Some new (p, q)-Dragomir–Agarwal and Iyengar type integral inequalities and their applications

<abstract><p>The main objective of this paper is to derive some new post quantum analogues of Dragomir–Agarwal and Iyengar type integral inequalities essentially by using the strongly $ \varphi $-preinvexity and strongly quasi $ \varphi $-preinvexity properties of the mappings, respectively. We also discuss several new special cases which show that the results obtained are quite unifying. In order to illustrate the efficiency of our main results, some applications regarding $ ({\mathrm{p}}, {\mathrm{q}}) $-differentiable mappings that are in absolute value bounded are given.</p></abstract>

Generalized fractional midpoint type inequalities for co-ordinated convex functions

In this research paper, we investigate generalized fractional integrals to obtain midpoint type inequalities for the co-ordinated convex functions. First of all, we establish an identity for twice partially differentiable mappings. By utilizing this equality, some midpoint type inequalities via generalized fractional integrals are proved. We also show that the main results reduce some midpoint inequalities given in earlier works for Riemann integrals and Riemann-Liouville fractional integrals. Finally, some new inequalities for $k$-Riemann-Liouville fractional integrals are presented as special cases of our results.

New version of generalized Ostrowski-Gruss type inequality

"Ostrowski inequality is one of the celebrated inequalities in Mathematics. The main purpose of our study is to generalize the result of Ostrowski-Gruss type inequality for first differentiable mappings and apply it to probability density functions, composite quadrature rules and special means."

On generalized Ostrowski, Simpson and Trapezoidal type inequalities for co-ordinated convex functions via generalized fractional integrals

In this study, we prove an identity for twice partially differentiable mappings involving the double generalized fractional integral and some parameters. By using this established identity, we offer some generalized inequalities for differentiable co-ordinated convex functions with a rectangle in the plane $\mathbb{R} ^{2}$ R 2 . Furthermore, by special choice of parameters in our main results, we obtain several well-known inequalities such as the Ostrowski inequality, trapezoidal inequality, and the Simpson inequality for Riemann and Riemann–Liouville fractional integrals.

Some parameterized Hermite-Hadamard and Simpson type inequalities for co-odinated convex functions

In this paper, we first obtain an identity for twice partially differentiable mappings involving some parameters. Moreover, by utilizing this identity and functions whose twice partially derivatives in absolute value are co-ordinated convex, we establish some inequalities which generalize several inequalities, such as trapezoid, midpoint and Simpson’s inequalities.

Hermite-Hadamard-Mercer type inequalities for fractional integrals

In the present note, we proved Hermite-Hadamard-Mercer inequalities for fractional integrals and we established some new fractional inequalities connected with the right and left-sides of Hermite-Hadamard-Mercer type inequalities for differentiable mappings whose derivatives in absolute value are convex.

Quantum Ostrowski-type inequalities for twice quantum differentiable functions in quantum calculus

In this paper, we first prove an identity for twice quantum differentiable functions. Then, by utilizing the convexity of ∣ D q 2 b f ∣ | {}^{b}D_{q}^{2}\hspace{0.08em}f| and ∣ D q 2 a f ∣ | {}_{a}D_{q}^{2}\hspace{0.08em}f| , we establish some quantum Ostrowski inequalities for twice quantum differentiable mappings involving q a {q}_{a} and q b {q}^{b} -quantum integrals. The results presented here are the generalization of already published ones.

Fractional trapezium-like inequalities involving generalized relative semi--preinvex mappings on an -invex set

UDC 517.5 The authors derive a fractional integral equality concerning twice differentiable mappings defined on -invex set. By using this identity, the authors obtain new estimates on generalization of trapezium-like inequalities for mappings whose second order derivatives are generalized relative semi--preinvex via fractional integrals. We also discuss some new special cases which can be deduced from our main results.

Some Grüss Type Inequalities for Fréchet Differentiable Mappings

Let X be a Hilbert C∗-module on C∗-algebra A and p ∈ A. We denote by Dp(A,X) the set of all continuous functions f : A → X, which are Fréchet differentiable on a open neighborhood U of p. Then, we introduce some generalized semi-inner products on Dp(A,X), and using them some Grüss type inequalities in semi-inner product C∗-module Dp(A,X) and Dp(A,Xn) are established.