Hermite–Jensen–Mercer-Type Inequalities via Caputo–Fabrizio Fractional Integral for h-Convex Function

Integral inequalities involving many fractional integral operators are used to solve various fractional differential equations. In the present paper, we will generalize the Hermite–Jensen–Mercer-type inequalities for an h-convex function via a Caputo–Fabrizio fractional integral. We develop some novel Caputo–Fabrizio fractional integral inequalities. We also present Caputo–Fabrizio fractional integral identities for differentiable mapping, and these will be used to give estimates for some fractional Hermite–Jensen–Mercer-type inequalities. Some familiar results are recaptured as special cases of our results.

A new version of Ostrowski type integral inequalities for different differentiable mapping

In this paper, improved and generalized version of Ostrowski’s type inequalities is established. The parameters used in the peano kernels help us to obtain previous results. The obtained bounds are then applied to numerical integration.

k -Fractional Variants of Hermite-Mercer-Type Inequalities via s -Convexity with Applications

This article is aimed at studying novel generalizations of Hermite-Mercer-type inequalities within the Riemann-Liouville k -fractional integral operators by employing s -convex functions. Two new auxiliary results are derived to govern the novel fractional variants of Hadamard-Mercer-type inequalities for differentiable mapping Ψ whose derivatives in the absolute values are convex. Moreover, the results also indicate new lemmas for Ψ ′ , Ψ ′ ′ , and Ψ ′ ′ ′ and new bounds for the Hadamard-Mercer-type inequalities via the well-known Hölder’s inequality. As an application viewpoint, certain estimates in respect of special functions and special means of real numbers are also illustrated to demonstrate the applicability and effectiveness of the suggested scheme.

A Differentiable Mapping of Mesh Cells Based on Finite Elements on Quadrilateral and Hexahedral Meshes

Finite elements of higher continuity, say conforming in {H^{2}} instead of {H^{1}}, require a mapping from reference cells to mesh cells which is continuously differentiable across cell interfaces. In this article, we propose an algorithm to obtain such mappings given a topologically regular mesh in the standard format of vertex coordinates and a description of the boundary. A variant of the algorithm with orthogonal edges in each vertex is proposed. We introduce necessary modifications in the case of adaptive mesh refinement with nonconforming edges. Furthermore, we discuss efficient storage of the necessary data.

New Variant of Hermite–Jensen–Mercer Inequalities via Riemann–Liouville Fractional Integral Operators

In this paper, certain Hermite–Hadamard–Mercer-type inequalities are proved via Riemann–-Liouville fractional integral operators. We established several new variants of Hermite–Hadamard’s inequalities for Riemann–Liouville fractional integral operators by utilizing Jensen–Mercer inequality for differentiable mapping ϒ whose derivatives in the absolute values are convex. Moreover, we construct new lemmas for differentiable functions ϒ′, ϒ″, and ϒ‴ and formulate related inequalities for these differentiable functions using variants of Hölder’s inequality.

Hermite–Jensen–Mercer Type Inequalities for Caputo Fractional Derivatives

In this article, certain Hermite–Jensen–Mercer type inequalities are proved via Caputo fractional derivatives. We established some new inequalities involving Caputo fractional derivatives, such as Hermite–Jensen–Mercer type inequalities, for differentiable mapping hn whose derivatives in the absolute values are convex.

Differentiable mapping generated by elliptic parabo­loid complexes

In three-dimensional equiaffine space, we consider a differentiable map generated by complexes with three-parameter families of elliptic paraboloids according to the method proposed by the author in the mate­rials of the international scientific conference on geometry and applica­tions in Bulgaria in 1986, as well as in works published earlier in the sci­entific collection of Differ. Geom. Mnogoobr. Figur. The study is carried out in the canonical frame, the vertex of which coincides with the top of the generating element of the manifold, the first two coordinate vectors are conjugate and lie in the tangent plane of the elliptic paraboloid at its vertex, the third coordinate vector is directed along the main diameter of the generating element so that the ends are, respectively, the sums of the first and third, and also the sums of the second and third coordinate vec­tors lay on a paraboloid, while the indicatrixes of all three coordinate vec­tors describe lines with tangents, parallel to the first coordinate vector. The existence theorem of the mapping under study is proved, according to which it exists and is determined with the arbitrariness of one function of one argument. The systems of equations of the indicatrix and the main directions of the mapping under consideration are obtained. The indicatrix and the cone of the main directions of the indicated mapping are geomet­rically characterized.

On generalization of Fejér type inequalities via fractional integral operators

In this paper we first prove a new lemma for differentiable mapping via a fractional integral operator. Then, using lemma, we establish some new Hermite-Hadamard-Fejer type results for convex functions via fractional integral operators. The results presented here would provide extensions of those given in earlier works.