This paper deals with the generalized version of Hermite-Hadamard and Fejér-type inequalities. Some classical results are extended to a newly introduced category of $p$-harmonic convex functions for which explicit bounds are also established. Additionally, novel discrete versions of existing inequalities for univariate $p$-harmonic convex functions over linear spaces are also provided. For validation, the classical results are retrieved by letting $p\to 1$, which clearly indicates the accuracy of the achieved results. Finally, tabular and graphical analysis is presented to show the improved results with $p$-harmonic convex functions over existing literature.