Document Type : Research Paper

Authors

• Maibam Ranjit Singh ¹
• Thangjam Bimol Singh ²
• Yumnam Mahendra Singh ³

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

Abstract

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.

Keywords

• compatible mappings of type (E)
• R-weakly commuting mappings of type (P)
• multiplicative metric space
• b-multiplicative metric space
• common fixed points
• compatible mapping
• R-multiplicative metric space
• orthogonal set