A new interpolative $(\varphi,\psi)$-type $\mathfrak{Z}$-contraction with application to nonlinear matrix equation systems

Irom Shashikanta  Singh; Y. Mahendra  Singh; G. A. Hirankumar  Sharma; Abdelhamid Moussaoui

doi:10.5269/bspm.77134

Irom Shashikanta Singh Department of Mathematics, Manipur University, Canchipur-795003, Manipur, India.
Y. Mahendra Singh Department of Basic Sciences and Humanities, Manipur Institute of Technology - A constituent college of Manipur University- Takyelpat -795004, Manipur, India
G. A. Hirankumar Sharma Department of Basic Sciences and Humanities, Manipur Institute of Technology - A constituent college of Manipur University- Takyelpat -795004, Manipur, India.
Abdelhamid Moussaoui Sultan Moulay Sliman University

Abstract

In this study, we introduce a new concept of interpolative $(\varphi,\psi)-$ type $\mathfrak{Z}-$ contraction via quasi-triangular $\theta-$admissible mapping and prove some related fixed point theorems in the context of $b-$ metric space. As an application of our results, we solve a system of non-linear matrix equations. Finally, a numerical example is presented to demonstrate the validity and practical significance of our approach.

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