In this manuscript, a new class of extended (m1,m2)-convex and concave functions is introduced. After some properties of (m1,m2)-convex functions have been given, the inequalities obtained with Hölder and Hölder-İşcan and power-mean and improwed power-mean integral inequalities have been compared and it has been shown that the inequality with Hölder-İşcan inequality gives a better approach than...

hold. This double inequality is known in the literature as the Hermite–Hadamard inequality for convex functions. In recent years many authors established several inequalities connected to this fact. For recent results, refinements, counterparts, generalizations and new Hermite-Hadamard’stype inequalities see [1]–[18]. We recall that the notion of quasi-convex function generalizes the notion of ...

The relevance of convex and non-convex functions in optimization research is well known. Due to the behavior its definition, idea convexity also plays a major role subject inequalities. main concern this paper establish new integral inequalities for newly defined left right interval-valued function on coordinates through pseudo order relation double integral. Some Hermite–Hadamard type product ...

Abstract In this paper, we establish Jensen’s inequality for s -convex functions in the first sense. By using inequalities, obtain some Cauchy type means p and Also, by Hermite–Hadamard inequalities respective generalized convex functions, find new means.

We obtain some inequalities related to the powers of numerical radius inequalities of Hilbert space operators. Some results that employ the Hermite-Hadamard inequality for vectors in normed linear spaces are also obtained. We improve and generalize some inequalities with respect to Specht's ratio. Among them, we show that, if $A, Bin mathcal{B(mathcal{H})}$ satisfy in some conditions, it follow...

Abstract In this paper, we introduce $(h_{1},h_{2})$ ( h 1 , 2 ) -preinvex interval-valued function and establish the Hermite–Hadamard inequality for preinvex functions by using Riemann–Liouville fracti...

In this study, Hermite-Hadamard type inequalities for harmonically-convex functions using fuzzy integrals are presented. Some examples also given to illustrate the obtained results.

In this paper, we give Hermite–Hadamard type inequalities of the Jensen–Mercer for Riemann–Liouville fractional integrals. We prove integral identities, and with help these identities some other eminent inequalities, such as Jensen, Hölder, power mean obtain bounds difference newly obtained inequalities.