Corina Karim, Ekadion Maulana, Ratno Bagus Edy Wibowo, Abdul Rouf Alghofari, Adem Kilicman, Nor Hanimah Kamis, Mila Kurniawaty
This paper establishes new operator versions of the Hermite-Hadamard and Fejér inequalities for the class of operator (h,m)-convex functions on Hilbert spaces. Operator (h,m)-convex functions generalize operator convex, operator m-convex and operator h-convex functions by including a nonnegative function h and a parameter m∈(0,1]. The results presented not only generalize and improve several known inequalities but also represent best possible generalizations for certain parameter selections such as h(μ)=μ and m=1. Additionally, Fejér type inequalities are derived by integrating symmetric weights, demanding integrability of the product of functions on operator domains. The approach generalizes integral inequality techniques in a classical manner to operators, offering new perspectives for functional analysis and operator theory. © 2026, University of Maragheh. All rights reserved.
DEPARTMENT OF MATHEMATICS, FACULTY OF MATHEMATICS AND NATURAL SCIENCES, UNIVERSITAS BRAWIJAYA, JL. VETERAN, MALANG, 65145, Indonesia; FACULTY OF COMPUTER AND MATHEMATICAL SCIENCES, UNIVERSITI TEKNOLOGI MARA, JL. ILMU 1/1, SHAH ALAM, 40450, Malaysia
