It is indispensable that the fixed point theory in the metric space has a crucial role in nonlinear analysis and has wide application potential in almost all quantitive sciences. In the last fifty years, discussing the existence and uniqueness of a fixed point of single and multivalued operators in various spaces has attracted the attention of several researchers of nonlinear analysis. Nonlinear analysis deals with solving nonlinear problems in many areas of theoretic disciplines and in industry. Fixed-point theory is an important branch of nonlinear analysis, to investigate the conditions under which single-valued or multivalued mappings have solutions. Fixed-point techniques have been applied in diverse fields such as physics, biology, chemistry, economics, engineering, and game theory.
The motivation behind this interest is the enormous potential applications of this theory to various braces of mathematics as well as the other quantitive sciences, such as engineering, chemistry, biology, economics, computer science, and other sciences.