On a new class of convex functions and integral inequalities

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.

Applied Mathematics & Information Sciences, 2015

In this paper, we consider a very useful and significant class of convex sets and convex functions that is relative convex sets and relative convex functions which was introduced and studied by Noor [20]. Several new inequalities of Hermite-Hadamard type for relative convex functions are established using different approaches. We also introduce relative h-convex functions and is shown that relative h-convex functions include Noor relative convex functions as special cases. Results obtained in this paper may inspire future research in convex analysis and related optimization fields.

In the paper, the authors establish a new integral identity. By this integral identity and Hölder's inequality, the authors obtain some new inequalities of the Hermite-Hadamard type for ε-convex functions.

Miskolc Mathematical Notes, 2018

In this article, we introduce some new class of convex functions involving two arbitrary auxiliary functions h 1 ; h 2 W I ! R; which are called .h 1 ; h 2 /-convex functions. We derive some new integral inequalities for these classes of convex functions. We also discuss some special cases which can be deduced from our main results. Results obtained in this paper may be viewed as a significant refinement and improvement of the previously known results. The ideas and techniques of this work may be a starting point for future research.

In this paper, we establish various inequalities for some differentiable mappings that are linked with the illustrious Hermite-Hadamard integral inequality for mappings whose derivatives are s-(α, m)-convex. The generalised integral inequalities contribute better estimates than some already presented. The inequalities are then applied to numerical integration and some special means.

In this paper, we establish some Hermite-Hadamard type Integral inequalities for a new class of convex function called λ-MT-convex function. Our results generalize and extend some existing results in literature.

Journal of Mathematical Analysis and Modeling, 2021

In this present case, we focus and explore the idea of a new family of convex function namely exponentialtype m–convex functions. To support this newly introduced idea, we elaborate some of its nice algebraicproperties. Employing this, we investigate the novel version of Hermite–Hadamard type integral inequality.Furthermore, to enhance the paper, we present several new refinements of Hermite–Hadamard (H−H) inequality.Further, in the manner of this newly introduced idea, we investigate some applications of specialmeans. These new results yield us some generalizations of the prior results in the literature. We believe, themethodology investigated in this paper will further inspire intrigued researchers.

2013

In this paper, we establish various inequalities for some mappings that are linked with the illustrious Hermite-Hadamard integral inequality for mappings whose absolute values belong to the class K α,s m,1 and K α,s m,2 .

SpringerPlus, 2016

In the paper, the authors introduce a new notion "[Formula: see text]-convex function on the co-ordinates" and establish some Hermite-Hadamard type integral inequalities for [Formula: see text]-convex functions on the co-ordinates.