Some new inequalities of Hermite-Hadamard type for s-convex functions with applications

In this paper, we present several new and generalized Hermite-Hadamard type inequalities for s-convex as well as s-concave functions via classical and Riemann-Liouville fractional integrals. As applications, we provide new error estimations for the trapezoidal formula.

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Bibliographic Details
Published inOpen mathematics (Warsaw, Poland) Vol. 15; no. 1; pp. 1414 - 1430
Main Authors Khan, Muhammad Adil, Chu, Yuming, Khan, Tahir Ullah, Khan, Jamroz
Format Journal Article
LanguageEnglish
Published Warsaw De Gruyter Open 09.12.2017
De Gruyter Poland
De Gruyter
Subjects
26A51
26D15
26D20
convex function
Fractional calculus
Hermite-Hadamard inequality
Hölder inequality
Inequalities
s-convex function
Trapezoidal formula
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Abstract In this paper, we present several new and generalized Hermite-Hadamard type inequalities for s-convex as well as s-concave functions via classical and Riemann-Liouville fractional integrals. As applications, we provide new error estimations for the trapezoidal formula.
AbstractList In this paper, we present several new and generalized Hermite-Hadamard type inequalities for s-convex as well as s-concave functions via classical and Riemann-Liouville fractional integrals. As applications, we provide new error estimations for the trapezoidal formula.
Author Khan, Muhammad Adil
Chu, Yuming
Khan, Tahir Ullah
Khan, Jamroz
Author_xml – sequence: 1
  givenname: Muhammad Adil
  surname: Khan
  fullname: Khan, Muhammad Adil
  email: adilswati@gmail.com
  organization: Department of Mathematics, University of Peshawar, 25000, Peshawar, Pakistan
– sequence: 2
  givenname: Yuming
  surname: Chu
  fullname: Chu, Yuming
  email: chuyuming2005@126.com
  organization: Department of Mathematics, Huzhou University, 313000, Huzhou, China
– sequence: 3
  givenname: Tahir Ullah
  surname: Khan
  fullname: Khan, Tahir Ullah
  organization: Department of Mathematics, University of Peshawar, 25000, Peshawar, Pakistan
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  givenname: Jamroz
  surname: Khan
  fullname: Khan, Jamroz
  organization: Department of Mathematics, University of Peshawar, 25000, Peshawar, Pakistan
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Snippet In this paper, we present several new and generalized Hermite-Hadamard type inequalities for s-convex as well as s-concave functions via classical and...
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SubjectTerms 26A51
26D15
26D20
convex function
Fractional calculus
Hermite-Hadamard inequality
Hölder inequality
Inequalities
s-convex function
Trapezoidal formula
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Title Some new inequalities of Hermite-Hadamard type for s-convex functions with applications
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