Fixed point theorems of non-commuting mappings in b-multiplicative metric spaces

Document Type : Research Paper


1 Department of Mathematics, Manipur, 795003, Manipur University, Canchipur Imphal, India

2 MU, Department of Mathematics, Manipur, 795003 Manipur University, Canchipur, Manipur, India.

3 Department of Humanities and Basic Sciences, Manipur Institute of Technology, Takyelpat-795004, Manipur, India


In this paper, we discuss some common fixed point theorems for compatible mappings of type $(E)$ and $R-$weakly commuting mappings of type $(P)$ of a complete $b-$multiplicative metric space along with some examples. As an application, we establish an existence and uniqueness theorem for a solution of a system of multiplicative integral equations. In the last section, we introduce the concept of $R-$multiplicative metric space by giving some examples and at the end of the section, we give an open question.