Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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HYPERBOLIC TYPE CONVEXITY AND SOME NEW INEQUALITIES

  • Toplu, Tekin (Institute of Science, Giresun University) ;
  • Iscan, Imdat (Department of Mathematics, Faculty of Arts and Sciences, Giresun University) ;
  • Kadakal, Mahir (Department of Mathematics, Faculty of Arts and Sciences, Giresun University)
  • Received : 2019.06.14
  • Accepted : 2020.02.25
  • Published : 2020.06.25
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Abstract

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.

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References

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