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Abstract In this paper, we study the Schur m-power convexity of the generalized geometric Bonferroni mean involving three parameters. Our result provides a unified generalization to the work that was done recently by Shi and Wu concerning the Schur convexity of generalized geometric Bonferroni mean.

Abstract In this paper, we present several discrete majorization type inequalities for the convex functions defined on rectangles.

Abstract In this paper, we discuss the Schur convexity, Schur geometric convexity and Schur harmonic convexity of the generalized geometric Bonferroni mean. Some inequalities related to the generalized geometric Bonferroni mean are established to illustrate the applications of the obtained results.

A new identity involving Riemann-Liouville fractional integral is proposed. The result is then used to obtain some estimates of upper bound for a function associated with Riemann-Liouville fractional integral via h-convex functions. An application for establishing the inequalities related to special means is also considered.

We establish some new Hermite-Hadamard type integral inequalities for functions whose second-order mixed derivatives are coordinated (s,m)-P-convex. An expression form of Hermite-Hadamard type integral inequalities via the beta function and the hypergeometric function is also presented. Our results provide a significant complement to the work of Wu et al. involving the Hermite-Hadamard type inequalities for coordinated (s,m)-P-convex functions in an earlier article.

In this paper, we introduce the definition of coordinated ((s,m),QC)-convex function and establish some Hermite-Hadamard type integral inequalities for coordinated ((s,m),QC)-convex functions.

We define a new generalized class of harmonically preinvex functions named harmonically (p,h,m)-preinvex functions, which includes harmonic (p,h)-preinvex functions, harmonic p-preinvex functions, harmonic h-preinvex functions, and m-convex functions as special cases. We also investigate the properties and characterizations of harmonically (p,h,m)-preinvex functions. Finally, we establish some integral inequalities to show the applications of harmonically (p,h,m)-preinvex functions.

We give a unified generalization of the generalized Muirhead means and the generalized Heronian means involving three parameters. The Schur-convexity of the generalized Muirhead-Heronian means is investigated. Our main result implies the sufficient conditions of the Schur-convexity of the generalized Heronian means and the generalized Muirhead means.

In this paper, operator m-convex and (α,m)-convex function on the co-ordinates are defined, and some new integral inequalities of Hermite-Hadamard type for operator mconvex and (α,m)-convex on the co-ordinates are established. [ABSTRACT FROM AUTHOR]

In this paper, we establish some inequalities of Hermite-Hadamard type for functions whose derivatives absolute values are harmonically extended s-convex functions. [ABSTRACT FROM AUTHOR]

In this paper, we establish new sharpened versions of Mitrinović-Adamović and Lazarević's inequalities. Further, we provide an application of our results to the improvements of Wilker's inequality for trigonometric and hyperbolic functions. We show that the coeffcient assigned to each of these sharpened inequalities is best possible. [ABSTRACT FROM AUTHOR]

In this paper, we give several improvements of Mitrinovi ć-Adamovi ć's inequality and Lazarevi ć's inequality. Our results show some interesting relationships between Mitrinovi ć-Adamovi ć's inequality and Lazarevi ć's inequality. At the end of the paper, the improved Lazarevi ć's inequality is applied to the sharpening of Wilker-type inequalities for hyperbolic functions. [ABSTRACT FROM AUTHOR]

In this paper, we present a geometric interpretation of Blundon's inequality and Ciamberlini's inequality. Our results provide a useful method for proving the inequalities concerning sides, circumradius, and inradius of a triangle. As applications, some improved inequalities are established to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we give a unified generalization of the Gini means and Heronian means. The Schur-geometric convexity of the generalized Gini-Heronian means are investigated. Our result generalizes an earlier result given by Shi et al. (J. Inequal. Appl. 2008:879273, 2008). At the end of the paper, two new inequalities related to the generalized Gini-Heronian means are established to illustrate the applicability of the given result. [ABSTRACT FROM AUTHOR]

By introducing the Taylor polynomials, a significantly refined version of Wilker's inequality is established. The result is then used to obtain several substantially more refined inequalities of the Wilker type. [ABSTRACT FROM AUTHOR]

In this paper, the classical Jordan's inequality is studied once again, a new sharpened and generalized version of Jordan's inequality is given by means of polynomial representation, and the result thus derived is then used to obtain several substantially more refined inequalities of Jordan type. Finally, an application of the results presented in this paper toward the improvement of the Yang Le inequality is considered. [ABSTRACT FROM AUTHOR]

In this paper, the authors first prove a weighted and exponential generalization of Wilker's inequality. The main result presented here is then applied with a view to deriving an improved version of the Sándor-Bencze conjectured inequality. Some other closely-related inequalities are also considered. [ABSTRACT FROM AUTHOR]

Abstract In the centered surround system S ( 2 ) { P , Γ } $S^{(2)} \{P,\varGamma \}$ , we establish the following gravity inequalities: ( 1 + 5 2 π e 2 1 − e 2 ) ( 2 π | Γ | ) 2 ≤ 1 | Γ | ∮ Γ 1 ∥ A − P ∥ 2 ≤ ( 1 + 16 − π 4 π e 2 1 − e 2 ) ( 2 π | Γ | ) 2 , $$\biggl(1+\frac{5}{2\pi}\frac{\mathrm{e}^{2}}{1-\mathrm{e}^{2}} \biggr) \biggl(\frac{2\pi}{|\varGamma |} \biggr)^{2}\leq\frac{1}{|\varGamma |} \oint_{\varGamma }\frac{1}{\|A-P\|^{2}} \leq\biggl(1+\frac{16-\pi}{4\pi} \frac{\mathrm{e}^{2}}{1-\mathrm{e}^{2}} \biggr) \biggl(\frac{2\pi }{|\varGamma |} \biggr)^{2}, $$ where Γ is an ellipse, P and e are one of the foci and the eccentricity of the ellipse, respectively, and A ∈ Γ $A\in \varGamma $ is a satellite of the centered surround system S ( 2 ) { P , Γ } $S^{(2)} \{P,\varGamma \}$ . We also demonstrate the applications of the inequalities in the temperature research, and we obtain an approximate mean temperature formula as follows: T ‾ ≈ ( 1 + 0.9095071300973198 … × e 2 1 − e 2 ) ( 2 π | Γ | ) 2 , ∀ e ∈ ( 0 , 1 ) , $$\overline{T}\approx\biggl(1+0.9095071300973198\ldots\times\frac{\mathrm {e}^{2}}{1-\mathrm{e}^{2}} \biggr) \biggl(\frac{2\pi}{|\varGamma |} \biggr)^{2}, \quad\forall\mathrm{e} \in(0,1), $$ where the T̅ is the mean temperature on a planet.