New fractional inequalities of midpoint type via s-convexity and their application

Abstract In this note, we obtain new some inequalities of Simpson’s type based on convexity. Some applications for special means of real numbers are also given.

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Generalized Integral Inequalities for Hermite-Hadamard Type via s-Convexity on Fractal Sets

10.20944/preprints201909.0272.v1 ◽

2019 ◽

Author(s):

Ohud Almutairi ◽

Adem Kilicman

Keyword(s):

Integral Inequalities ◽

Fractal Sets ◽

Second Derivatives ◽

The Absolute ◽

New Inequalities ◽

Generalized Integral Inequalities

In this article, the new Hermite–Hadamard type inequalities are studied via generalized s-convexity on fractal sets. These inequalities derived on fractal sets are shown to be the generalized s-convexity on fractal sets. We proved that the absolute values of the first and second derivatives for the new inequalities are the generalization of s-convexity on fractal sets.

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New Hermite Hadamard type inequalities for twice differentiable convex mappings via Green function and applications

Moroccan Journal of Pure and Applied Analysis ◽

10.7603/s40956-016-0009-x ◽

2016 ◽

Vol 2 (2) ◽

pp. 107-118 ◽

Cited By ~ 1

Author(s):

Samet Erden ◽

Mehmet Zeki Sarikaya

Keyword(s):

Green Function ◽

Integral Inequalities ◽

Real Numbers ◽

Absolute Value ◽

Convex Mappings ◽

Trapezoidal Formula ◽

Special Means ◽

Second Derivatives ◽

Type Integral

Abstract We derive some Hermite Hamamard type integral inequalities for functions whose second derivatives absolute value are convex. Some eror estimates for the trapezoidal formula are obtained. Finally, some natural applications to special means of real numbers are given

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Some New Inequalities on Generalization of Hermite-Hadamard and Bullen Type Inequalities, Applications to Trapezoidal and Midpoint Formula

Kragujevac Journal of Mathematics ◽

10.46793/kgjmat2104.647i ◽

2021 ◽

Vol 45 (4) ◽

pp. 647-657

Author(s):

İMDAT İŞCAN ◽

◽

TEKİN TOPLU ◽

FATİH YETGİN ◽

◽

...

Keyword(s):

Error Estimates ◽

Real Numbers ◽

Absolute Value ◽

General Identity ◽

Differentiable Functions ◽

Special Means ◽

New Inequalities

In this paper, we give a new general identity for diﬀerentiable functions. A consequence of the identity is that we obtain some new general inequalities containing all of the Hermite-Hadamard and Bullen type for functions whose derivatives in absolute value at certain power are convex. Some applications to special means of real numbers are also given. Finally, some error estimates for the trapezoidal and midpoint formula are addressed.

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Fractional Integral Inequalities for Differentiable Convex Mappings and Applications to Special Means and a Midpoint Formula

Journal of Applied Mathematics Statistics and Informatics ◽

10.2478/v10294-012-0011-5 ◽

2012 ◽

Vol 8 (2) ◽

pp. 21-28 ◽

Cited By ~ 12

Author(s):

Chun Zhu ◽

Michal Fečkan ◽

Jinrong Wang

Keyword(s):

Error Estimates ◽

Integral Identity ◽

Fractional Integral ◽

Integral Inequalities ◽

Real Numbers ◽

Liouville Type ◽

Convex Mappings ◽

Special Means

Abstract In this paper, Riemann-Liouville type fractional integral identity and inequality for differentiable convex mappings are studied. Some applications to special means of real numbers are given. Finally, error estimates for a midpoint formula are also obtained.

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Generalized Integral Inequalities for Hermite-Hadamard Type via s-Convexity on Fractal Sets

10.20944/preprints201911.0157.v1 ◽

2019 ◽

Author(s):

Ohud Almutairi ◽

Adem Kilicman

Keyword(s):

Integral Inequalities ◽

Fractal Sets ◽

Second Derivatives ◽

The Absolute ◽

New Inequalities ◽

Generalized Integral Inequalities

In this article, the new Hermite–Hadamard type inequalities are studied via generalized s-convexity on fractal sets. These inequalities derived on fractal sets are shown to be the generalized s-convexity on fractal sets. We proved that the absolute values of the first and second derivatives for the new inequalities are the generalization of s-convexity on fractal sets.

