Fixed Point Theorems via Auxiliary Functions

Fixed point theory is one of fundamental tools of nonlinear functional analysis. Since the fixed point theory has a wide application area in almost all quantitative sciences, many authors have been working on this field. One of the impressive initial results in this direction was given by Banach 1 , known as Banach Contraction Mapping Principle. It states that each contraction in a complete metric space has a unique fixed point. Since then, a number of papers have been reported on various generalization of celebrated Banach Contraction Mapping Principle. In 2008, Dutta and Choudhury proved the following theorem.