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...

An inequality for convex functions defined on linear spaces is obtained which contains in a particular case a refinement for the second part of the celebrated Hermite-Hadamard inequality. Applications for semi-inner products on normed linear spaces are also provided.

In the frame of fractional calculus, term convexity is primarily utilized to address several challenges in both pure and applied research. The main focus objective this review paper present Hermite–Hadamard (H-H)-type inequalities involving a variety classes convexities pertaining integral operators. Included various are classical convex functions, m-convex r-convex (α,m)-convex (α,m)-geometric...

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 paper, we establish some new quantum Hermite-Hadamard type inequalities for differentiable convex functions by using the q?2-quantum integral. The results presented in paper extend of Bermudo et al. (On q-Hermite-Hadamard general functions, Acta Mathematica Hungarica, 2020, 162, 363-374). Finally, give examples to show validation paper.

Abstract In this article, the notion of interval-valued preinvex functions involving Riemann–Liouville fractional integral is described. By applying this, some new refinements Hermite–Hadamard inequality for operator are presented. Some novel special cases presented results discussed as well. Also, examples to validate our results. The established outcomes article may open another direction dif...

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...

In this paper, the author introduced the concept of generalized harmonically convex function on fractal sets Rα(0 < α 6 1) of real line numbers and established generalized Hermite-Hadamard’s inequalities for generalized harmonically convex function. Then, by creating a local fractional integral identity, obtained some Hermite-Hadamard type inequalities of these classes of functions. c ©2017 All...

We derive the Levinson type generalization of the Jensen and the converse Jensen inequality for real Stieltjes measure, not necessarily positive. As a consequence, also the Levinson type generalization of the Hermite-Hadamard inequality is obtained. Similarly, we derive the Levinson type generalization of Giaccardi's inequality. The obtained results are then applied for establishing new mean-va...