New integral inequalities in the class of functions (h, m)-convex

Acta Universitatis Sapientiae, Mathematica, 2014

In this paper, we establish several weighted inequalities for some differantiable mappings that are connected with the celebrated Hermite-Hadamard-Fejér type and Ostrowski type integral inequalities. The results presented here would provide extensions of those given in earlier works.

BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS, 2019

Some new integral inequalities for (s, m)-convex and (α, m)-convex functions The paper considers several new integral inequalities for functions the second derivatives of which, with respect to the absolute value, are (s, m)-convex and (α, m)-convex functions. These results are related to well-known Hermite-Hadamard type integral inequality, Simpson type integral inequality, and Jensen type inequality. In other words, new upper bounds for these inequalities using the indicated classes of convex functions have been obtained. These estimates are obtained using a direct definition for a convex function, classical integral inequalities of Hölder and power mean types. Along with the new outcomes, the paper presents results confirming the existing in literature upper bound estimates for integral inequalities (in particular well known in literature results obtained by U. Kırmacı in [7] and M.Z. Sarıkaya and N. Aktan in [35]). The last section presents some applications of the obtained estimates for special computing facilities (arithmetic, logarithmic, generalized logarithmic average and harmonic average for various quantities).

Sigma Journal of Engineering and Natural Sciences, 2018

In this study, we obtained the Hermite-Hadamard integral inequality for MφA-P-function. Then we gave a new identity for MφA-P-function and using these identity, we obtained the theorems and the results.

Journal of Inequalities and Applications, 2019

The aim of this paper is to introduce a new extension of convexity called σ-convexity. We show that the class of σ-convex functions includes several other classes of convex functions. Some new integral inequalities of Hermite-Hadamard type are established to illustrate the applications of σ-convex functions.

In this paper, by using some classical inequalities from the Theory of Inequality and integral identity, we establish two new general inequalities. Our results have some relationships with certain integral inequalities obtained by Sarikaya and Aktan.

American Journal of Applied Mathematics, 2015

In this paper, we introduce a new class of convex functions, which is called nonconvex functions. We show that this class unifies several previously known and new classes of convex functions. We derive several new inequalities of Hermite-Hadamard type for nonconvex functions. Some special cases are also discussed. Results proved in this paper continue to hold for these special cases.

Issues of Analysis

In this work, we use weighted integrals to obtain new integral inequalities of the Simpson type for the class of pℎ, , q-convex functions of the second type. In the work we show that the obtained results include some known from the literature, as particular cases.

In this paper, we establish some new inequalities of f Simpson's type based on quasi   convex for differentiable mapping that are linked with the illustrious Simpson's type inequality for mappings whose derivative in absolute values are quasi   convex .

Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta

In this article, we establish several inequalities for $(h,m)$-convex maps, related to weighted integrals, used in previous works. Throughout the work, we show that our results generalize several of the integral inequalities known from the literature.

Carpathian Mathematical Publications, 2023

In this paper, we present some new integral inequalities of Hermite-Hadamard type. To obtain these results, general convex functions of various type are considered such as (h, m)-convex functions. The main results extend some previously known inequalities by taking fractional integral operators.