Integral inequalities of Simpsons type for (α,m )-convex functions

Shuang, Ye; Wang, Yan; Qi, Feng

doi:10.22436/jnsa.009.12.36

Cited by 12 publications

(11 citation statements)

References 6 publications

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“…Substituting these inequalities for (20) and (21) into inequality (19) and rearranging we complete the proof.…”

Section: Some New Results For (S M)-convex Functionsmentioning

confidence: 90%

Some new integral inequalities for (s, m)-convex and (α, m)-convex functions

Bayraktar¹

2019

Bul. Kar. Univ. - Math.

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Some new integral inequalities for (s, m)-convex and (α, m)-convex functions The paper considers several new integral inequalities for functions the second derivatives of which, with respect to the absolute value, are (s, m)-convex and (α, m)-convex functions. These results are related to well-known Hermite-Hadamard type integral inequality, Simpson type integral inequality, and Jensen type inequality. In other words, new upper bounds for these inequalities using the indicated classes of convex functions have been obtained. These estimates are obtained using a direct definition for a convex function, classical integral inequalities of Hölder and power mean types. Along with the new outcomes, the paper presents results confirming the existing in literature upper bound estimates for integral inequalities (in particular well known in literature results obtained by U. Kırmacı in [7] and M.Z. Sarıkaya and N. Aktan in [35]). The last section presents some applications of the obtained estimates for special computing facilities (arithmetic, logarithmic, generalized logarithmic average and harmonic average for various quantities).

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“…Substituting these inequalities for (20) and (21) into inequality (19) and rearranging we complete the proof.…”

Section: Some New Results For (S M)-convex Functionsmentioning

confidence: 90%

Some new integral inequalities for (s, m)-convex and (α, m)-convex functions

Bayraktar¹

2019

Bul. Kar. Univ. - Math.

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“…In Lemma 2.1, if we take , then identity (2.1) becomes the following equation proved by Shuang et al [28]: …”

Section: Resultsmentioning

confidence: 99%

“…Let us recall that Miheşan [20] presented a class of mappings, called -convex functions, as follows: A mapping , , is said to be -convex if for all and with some fixed . Shuang et al [28] proved the following result for such mappings.…”

Section: Introductionmentioning

confidence: 99%

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Certain new bounds considering the weighted Simpson-like type inequality and applications

Luo

Kunt

et al. 2018

J Inequal Appl

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“…In 2016, Shuang et al [25] established the following lemma. On the basis of the above obtained identity, they developed some Simpson type inequalities via (α, m)-convex.…”

Section: Introductionmentioning

confidence: 99%