Some estimates on the Hermite-Hadamard inequality through quasi-convex functions

By Daniel Alexandru Ion. 2007

170 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/f9eee7602ce077b0ff4eb5d460c7ed8bed7c8afc

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Citations in the corpus

New inequalities of Hermite-Hadamard type for functions whose second derivatives absolute values are convex and quasi-convex (2010, background): “Furthermore, there exist quasi-convex functions which are not convex (see [4]).”
New integral inequalities involving beta function via $P$-convexity (2014, background): “Furthermore, there exist quasi-convex functions which are not convex (see [11]).”
Hermite-Hadamard type inequalities for MT-convex functions via classical integrals and fractional integrals (2016, background): “For other recent results concerning Hermite-Hadamard type inequalities through various classes of convex functions, see [1, 3, 5, 7, 8, 9, 12, 10, 17, 20, 22, 24, 25, 28] and the references cited therein.”
New inequalities of Hermite-Hadamard type for functions whose second derivatives absolute values are quasi-convex (2010, unknown): “Furthermore, there exist quasiconvex functions which are not convex, (see for instance [1]–[5] and [12]).”
Hermite-Hadamard inequality for functions whose derivatives absolute values are preinvex (2012, background): “In This paper we generalize the results in [10] for functions whose first derivatives absolute values are preinvex.”
New estimates on generalization of some integral inequalities for s-convex functions and their applications (2012, background): “See [1, 3, 4, 6, 7, 9], the results of the generalization, improvement and extention of the famous integral inequality (1.”
Some q-analogues of Hermite–Hadamard inequality of functions of two variables on finite rectangles in the plane (2017, background): “…inequalities and theory of convex functions have been observed to be profoundly dependent on each other and consequently a vast literature on inequalities has been produced by a number of researchers using convex functions, see Dragomir and Pearce (2000), Dragomir and Agarwal (1998) and Ion (2007).”
Inequalities of Hermite-Hadamard's Type for Functions Whose Derivatives Absolute Values are Quasi-Convex (2009, unknown): “More precisely, a function f : for any x; y 2 [ a; b ] and 2 [0 ; 1] : Clearly, any convex function is a quasi-convex function. there Furthermore, exist quasi-convex functions which are not convex (see [6]).”