In this paper, we establish integral inequalities of Hermite-Hadamard type for multiplicativelys-preinvex functions. We also obtain some new inequalities involving multiplicative integralsby using some properties of multiplicatively s-preinvex and preinvex functions.

Abstract In this article, we have established some new bounds of Fejér-type Hermite-Hadamard inequality for k k -fractional integrals involving r r -times differentiable preinvex functions. It is noteworthy that in the past, there was no weighted version left and right sides generalized convex functions av...

In this paper, we present some new refinements of Hermite–Hadamard inequalities for continuous convex functions by using (p,q)-calculus. Moreover, study (p,q)-Hermite–Hadamard multiple integrals. Many results given in paper provide extensions others previous research.

Fractional derivative and integral operators are often employed to present new generalizations of mathematical inequalities. The introduction fractional has prompted another direction in different branches mathematics applied sciences. First, we investigate prove equality. Considering this equality as the auxiliary result, attain some estimations a Hermite–Hadamard type inequality involving s-p...

In this study, we present new variants of the Hermite–Hadamard inequality via non-conformable fractional integrals. These inequalities are proven for convex functions and differentiable whose derivatives in absolute value generally convex. Our main results established using classical Jensen–Mercer its (h,m)-convex modified paper. addition to showing that our support previously known from litera...

The fuzzy-number valued up and down λ-convex mapping is originally proposed as an intriguing generalization of the convex mappings. newly suggested mappings are then used to create certain Hermite–Hadamard- Pachpatte-type integral fuzzy inclusion relations in fractional calculus. It also revise Hermite–Hadamard inclusions with regard (U∙D F-N∙V∙Ms). Moreover, Hermite–Hadamard–Fejér has been pro...

For k-Riemann–Liouville fractional integral operators, the Hermite–Hadamard inequality is already well-known in literature. In this regard, paper presents inequalities for operators by using a novel method based on Green’s function. Additionally, applying these identities to convex and monotone functions, new type are established. Furthermore, different form of also obtained approach. conclusio...

It is the purpose of this paper to propose a novel class convex functions associated with strong ?-convexity. A relationship between newly defined function and an earlier generalized hereby established. To point out importance new functions, some examples are presented. Additionally, famous Hermite–Hadamard inequality derived for family functions. Furthermore, inequalities results ?-convex also...