Fixed point results for theta-phi interpolative mappings in super metric space with an application

Abstract

This paper aims at introducing the notion of generalized interpolative theta-phi contraction, interpolative Matkowski type contraction and an interpolative theta-phi Kannan type contraction in frame of Super metric space. The result proved in this paper improve and extend the corresponding results due to Matkowski and Karapinar [ E. Karapinar et al., TWMS J. Pure Appl. Math., 11 (2) (2020), 204-212], Kannan and Karapinar [ E. Karapinar, Adv. Theory Nonlinear Anal. Appl., 2(2) (2018), 85-87]. Examples are given to demonstrate the relevance of our results. As application, we obtain the solution for the non-linear matrix equations.