Explore the vast range of titles available.

In the article, we provide an example for a η-convex function defined on rectangle is not convex, prove that every η-convex function defined on rectangle is coordinate η-convex and its converse is not true in general, define the coordinate (η1,η2)\\((\\eta _{1}, \\eta _{2})\\)-convex function and establish its Hermite–Hadamard type inequality.

Some new integral inequalities for strongly (α,h−m)-convex functions via generalized Riemann–Liouville fractional integrals are established. The outcomes of this paper provide refinements of some fractional integral inequalities for strongly convex, strongly m-convex, strongly (α,m)-convex, and strongly (h−m)-convex functions. Also, the refinements of error estimations of these inequalities are obtained by using two fractional integral identities. Moreover, using a parameter substitution and a constant multiplier, k-fractional versions of established inequalities are also given.

New ways for comparing and bounding strongly ( s , m ) -convex functions using Caputo fractional derivatives and Caputo-Fabrizio integral operators are explored. These operators generalize some classic inequalities of Hermite-Hadamard for functions with strongly ( s , m ) -convex derivatives. The findings are also applied to special functions and means involving the digamma function. Additionally, we relate our findings to applications in biomedicine, engineering, robotics, the automotive industry, and electronics.

In the article, we establish an inequality for Csiszár divergence associated with s-convex functions, present several inequalities for Kullback–Leibler, Renyi, Hellinger, Chi-square, Jeffery’s, and variational distance divergences by using particular s-convex functions in the Csiszár divergence. We also provide new bounds for Bhattacharyya divergence.

The Hermite-Hadamard-Fejér inequalities for a harmonically-h-convex function are explored in this study, and the findings for specific classes of functions are highlighted. Several generalizations of the Hermite-Hadamard inequalities are also discussed. Some properties of functions 𝓗 and 𝓕, which are naturally defined for Hermite-Hadamard-Fejér type inequalities for harmonically-h-convex functions, have also been studied. Finally, we find applications of the results concerning the p-logarithmic mean and the order p mean.

In the paper, the authors introduce a notion of (α,m)-geometric-arithmetic-F-convex functions and, via an integral identity and other analytic techniques, establish several integral inequalities of the Hermite–Hadamard type for (α,m)-GA-F-convex functions.

In 2001, S. S. Dragomir introduced a generalized class of convexity, the so-called -convex functions, which covers many other classes of convexity. In this article, we prove some useful characterizations of this generalized class of convex functions. We obtain majorization-type inequalities for -convex functions, providing also applications to new estimates for some well-known mean inequalities.

In this study, the Hermite–Hadamard–Fejér inequalities for GA-h-convex are proved, and the results for particular classes of functions are highlighted. In addition, several generalizations of the Hermite–Hadamard inequalities are presented. Some features of functions H and F that are naturally linked to the Hermite–Hadamard–Fejér-type inequalities for GA-h-convex have also been discussed. Finally, we obtain applications of the results related to the p-logarithmic mean and the mean of order p.

In this paper, we introduce the notion of exponentially p-convex function and exponentially s-convex function in the second sense. We establish several Hermite–Hadamard type inequalities for exponentially p-convex functions and exponentially s-convex functions in second sense. The present investigation is an extension of several well known results.

In this paper, we establish some new integral inequalities of Hermite–Hadamard type for s-convex functions by using the Hölder–İşcan integral inequality. We also compare our new results with the known results and show that the results which we obtained are better than the known results. Finally, we give some applications to trapezoidal formula and to special means.