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In this paper, we introduce the concept of Mν$M_{\nu}$-metric as a generalization of M-metric and ν-generalized metric and also prove an analogue of Banach contraction principle in an Mν$M_{\nu}$-metric space. Also, we adopt an example to highlight the utility of our main result which extends and improves the corresponding relevant results of the existing literature. Finally, we use our main result to examine the existence and uniqueness of solution for a Fredholm integral equation.

Fixed point results in $M_{\nu }$-metric spaces with an application