Search

In this paper, we prove a quantum version of Montgomery identity and prove some new Ostrowski-type inequalities for convex functions in the setting of quantum calculus. Moreover, we discuss several special cases of newly established inequalities and obtain different new and existing inequalities in the field of integral inequalities.

In this paper, we first obtain two new quantum Hermite-Hadamard-type inequalities for newly defined quantum integral. Then we establish several refinements of quantum Hermite-Hadamard inequalities.

The present paper aims to find some new midpoint-type inequalities for twice quantum differentiable convex functions. The consequences derived in this paper are unification and generalization of the comparable consequences in the literature on midpoint inequalities.

In this paper, we first prove an identity for twice quantum differentiable functions. Then, by utilizing the convexity of ∣Dq2bf∣| {}^{b}D_{q}^{2}\hspace{0.08em}f| and ∣Dq2af∣| {}_{a}D_{q}^{2}\hspace{0.08em}f| , we establish some quantum Ostrowski inequalities for twice quantum differentiable mappings involving qa{q}_{a} and qb{q}^{b}-quantum integrals. The results presented here are the generalization of already published ones.

In this paper, we first establish two quantum integral (q-integral) identities with the help of derivatives and integrals of the quantum types. Then, we prove some new q-midpoint and q-trapezoidal estimates for the newly established q-Hermite-Hadamard inequality (involving left and right integrals proved by Bermudo et al.) under q-differentiable convex functions. Finally, we provide some examples to illustrate the validity of newly obtained quantum inequalities. [ABSTRACT FROM AUTHOR]

In this work, Hermite-Hadamard type inequalities for subadditive functions via quantum integrals are established. Moreover, Hermite-Hadamard type inequalities for the product of two subadditive functions are also obtained. It is worth to mentioning that some existing inequalities of Hermite-Hadamard type for subadditive functions are obtained by considering the limit of the real number q ∈ (0,1) as q → 1− in the key results. [ABSTRACT FROM AUTHOR]

In this paper, using the quantum derivatives and quantum integrals, we prove some new quantum Ostrowski's type inequalities for pre-invex functions. Furthermore, in the special cases of newly developed inequalities, we obtain different new and existing Ostrowski's type inequalities. [ABSTRACT FROM AUTHOR]

In this paper, we establish some new versions of Hermite–Hadamard type inequalities for co-ordinated convex functions via q 1 , q 2 -integrals. Since the inequalities are newly proved, we therefore consider some examples of co-ordinated convex functions and show their validity for particular choices of q 1 , q 2 ∈ (0 , 1) . We hope that the readers show their interest in these results. [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 paper, we prove two identities involving quantum derivatives, quantum integrals, and certain parameters. Using the newly proved identities, we prove new inequalities of Simpson's and Newton's type for quantum differentiable convex functions under certain assumptions. Moreover, we discuss the special cases of our main results and obtain some new and existing Simpson's type inequalities, Newton's type inequalities, midpoint type inequalities, and trapezoidal type inequalities. [ABSTRACT FROM AUTHOR]

In this paper, we prove a new quantum integral equality involving a parameter, left and right quantum derivatives. Then, we use the newly established equality and prove some new estimates of quantum Ostrowski, quantum midpoint, quantum trapezoidal and quantum Simpson's type inequalities for q-differentiable convex functions. It is also shown that the newly established inequalities are the refinements of the existing inequalities inside the literature. Finally, some examples and applications are given to illustrate the investigated results. [ABSTRACT FROM AUTHOR]

In this study, we established some new inequalities of Ostrowski type for the functions of two variables by using the concept of newly defined double quantum integrals. We also revealed that the results presented in this paper are the consolidation and generalization of some existing results on the literature of Ostrowski inequalities. [ABSTRACT FROM AUTHOR]

In this article, by using the notion of newly defined q1q2 derivatives and integrals, some new Simpson's type inequalities for coordinated convex functions are proved. The outcomes raised in this paper are extensions and generalizations of the comparable results in the literature on Simpson's inequalities for coordinated convex functions. [ABSTRACT FROM AUTHOR]

In this paper, we give some new definitions for quantum integrals of two-variable functions. We establish quantum Hermite–Hadamard-type inequalities for coordinated convex functions via newly defined quantum integrals. [ABSTRACT FROM AUTHOR]

The main objective of this study is to establish two important right q-integral equalities involving a right-quantum derivative with parameter m ∈ [ 0 , 1 ] . Then, utilizing these equalities, we derive some new variants for midpoint- and trapezoid-type inequalities for the right-quantum integral via differentiable (α , m) -convex functions. The fundamental benefit of these inequalities is that they may be transformed into q-midpoint- and q-trapezoid-type inequalities for convex functions, classical midpoint inequalities for convex functions and classical trapezoid-type inequalities for convex functions are transformed without having to prove each one independently. In addition, we present some applications of our results to special means of positive real numbers. It is expected that the ideas and techniques may stimulate further research in this field. [ABSTRACT FROM AUTHOR]

In this paper, we first establish two right-quantum integral equalities involving a right-quantum derivative and a parameter m ∈   0 , 1 . Then, we prove modified versions of Simpson's and Newton's type inequalities using established equalities for right-quantum differentiable α , m -convex functions. The newly developed inequalities are also proven to be expansions of comparable inequalities found in the literature. [ABSTRACT FROM AUTHOR]

In this paper, using the notions of q κ 2 -quantum integral and q κ 2 -quantum derivative, we present some new identities that enable us to obtain new quantum Simpson's and quantum Newton's type inequalities for quantum differentiable convex functions. This paper, in particular, generalizes and expands previous findings in the field of quantum and classical integral inequalities obtained by various authors. [ABSTRACT FROM AUTHOR]

In this article, we use quantum integrals to derive Hermite–Hadamard inequalities for preinvex functions and demonstrate their validity with mathematical examples. We use the q ϰ 2 -quantum integral to show midpoint and trapezoidal inequalities for q ϰ 2 -differentiable preinvex functions. Furthermore, we demonstrate with an example that the previously proved Hermite–Hadamard-type inequality for preinvex functions via q ϰ 1 -quantum integral is not valid for preinvex functions, and we present its proper form. We use q ϰ 1 -quantum integrals to show midpoint inequalities for q ϰ 1 -differentiable preinvex functions. It is also demonstrated that by considering the limit q → 1 − and η ϰ 2 , ϰ 1 = − η ϰ 1 , ϰ 2 = ϰ 2 − ϰ 1 in the newly derived results, the newly proved findings can be turned into certain known results. [ABSTRACT FROM AUTHOR]

In this investigation, for convex functions, some new (p , q) –Hermite–Hadamard-type inequalities using the notions of (p , q) π 2 derivative and (p , q) π 2 integral are obtained. Furthermore, for (p , q) π 2 -differentiable convex functions, some new ( p , q ) estimates for midpoint and trapezoidal-type inequalities using the notions of (p , q) π 2 integral are offered. It is also shown that the newly proved results for p = 1 and q → 1 − can be converted into some existing results. Finally, we discuss how the special means can be used to address newly discovered inequalities. [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]

In this paper, we prove some new Ostrowski-type integral inequalities for q-differentiable bounded functions. It is also shown that the results presented in this paper are a generalization of know results in the literarure. Applications to special means are also discussed. [ABSTRACT FROM AUTHOR]