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Some new bounds оf Gauss – Jacobi аnd Hermite – Hadamard type integral inequalities

Ukrains’kyi Matematychnyi Zhurnal ◽

10.37863/umzh.v73i8.603 ◽

2021 ◽

Vol 73 (8) ◽

pp. 1067-1084

Author(s):

A. Kashuri ◽

M. Ramosaçaj ◽

R. Liko

Keyword(s):

Error Estimates ◽

Integral Inequalities ◽

Fractional Integrals ◽

Auxiliary Result ◽

Real Numbers ◽

Positive Real ◽

Special Means ◽

Special Cases ◽

Type Integral

UDC 517.5 In this paper, authors discover two interesting identities regarding Gauss–Jacobi and Hermite–Hadamard type integral inequalities. By using the first lemma as an auxiliary result, some new bounds with respect to Gauss–Jacobi type integral inequalities are established. Also, using the second lemma, some new estimates with respect to Hermite–Hadamard type integral inequalities via general fractional integrals are obtained. It is pointed out that some new special cases can be deduced from main results. Some applications to special means for different positive real numbers and new error estimates for the trapezoidal are provided as well. These results give us the generalizations, refinement and significant improvements of the new and previous known results. The ideas and techniques of this paper may stimulate further research.

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New Inequalities of Fejer´ and Hermite-Hadamard type Concerning Convex and QuasiConvex Functions With Applications

Punjab University Journal of Mathematics ◽

10.52280/pujm.2021.530201 ◽

2021 ◽

pp. 83-99

Author(s):

Muhammad Amer Latif ◽

Sever Silvestru Dragomir ◽

Sofian Obeidat

Keyword(s):

Convex Functions ◽

Integral Inequalities ◽

Quasiconvex Functions ◽

Real Numbers ◽

Positive Real ◽

Special Means ◽

New Inequalities

This research contains new integral inequalities of Fejer and ´ Hermite-Hadamard type involving convex and quasi-convex functions. Applications of the newly established results for special means of positive real numbers are given.

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New inequalities for Hermite-Hadamard and Simpson type with applications

Tamkang Journal of Mathematics ◽

10.5556/j.tkjm.44.2013.1179 ◽

2013 ◽

Vol 44 (2) ◽

pp. 209-216 ◽

Cited By ~ 2

Author(s):

M. Emin Özdemir ◽

Çetin Yildiz

Keyword(s):

Real Numbers ◽

Special Means ◽

Second Derivatives ◽

New Inequalities

In this paper, we obtain new bounds for the inequalities of Simpson and Hermite-Hadamard type for functions whose second derivatives absolute values are $P$-convex. Some applications for special means of real numbers are also given.

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New inequalities of Hermite-Hadamard type for n-times differentiable convex and concave functions with applications

Filomat ◽

10.2298/fil1610609l ◽

2016 ◽

Vol 30 (10) ◽

pp. 2609-2621

Author(s):

M.A. Latif ◽

S.S. Dragomir

Keyword(s):

Concave Functions ◽

Absolute Value ◽

Trapezoidal Formula ◽

Special Means ◽

Second Derivatives ◽

Special Cases ◽

New Inequalities

In this paper, a new identity for n-times differntiable functions is established and by using the obtained identity, some new inequalities Hermite-Hadamard type are obtained for functions whose nth derivatives in absolute value are convex and concave functions. From our results, several inequalities of Hermite-Hadamard type can be derived in terms of functions whose first and second derivatives in absolute value are convex and concave functions as special cases. Our results may provide refinements of some results already exist in literature. Applications to trapezoidal formula and special means of established results are given.

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