study of fixed point theory has been gained an important role because of its wide applications in proving the existence and uniqueness of solutions of differential, integral, integro - differential and impulsive differential equations and in obtaining solutions of optimization problems, in approximation theory and non-linear analysis.