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Abstract In this article, we introduce a class of functions U ( p ) $\mathfrak{U}(\mathfrak{p})$ with integral representation defined over a measure space with σ-finite measure. The main purpose of this paper is to extend the Minkowski and related inequalities by considering general kernels. As a consequence of our general results, we connect our results with various variants for the fractional integrals operators. Such applications have wide use and importance in the field of applied sciences.