In this paper, we deal with the subdierential concept onHadamard spaces. Flat Hadamard spaces are characterized, and nec-essary and sucient conditions are presented to prove that the subdif-ferential set in Hadamard spaces is nonempty. Proximal subdierentialin Hadamard spaces is addressed and some basic properties are high-lighted. Finally, a density theorem for subdierential set is established.

In this paper, by using Jensen–Mercer’s inequality we obtain Hermite–Hadamard–Mercer’s type inequalities for a convex function employing left-sided (k, ψ)-proportional fractional integral operators involving continuous strictly increasing function. Our findings are generalization of some results that existed in the literature.

Abstract In this work, we established some new general integral inequalities of Hermite–Hadamard type for s -convex functions. To obtain these inequalities, used the Hölder inequality, power-mean and generalizations associated with inequalities. Also compared (e.g., Theorem 6 8). Finally, gave applications special means.

where χ(S) is the Euler characteristic of the surface, B r denotes the geodesic r-ball in Hn(b) and Vol(S 2∩Bb,n r ) Vol(B r ) is the volume growth of the domains S2 ∩B r . A natural question arises in this context: can we prove the finiteness of the topology of a not necessarily minimal surface in a Cartan–Hadamard manifold and, moreover, establish a Chern–Osserman-type inequality for its Eule...

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...

The main goal of this work is to provide quantum parametrized Hermite-Hadamard like type integral inequalities for functions whose second derivatives in absolute values follow different convexities. A new identity derived twice differentiable functions, which used as a key element our demonstrations along with several basic such as: power mean inequality, and Holder’s inequality. symmetry the s...

We establish various fractional convex inequalities of the Hermite–Hadamard type with addition to many other inequalities. Various types such are obtained, as (p,h) inequality and others, (p,h)-convexity is generalization As a consequence (h,m)-convexity, (s,m)-type obtained. Many consequences generalizations

Abstract We introduce new time scales on $\mathbb{Z}$ Z . Based this, we investigate the discrete inequality of Hermite–Hadamard type for convex functions. Finally, improve our result to fractional functions involving left nabla and right delta sums.