The fuzzy integrals are a kind of fuzzy measures acting on fuzzy sets. They can be viewed as an average membershipvalue of fuzzy sets. The value of the fuzzy integral in a decision making environment where uncertainty is presenthas been well established. Most of the integral inequalities studied in the fuzzy integration context normally considerconditions such as monotonicity or comonotonicity....

It is well known that the Hermite–Hadamard inequality (called HH inequality) refines definition of convexity function f(x) defined on [a,b] by using integral from a to b. There are many generalizations or refinements inequality. Furthermore has applications several fields mathematics, including numerical analysis, functional and operator Recently, we gave types refined inequalities obtained whi...

Abstract In this paper, we obtain Hermite–Hadamard-type inequalities of convex functions by applying the notion $q^{b}$ qb -integral. We prove some new related with right-hand sides -Hermite–Hadamard for differentiable absolute values second derivatives. The results present...

Abstract We establish necessary conditions for the existence of solutions to various systems partial differential inequalities in plane. The obtained provide new Hermite-Hadamard-type differentiable functions In particular, we obtain a refinement an inequality due Dragomir [ On Hadamard’s convex on co-ordinates rectangle from plane , Taiwan. J. Math. 5 (2001), no. 4, 775–788] coordinates.

In this paper, the authors defined a new general class of functions, so-called strongly (h1,h2)-nonconvex function involving F??,?(?) (Raina function). Utilizing this, some Hermite-Hadamard type integral inequalities via generalized fractional operator are obtained. Some results as special cases given well.

Abstract In this paper, we explore a class of Hermite–Hadamard integral inequalities for convex and m -convex functions. The Hölder inequality is used to create class, which has wide range applications in optimization theory. Some trapezoid-type midpoint error estimates are investigated. Inequalities several q -special functions highlighted. As particular cases, have included previous results.

Abstract In this paper, we offer a new quantum integral identity, the result is then used to obtain some estimates of Hermite–Hadamard inequalities for integrals. The results presented in paper are generalizations comparable literature on inequalities. Several inequalities, such as midpoint-like inequality, Simpson-like averaged midpoint–trapezoid-like and trapezoid-like obtained special cases ...

Several fractional integral inequalities of the Hermite–Hadamard type are presented for class (h,g;m)-convex functions. Applied operators contain extended generalized Mittag-Leffler functions as their kernel, thus enabling new that extend and generalize known results. As an application, upper bounds given.