Aequat. Math. c  Springer International Publishing AG, part of Springer Nature 2018 https://doi.org/10.1007/s00010-018-0562-7 Aequationes Mathematicae An extension of Matkowski’s and Wardowski’s fixed point theorems with applications to functional equations Deepak Khantwal and U. C. Gairola Abstract. In this paper, we prove a fixed point theorem for a system of maps on the finite product of metric spaces. Our result generalizes the result of Matkowski (Bull Acad Pol Sci S´ er Sci Math Astron Phys 21:323–324, 1973), Cosentino and Vetro (Filomat 28(4):715–722, 2014) and Hardy and Rogers (Can Math Bull 16(2):201–206, 1973) and other results in the literature. Moreover, we have an application for a system of functional equations and an example to illustrate our result. Mathematics Subject Classification. Primary 47H10; Secondary 54H25, 39B12. Keywords. Fixed point, Matkowski contraction, Wardowski contraction, Product space, Iter- ative functional equation, Bounded solution. 1. Introduction The Banach contraction principle is one of the most fundamental and milestone theorems in nonlinear analysis with a wide range of applications in different branches of Mathematics. Several authors have obtained various extensions and generalizations of the Banach contraction principle in different directions. In this sequel, Matkowski [12, 13] generalized the Banach contraction principle for a system of n maps on a finite product of metric spaces and gave an interesting result for such a system of maps. Now, this result is usually known as the Matkowski contraction principle or Matkowski’s fixed point theorem (see [25]). Due to the applicability of finding the solution of a system of functional equations, the result of Matkowski has attracted several authors to do work along this line. Therefore several author have extended and generalized the Matkowski contraction principle for systems of single-valued maps as well as systems of multi-valued maps (see, for instance [1, 3–8, 15, 18, 19, 21–25] and others).