New variants of the Hermite-Hadamard inequality via modified (h,m)-convex functions of the second type

Juan Gabriel Galeano Delgado, Juan E. Nápoles Valdés, Abel Alvarez Bustos

Abstract


In this study, we derive novel variants of the Hermite-Hadamard inequality using modified (h, m)-convex functions of the second type. Our approach leverages the generalized fractional integral operator to establish these variants, grounded in the theoretical underpinnings of (h, m)-convex functions that extend classical convex functions. By integrating the generalized fractional integral operator with modified (h, m)-convex functions, we formulate hypotheses that extend the Hermite-Hadamard inequality, exploring fresh boundaries and relationships within this mathematical framework. Several findings from the existing literature are extrapolated from our research, underscoring the robustness and practical relevance of the newly introduced Hermite-Hadamard inequality versions in this paper.

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DOI: https://doi.org/10.52846/ami.v53i1.2068