Some Hadamard–Fejér Type Inequalities for LR-Convex Interval-Valued Functions

The purpose of this study is to introduce the new class of Hermite–Hadamard inequality for LR-convex interval-valued functions known as LR-interval Hermite–Hadamard inequality, by means of pseudo-order relation ( <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mo>≤</mo><mi>p</mi></msub></mrow></semantics></math></inline-formula> ). This order relation is defined on interval space. We have proved that if the interval-valued function is LR-convex then the inclusion relation “ <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>⊆</mo></semantics></math></inline-formula> ” coincident to pseudo-order relation “ <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mo>≤</mo><mi>p</mi></msub></mrow></semantics></math></inline-formula> ” under some suitable conditions. Moreover, the interval Hermite–Hadamard–Fejér inequality is also derived for LR-convex interval-valued functions. These inequalities also generalize some new and known results. Useful examples that verify the applicability of the theory developed in this study are presented. The concepts and techniques of this paper may be a starting point for further research in this area.