Remarks On Some Generalizations Of θ-Contraction

Abstract

The concept of θ-contraction was modified and generalized in several ways during the last decade. Some assumptions concerning the class Θ are shown to be super-fluous in order to obtain a unique fixed point for a θ-type contraction, θ-Suzuki type and, consequently, θ-contraction. Improvement of several previously published results are de-rived with a modified contractive condition and we have presented an example of possible application. The same approach was used for the F-Suzuki contraction and numerous generalizations are made.