Some integral inequalities of Hermite-Hadamard type for multiplicatively preinvex functions

Özcan, Serap

doi:10.3934/math.2020103

Cited by 22 publications

(8 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Since the publication of the aforementioned paper, several works concerning multiplicative inequalities have been published (see, for instance, [15,[17][18][19][20]).…”

Section: Theorem 1 ([14]mentioning

confidence: 99%

Fractional Maclaurin-Type Inequalities for Multiplicatively Convex Functions

Merad,

Meftah,

Moumen

et al. 2023

Fractal Fract

View full text Add to dashboard Cite

This paper’s major goal is to prove some symmetrical Maclaurin-type integral inequalities inside the framework of multiplicative calculus. In order to accomplish this and after giving some basic tools, we have established a new integral identity. Based on this identity, some symmetrical Maclaurin-type inequalities have been constructed for functions whose multiplicative derivatives are bounded as well as convex. At the end, some applications to special means are provided.

show abstract

“…Since the publication of the aforementioned paper, several works concerning multiplicative inequalities have been published (see, for instance, [15,[17][18][19][20]).…”

Section: Theorem 1 ([14]mentioning

confidence: 99%

Fractional Maclaurin-Type Inequalities for Multiplicatively Convex Functions

Merad,

Meftah,

Moumen

et al. 2023

Fractal Fract

View full text Add to dashboard Cite

show abstract

“…In a recent paper, Noor [15] has obtained the following Hermite-Hadamard type integral inequalities for the preinvex functions. For several recent results on inequalities for preinvex and prequasiinvex functions which are connected to (1.3), we refer the interested reader to [3,11,13,19,20] and the references therein. Let 0 < a < b, throughout this paper we will use…”

Section: Definition 15 ( [2]mentioning

confidence: 99%

Differentiable Preinvex and Prequasiinvex Functions

Kadakal

2020

Universal Journal of Mathematics and Applications

View full text Add to dashboard Cite

In this paper, a new identity for functions defined on an open invex subset of set of real numbers is established, and by using this identity and the Hölder and Power mean integral inequalities we present new integral inequalities for functions whose powers of derivatives in absolute value are preinvex and prequasiinvex. We should especially mention that the results obtained in special cases coincide with the well-known results in the literature.

show abstract

“…The convexity of functions is a strong tool for dealing with a wide range of pure and applied scientific problems. Many scholars have devoted themselves in recent decades to exploring the features and inequalities associated with convexity in various directions, see ([1]- [5]) and the references listed therein. Hermite-Hadamard inequality, which is frequently used in many different disciplines of applied mathematics, is one of the most important mathematical inequalities involving convex mapping.…”

Section: Introductionmentioning

confidence: 99%

Generalization of Some Integral Inequalities in Multiplicative Calculus With Their Computational Analysis

Mateen,

Zhang,

Ali

et al. 2024

Preprint

View full text Add to dashboard Cite

This paper focuses on the generalization of some multiplicative integral inequalities for twice differentiable functions. First, we derive multiplicative integral identity for multiplicatvely twice differentiable functions. Then, with the help of integral identity, we prove a family of integral inequalities such that Simpson’s, Hermite-Hadamard, Midpoint, Trapezoid and Bullen’s types inequalities for multiplicatively convex functions. Moreover, we provide some numerical examples and computational analysis of these newly established inequalities to show the validity of the results for multiplicatively convex functions. The generalized forms derive in this research offer valuable tools for researchers in various fields. 2010 Mathematics Subject Classification. 34A08, 26A51, 26D15.

show abstract

Some integral inequalities of Hermite-Hadamard type for multiplicatively preinvex functions

Cited by 22 publications

References 8 publications

Fractional Maclaurin-Type Inequalities for Multiplicatively Convex Functions

Fractional Maclaurin-Type Inequalities for Multiplicatively Convex Functions

Differentiable Preinvex and Prequasiinvex Functions

Generalization of Some Integral Inequalities in Multiplicative Calculus With Their Computational Analysis

Contact Info

Product

Resources

About