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The striking goal of this study is to introduce a q -identity for a parameterized integral operator via differentiable function. First, we discover the parameterized lemma for the q -integral. After that, we provide several q -differentiable inequalities. By taking suitable choices, some interesting results are obtained. With all of these, we displayed the findings from the traditional analysis utilizing q → 1 − . [ABSTRACT FROM AUTHOR]

In this paper, firstly, we present an integral identity for functions of two variables via Riemann–Liouville fractional integrals. Then, a Newton-type inequality via partially differentiable coordinated convex mappings is derived by taking the absolute value of the obtained identity. Moreover, several inequalities are obtained with the aid of the Hölder and power mean inequality. In addition, we investigate some Newton-type inequalities utilizing mappings of two variables with bounded variation. Finally, we gave some mathematical examples and their graphical behavior to validate the obtained inequalities. [ABSTRACT FROM AUTHOR]

In this paper, we give the generalized version of the quantum Simpson's and quantum Newton's formula type inequalities via quantum differentiable α , m -convex functions. The main advantage of these new inequalities is that they can be converted into quantum Simpson and quantum Newton for convex functions, Simpson's type inequalities α , m -convex function, and Simpson's type inequalities without proving each separately. These inequalities can be helpful in finding the error bounds of Simpson's and Newton's formulas in numerical integration. Analytic inequalities of this type as well as particularly related strategies have applications for various fields where symmetry plays an important role. [ABSTRACT FROM AUTHOR]

In this study, we first prove a parameterized integral identity involving differentiable functions. Then, for differentiable harmonically convex functions, we use this result to establish some new inequalities of a midpoint type, trapezoidal type, and Simpson type. Analytic inequalities of this type, as well as the approaches for solving them, have applications in a variety of domains where symmetry is important. Finally, several particular cases of recently discovered results are discussed, as well as applications to the special means of real numbers. [ABSTRACT FROM AUTHOR]

In this work, we prove a new (p , q) -integral identity involving a (p , q) -derivative and (p , q) -integral. The newly established identity is then used to show some new Simpson's formula type inequalities for (p , q) -differentiable convex functions. Finally, the newly discovered results are shown to be refinements of comparable results in the literature. Analytic inequalities of this type, as well as the techniques used to solve them, have applications in a variety of fields where symmetry is important. [ABSTRACT FROM AUTHOR]

From the past to the present, various works have been dedicated to Simpson's inequality for differentiable convex functions. Simpson-type inequalities for twice-differentiable functions have been the subject of some research. In this paper, we establish a new generalized fractional integral identity involving twice-differentiable functions, then we use this result to prove some new Simpson's-formula-type inequalities for twice-differentiable convex functions. Furthermore, we examine a few special cases of newly established inequalities and obtain several new and old Simpson's-formula-type inequalities. These types of analytic inequalities, as well as the methodologies for solving them, have applications in a wide range of fields where symmetry is crucial. [ABSTRACT FROM AUTHOR]

In this paper, we establish some new Hermite–Hadamard type inequalities for preinvex functions and left-right estimates of newly established inequalities for p , q -differentiable preinvex functions in the context of p , q -calculus. We also show that the results established in this paper are generalizations of comparable results in the literature of integral inequalities. Analytic inequalities of this nature and especially the techniques involved have applications in various areas in which symmetry plays a prominent role. [ABSTRACT FROM AUTHOR]

In this paper, we first prove three identities for functions of bounded variations. Then, by using these equalities, we obtain several trapezoid- and Ostrowski-type inequalities via generalized fractional integrals for functions of bounded variations with two variables. Moreover, we present some results for Riemann–Liouville fractional integrals by special choice of the main results. Finally, we investigate the connections between our results and those in earlier works. Analytic inequalities of this nature and especially the techniques involved have applications in various areas in which symmetry plays a prominent role. [ABSTRACT FROM AUTHOR]

Quantum information theory, an interdisciplinary field that includes computer science, information theory, philosophy, cryptography, and symmetry, has various applications for quantum calculus. Inequalities has a strong association with convex and symmetric convex functions. In this study, first we establish a p , q -integral identity involving the second p , q -derivative and then we used this result to prove some new trapezoidal type inequalities for twice p , q -differentiable convex functions. It is also shown that the newly established results are the refinements of some existing results in the field of integral inequalities. Analytic inequalities of this nature and especially the techniques involved have applications in various areas in which symmetry plays a prominent role. [ABSTRACT FROM AUTHOR]

In this paper, the notions of post-quantum integrals for two-variable interval-valued functions are presented. The newly described integrals are then used to prove some new Hermite–Hadamard inclusions for co-ordinated convex interval-valued functions. Many of the findings in this paper are important extensions of previous findings in the literature. Finally, we present a few examples of our new findings. Analytic inequalities of this nature and especially the techniques involved have applications in various areas in which symmetry plays a prominent role. [ABSTRACT FROM AUTHOR]