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The main aim of this paper is to study and establish some new coincidence point and common fixed point theorems in the product space of mixed-monotonically complete quasi-ordered metric space. Especially, we shall study the fixed points of functions having the monotone property or the comparable property in the product space of quasi-ordered metric space. An interesting application is to investigate the existence and uniqueness of a solution for the system of integral equations.

Fixed point theorems for the functions having monotone property or comparable property in the product spaces