Related papers: On Hermite-Hadamard Type Integral Inequalities for…
In this paper, we introduce a new second-order directional derivative and a second-order subdifferential of Hadamard type for an arbitrary nondifferentiable function. We derive several second-order optimality conditions for a local and a…
In this paper, we establish some new Ostrowski type inequalities for s-logarithmically convex functions by using Riemann-Liouville fractional integrals. Some applications of our results to P.D.F.'s are given.
We give a slight extension of the Hermite-Hadamard inequality on simplices and we use it to establish error bounds of the operators connected with the approximate integration.
The author introduces the concept of harmonically s-convex functions and establishes some Ostrowski type inequalities and Hermite-Hadamard type inequality of these classes of functions.
In this paper some Hadamard-type inequalities for convex functions of 3-variables on a rectanguler box are given. We also define a mapping related to convex functions on a rectanguler box.
In this paper, we derive new estimates for the remainder term of the midpoint, trapezoid, and Simpson formulae for functions whose derivatives in absolute value at certain power are ({\alpha},m)-convex.
We present a tight parametrical Hermite-Hadamard type inequality with probability measure, which yields a considerably closer upper bound for the mean value of convex function than the classical one. Our inequality becomes equality not only…
In this paper, we first obtain a generalized integral identity for twice local differentiable functions. Then, using functions whose second derivatives in absolute value at certain powers are generalized s convex in the second sense, we…
In this paper we defined $r-$convexity on the coordinates and we established some Hadamard-Type Inequalities.
Fractal geometry and analysis constitute a growing field, with numerous applications, based on the principles of fractional calculus. Fractals sets are highly effective in improving convex inequalities and their generalisations. In this…
In this paper, we establish the modified concavity inequality for complex Hessian equations under the semi-convexity assumption inspired by Lu \cite{Lu23} and Zhang \cite{Z24} for real case. Then second order estimates for admissible…
In this paper, we establish several inequalities for different convex mappings that are connected with the Riemann-Liouville fractional integrals. Our results have some relationships with certain integral inequalities in the literature.
In this paper we established a new Simpson type conformable fractional integral equality for convex functions. Based on this identity, some results related to Simpson-like type inequalities are obtained. These results are then applied to…
In this study, we establish and generalize some inequalities of Hadamard and Simpson type based on s-convexity in the second sense. Some applications to special means of positive real numbers are also given and generalized. Examples are…
The paper is devoted to a comprehensive second-order study of a remarkable class of convex extended-real-valued functions that is highly important in many aspects of nonlinear and variational analysis, specifically those related to…
In this paper, a new identity for convex functions is derived. A consequence of the identity is that we can derive new estimates for the remainder term of the midpoint, trapezoid, and Simpson formulae for functions whose derivatives in…
In this study, we establish a new integral inequalities of Hermite-Hadamard type for $s$-convexity via Katugampola fractional integral. This generalizes the Hadamard fractional integrals and Riemann-Liouville into a single form. We show…
We presented here a refinement of Hermite-Hadamard inequality as a linear combination of its end-points. The problem of best possible constants is closely connected with well known Simpson's rule in numerical integration. It is solved here…
In this paper, some new inequalities of Ostrowski type established for the class of m- and (alpha,m)-geometrically convex functions which are generalizations of geometric convex functions.
We observe that the Hermite-Hadamard inequality written in the form $$f\left(\frac{x+y}{2}\right)\leq\frac{F(y)-F(x)}{y-x}\leq\frac{f(x)+f(y)}{2}$$ may be viewed as an inequality between two quadrature operators…