On Ostrowski type inequalities and Cebysev type inequalities with applications

Sarıkaya, Mehmet Zeki; Ki̇ri̇ş, Mehmet Eyüp

doi:10.2298/fil1508695k

Cited by 10 publications

(6 citation statements)

References 21 publications

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“…This is well known in the literature as Ostrowski's inequality. Due to its wide range of applications in numerical analysis and in probability, many researchers have established generalizations, extensions, and variants of inequality (1); we refer readers to [2][3][4][5][6][7][8][9][10] and the references cited therein.…”

Section: Introductionmentioning

confidence: 99%

Ostrowski Inequalities for Functions Whose First Derivatives Are Logarithmically Preinvex

Meftah

2016

Chinese Journal of Mathematics

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Section: Introductionmentioning

confidence: 99%

Ostrowski Inequalities for Functions Whose First Derivatives Are Logarithmically Preinvex

Meftah

2016

Chinese Journal of Mathematics

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“…Furthermore, there are additional opportunities for further development and exploration. For instance, new versions of Ostrowski and Čebyšev type inequalities can be derived for various unique means, such as arithmetic mean, geometric mean, harmonic mean, and so on [ 17 ]. In future research, it is intended to utilize these new and exciting inequalities for fuzzy-interval-valued functions.…”

Section: Discussionmentioning

confidence: 99%

“…p is the best possible. For details of other Čebys ˇev and Ostrowski type inequalities, we refer the interested reader to [11][12][13][14][15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Ostrowski and Čebyšev type inequalities for interval-valued functions and applications

Guo,

Zhu,

et al. 2023

PLoS ONE

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As an essential part of classical analysis, Ostrowski and Čebyšev type inequalities have recently attracted considerable attention. Due to its universality, the non-additive integral inequality takes several forms, including Sugeno integrals, Choquet integrals, and pseudo-integrals. Set-valued analysis, a well-known generalization of classical analysis, is frequently employed in studying mathematical economics, control theory, etc. Inspired by pioneering work on interval-valued inequalities, this paper establishes specific Ostrowski and Čebyšev type inequalities for interval-valued functions. Moreover, the error estimation to quadrature rules is presented as some applications for illustrating our results. In addition, illustrative examples are offered to demonstrate the applicability of the mathematical methods presented.

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“…On the basis of such applicability, inequalities and their associated theory have been developed rapidly, where various new and generalized forms of them have come to the surface. For instance, the Hermite-Hadamard inequality [3], Jensen's inequality [4], the Jensen-Mercer inequality [5], the Ostrowski inequality [6], and the Fejér inequality [7] are some names that are immensely popular with researchers. In the present age, researchers are particularly taking interest in generalized inequalities containing various of the above-mentioned versions in one form.…”

Section: Introductionmentioning

confidence: 99%

New “Conticrete” Hermite–Hadamard–Jensen–Mercer Fractional Inequalities

Faisal

Khan

et al. 2022

Symmetry

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The theory of symmetry has a significant influence in many research areas of mathematics. The class of symmetric functions has wide connections with other classes of functions. Among these, one is the class of convex functions, which has deep relations with the concept of symmetry. In recent years, the Schur convexity, convex geometry, probability theory on convex sets, and Schur geometric and harmonic convexities of various symmetric functions have been extensively studied topics of research in inequalities. The present attempt provides novel portmanteauHermite–Hadamard–Jensen–Mercer-type inequalities for convex functions that unify continuous and discrete versions into single forms. They come as a result of using Riemann–Liouville fractional operators with the joint implementations of the notions of majorization theory and convex functions. The obtained inequalities are in compact forms, containing both weighted and unweighted results, where by fixing the parameters, new and old versions of the discrete and continuous inequalities are obtained. Moreover, some new identities are discovered, upon employing which, the bounds for the absolute difference of the two left-most and right-most sides of the main results are established.

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On Ostrowski type inequalities and Cebysev type inequalities with applications

Cited by 10 publications

References 21 publications

Ostrowski Inequalities for Functions Whose First Derivatives Are Logarithmically Preinvex

Ostrowski Inequalities for Functions Whose First Derivatives Are Logarithmically Preinvex

Ostrowski and Čebyšev type inequalities for interval-valued functions and applications

New “Conticrete” Hermite–Hadamard–Jensen–Mercer Fractional Inequalities

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