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Convex functions play a crucial role in various fields of mathematics, optimization, economics, and machine learning due to their distinctive properties and applications. In this paper, a new class of convex functions, called the RT-convex functions, is presented. Moreover, Hermite-Hadamard-type inequalities for the RT-convex functions are discussed. A number of applications of the RT-convex functions is also discussed. [ABSTRACT FROM AUTHOR]

In this paper, we introduce new subclasses ... and of analytic functions in the open unit disk with negative coefficients defined by generalized Mittag-Leffler function. The object of the present paper is to determine coefficient inequalities, inclusion relations and neighborhoods properties for functions belonging to these subclasses. [ABSTRACT FROM AUTHOR]

In this study, we introduce and study the concept of strongly hyperbolic type convexity functions and their some algebraic properties. We obtain Hermite-Hadamard type inequalities for the strongly hyperbolic type convex functions. After that, by using an identity, we get some inequalities for strongly hyperbolic type convex functions. In addition, we compare the results obtained with both Hölder, Hölder-İşcan inequalities and power-mean, improved power-mean integral inequalities. [ABSTRACT FROM AUTHOR]

In this study, using both Hölder's integral inequality and Hölder-İşcan integral inequality, some inequalities of Hermite Hadamard type obtained for multiplicatively preinvex P-functions are given. Afterwards, the result obtained with Hölder-İşcan inequality has been shown to be better than that obtained with Hölder's integral inequality. [ABSTRACT FROM AUTHOR]

The aim of this article is to give new generalized Hermite-Hadamard type inequalities involving the Riemann-Liouville fractional integral for functions whose absolute values of third derivatives are s-convex in the second sense. In order to do that an integral identity for three times differentiable mapping involving fractional integral operators is established. Several consequences are then presented in some special cases. [ABSTRACT FROM AUTHOR]

The main purpose of the article is to introduce an active teaching method, based on the nature of a familiar mathematical concept. Specifically, this paper presents the application of the visual image of convex function and concave function graphs concave function on demonstrating some inequality in the primary curriculum. Also, some results and comments concerning the proving method of such as inequalities are stated. [ABSTRACT FROM AUTHOR]

In this investigation, we established some new post quantum-Hermite-Hadamard inequalities for differentiable convex function with critical point by using the notion of -integeral. The perseverance of this article is to establish different results on the left hand side of - Hermite-Hadamard inequality for differentiable convex function along with critical a point. Some Special cases are obtain for different - Hermite Hadamard inequalies at critical point c for some specific values of q. [ABSTRACT FROM AUTHOR]

In this study, we obtained some new post quantum-Hermite-Hadamard inequalities for differentiable convex function with critical point by using generalized (p, q)- Hermite-Hadamard Inequality. The perseverance of this article is to establish different results on the left-hand side of (p,q) -Hermite-Hadamard inequality for differentiable convex function along with critical point. Special cases were obtained for different (p, q)-Hermite Hadamard inequalies with the critical point c for some special values of q. [ABSTRACT FROM AUTHOR]

Present article takes into account results on Hadamard type inequality. It intents to generalize some of the existing fractional integral inequalities of Hadamard type inequality for harmonically convex functions to corresponding k-fractional inequalities, by using the classic k-fractional integrals. For this purpose first a significant Hadamard type inequality for harmonically convex functions via k-fractional integrals is procured. Then the differences of middle term with right and left terms of the aforesaid inequalities are estimated. [ABSTRACT FROM AUTHOR]

Present study introduces a new class of strongly harmonic h -- convex functions and its relationship with harmonically h -- convex functions. Some new Hermite- Hadamard type inequalities for class of strongly harmonic h -- convex are also established which generalizes previous results. [ABSTRACT FROM AUTHOR]

In this paper we present a refinement of inequality: ΣsinA/2≥5/4+r/2R who are true in any acute triangle ABC and some consequences of DRIMBE inequality. [ABSTRACT FROM AUTHOR]