Weak Contraction Condition Involving Cubic Terms of d x , y under the Fixed Point Consideration

Source abstract

A fixed point theorem is presented for single-valued map with using generalized φ -weak contractive condition involving various combinations of d x , y on a complete metric space. Our result is an extension as well as a generalization of Alber and Guerre-Delabriere (1997) in particular. It also generalizes the results of Rhoades (2001), Choudhury and Dutta, (2000), and Dutta and Choudhury, (2008).