Inequalities for $\log -$convex functions and $P-$functions

Set, Erhan; Ardıç, Merve Avcı

doi:10.18514/mmn.2017.1798

Cited by 14 publications

(5 citation statements)

References 9 publications

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“…Dragomir [22] presented some unweighted and weighted inequalities of Hermite-Hadamard type related to multiplicatively convex functions on real intervals. Set and Ardiç [23] established Hermite-Hadamard-like type integral inequalities using multiplicatively convex functions and p-functions. Zhang and Jiang [24] examined some properties for multiplicatively convex function.…”

Section: Multiplicative Calculusmentioning

confidence: 99%

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

Mateen,

Zhang,

Ali

et al. 2024

Preprint

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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.

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Section: Multiplicative Calculusmentioning

confidence: 99%

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

Mateen,

Zhang,

Ali

et al. 2024

Preprint

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“…The H-H inequality has been a potent instrument to obtain a lot of excellent results in integral inequalities and optimization theory because of its crucial role in convex analysis. It has recently been generalized using other convexity types, particularly s-convex functions [1][2][3][4], log-convex functions [5][6][7], harmonic convexity [8], and particularly for h-convex functions [9]. Since 2007, numerous H-H inequalities for h-convex function extensions and generalizations have been established in [10][11][12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Hermite–Hadamard and Pachpatte Type Inequalities for Coordinated Preinvex Fuzzy-Interval-Valued Functions Pertaining to a Fuzzy-Interval Double Integral Operator

et al. 2022

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Many authors have recently examined the relationship between symmetry and generalized convexity. Generalized convexity and symmetry have become a new area of study in the field of inequalities as a result of this close relationship. In this article, we introduce the idea of preinvex fuzzy-interval-valued functions (preinvex F∙I-V∙F) on coordinates in a rectangle drawn on a plane and show that these functions have Hermite–Hadamard-type inclusions. We also develop Hermite–Hadamard-type inclusions for the combination of two coordinated preinvex functions with interval values. The weighted Hermite–Hadamard-type inclusions for products of coordinated convex interval-valued functions discussed in a recent publication by Khan et al. in 2022 served as the inspiration for our conclusions. Our proven results expand and generalize several previous findings made in the body of literature. Additionally, we offer appropriate examples to corroborate our theoretical main findings.

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“…In recent years, for example, generalized concepts such as s-convexity, h-convexity, M T -convexity, log-convexity, P -convexity, η-convexity, quasi convexity and others, as well as combinations of these new concepts have been introduced. The following references give more information about the research in this area [1,5,11,14,16,18,22,29].…”

Section: Introductionmentioning

confidence: 99%

ON (m, h1, h2)-G-CONVEX DOMINATED STOCHASTIC PROCESSES

HERNÁNDEZ¹

2022

KgJMat

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In this paper is introduced the concept of (m, h1, h2)-convexity for stochastic processes dominated by other stochastic processes with the same property, some mean square integral Hermite-Hadamard type inequalities for this kind of generalized convexity are established and from the founded results, other mean square integral inequalities for the classical convex, s-convex in the first and second sense, P-convex and MT-convex stochastic processes are deduced.

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Inequalities for $\log -$convex functions and $P-$functions

Abstract: In this paper we obtain some new integral inequalities like Hermite-Hadamard type for log convex functions and P functions.

Cited by 14 publications

References 9 publications

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

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

Hermite–Hadamard and Pachpatte Type Inequalities for Coordinated Preinvex Fuzzy-Interval-Valued Functions Pertaining to a Fuzzy-Interval Double Integral Operator

ON (m, h1, h2)-G-CONVEX DOMINATED STOCHASTIC PROCESSES

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