G. Siva - Department of Mathematics, Alagappa University, Karaikudi-۶۳۰ ۰۰۳, India

The concept of tricomplex valued S-metric space is introduced in this article, and some properties are derived. Also, some fixed point results of contraction maps satisfying various types of rational inequalities are proved for tricomplex valued S-metric spaces. Moreover, an example is given to illustrate our main result. Furthermore, an existence theorem for the unique solution to the linear system of equations is obtained by using our main result.

Complex number, Partial order, S-metric space, Nonsingular