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Generalized Convexity: A contemporary vision about Convexity
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We introduce the concept of operator h-convex functions for positive linear maps, and prove some Hermite-Hadamard type inequalities for these functions. As applications, we obtain several trace inequalities for operators.
We consider and study a new class of convex functions that are called relative m−semilogarithmic convex functions. Some Hermite-Hadamard inequalities for this a kind of generalized convex function are derived.
In the present paper we introduce the notion of operator h-convex function. Also, we obtain new Jensen and Hermite-Hadamard inequalities for these operator h-convex functions in Hilbert spaces.
In this paper, we establish some new results related to the left- hand of the Hermite-Hadamard type inequalities for the class of functions whose second derivatives are strongly s-convex functions in the second sense. Some previous results are also recaptured as a special case.
We introduce the class of strongly (s,m)-convex functions modulus c > 0 in the second sense, and prove inequalities of Hermite-Hadamard-Fejér type for such mappings. This strengthen results given for (s,m)-convex functions in [7].
