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The main purpose of this paper is to study the coincidence point and common fixed point theorems in the product spaces of mixed-monotonically complete quasi-ordered metric spaces based on some new types of contractive inequalities. In order to investigate the existence and chain-uniqueness of solutions for the systems of integral equations and ordinary differential equations, we shall also study the fixed point theorems for the functions having mixed monotone property or comparable property in the product space of quasi-ordered metric space. MSC: 47H10, 54H25.

journal of inequalities and applications

Coincidence point and common fixed point theorems in the product spaces of mixed-monotonically complete quasi-ordered metric spaces and their applications to the systems of integral equations and ordinary differential equations