• Title, Summary, Keyword: Hermite-Hadamard inequality

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ON HERMITE-HADAMARD-TYPE INEQUALITIES FOR DIFFERENTIABLE QUASI-CONVEX FUNCTIONS ON THE CO-ORDINATES

  • Chen, Feixiang
    • Journal of applied mathematics & informatics
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    • v.32 no.3_4
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    • pp.303-314
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    • 2014
  • In this paper, a new lemma is established and several new inequalities for differentiable co-ordinated quasi-convex functions in two variables which are related to the left-hand side of Hermite-Hadamard type inequality for co-ordinated quasi-convex functions in two variables are obtained.

REFINEMENTS OF HERMITE-HADAMARD TYPE INEQUALITIES FOR CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS

  • Xiang, Ruiyin
    • Journal of applied mathematics & informatics
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    • v.33 no.1_2
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    • pp.119-125
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    • 2015
  • In this note, two new mappings associated with convexity are propoesd, by which we obtain some new Hermite-Hadamard type inequalities for convex functions via Riemann-Liouville fractional integrals. We conclude that the results obtained in this work are the refinements of the earlier results.

HYPERBOLIC TYPE CONVEXITY AND SOME NEW INEQUALITIES

  • Toplu, Tekin;Iscan, Imdat;Kadakal, Mahir
    • Honam Mathematical Journal
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    • v.42 no.2
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    • pp.301-318
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    • 2020
  • In this paper, we introduce and study the concept of hyperbolic type convexity functions and their some algebraic properties. We obtain Hermite-Hadamard type inequalities for this class of functions. In addition, we obtain some refinements of the Hermite-Hadamard inequality for functions whose first derivative in absolute value, raised to a certain power which is greater than one, respectively at least one, is hyperbolic convexity. Moreover, we compare the results obtained with both Hölder, Hölder-İşcan inequalities and power-mean, improved-power-mean integral inequalities.

SUPERQUADRATIC FUNCTIONS AND REFINEMENTS OF SOME CLASSICAL INEQUALITIES

  • Banic, Senka;Pecaric, Josip;Varosanec, Sanja
    • Journal of the Korean Mathematical Society
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    • v.45 no.2
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    • pp.513-525
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    • 2008
  • Using known properties of superquadratic functions we obtain a sequence of inequalities for superquadratic functions such as the Converse and the Reverse Jensen type inequalities, the Giaccardi and the Petrovic type inequalities and Hermite-Hadamard's inequalities. Especially, when the superquadratic function is convex at the same time, then we get refinements of classical known results for convex functions. Some other properties of superquadratic functions are also given.

HERMITE-HADAMARD TYPE INEQUALITIES FOR GEOMETRIC-ARITHMETICALLY s-CONVEX FUNCTIONS

  • Hua, Ju;Xi, Bo-Yan;Qi, Feng
    • Communications of the Korean Mathematical Society
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    • v.29 no.1
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    • pp.51-63
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    • 2014
  • In the paper, several properties of geometric-arithmetically s-convex functions are provided, an integral identity in which the integrands are products of a function and a derivative is found, and then some inequalities of Hermite-Hadamard type for integrals whose integrands are products of a derivative and a function whose derivative is of the geometric-arithmetic s-convexity are established.

SOME NEW ESTIMATES FOR EXPONENTIALLY (ħ, m)-CONVEX FUNCTIONS VIA EXTENDED GENERALIZED FRACTIONAL INTEGRAL OPERATORS

  • Rashid, Saima;Noor, Muhammad Aslam;Noor, Khalida Inayat
    • Korean Journal of Mathematics
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    • v.27 no.4
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    • pp.843-860
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    • 2019
  • In the article, we present several new Hermite-Hadamard and Hermite-Hadamard-Fejér type inequalities for the exponentially (ħ, m)-convex functions via an extended generalized Mittag-Leffler function. As applications, some variants for certain typ e of fractional integral operators are established and some remarkable special cases of our results are also have been obtained.