Jñānābha, Vol. 51 (1) (2021), (64-67)
A NEW APPROACH TO THE STUDY OF FIXED POINT THEORY FOR EXPANSIVE MAPPINGS
St. Andrew’s College of Arts, Science and Commerce
St. Domnic Road, Bandra West-400050, Mumbai, Maharashtra, India
(Received : October 28, 2020; Revised : April 13, 2021)
Fixed Point Theory has become one of the most beneficial branches of Nonlinear Analysis due to its possible applications. In 2017, Ahmad et al. [Journal of Nonlinear Sciences and Applications, 10 (2017), 2350-2358] extended and modified the notion of θ-contraction introduced by Jleli and Samet [Journal of Inequalities and Applications, 38 (2014)] to metric spaces. Also, Khojasteh et al. [Filomat,29 (2015), 1189-1194] introduced the notion of simulation function in order to express different contractivity conditions in a unified way and proved some related fixed point results. To complement these notions, in this paper, we introduce two new types of expansive mappings called θ-expansion and Z-expansion. The related fixed point theorems are also proved. The presented results improve, generalize, and unify many existing famous results in the corresponding literature.
2010 Mathematics Subject Classifications: 54H25, 47H10, 54E50.
Keywords and phrases: Expansive mapping; complete metric space; fixed point; simulation function