Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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EXTENDED HERMITE-HADAMARD(H-H) AND FEJER'S INEQUALITIES BASED ON GEOMETRICALLY-s-CONVEX FUNCTIONS IN THIRD AND FOURTH SENSE

  • SABIR YASIN (Department of Mathematics and Statistics, School of Quantitative Sciences, Universiti Utara) ;
  • MASNITA MISIRAN (Department of Mathematics and Statistics, School of Quantitative Sciences, Universiti Utara, Centre for Testing, Measurement and Appraisal, Universiti Utara Malaysia) ;
  • ZURNI OMAR (Department of Mathematics and Statistics, School of Quantitative Sciences, Universiti Utara) ;
  • RABIA LUQMAN (Department of Management, COMSATS University, Islamabad. Vehari Campus)
  • Received : 2022.06.23
  • Accepted : 2023.05.28
  • Published : 2023.09.30
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Abstract

In this paper, geometrically convex and s-convex functions in third and fourth sense are merged to form (g, s)-convex function. Characterizations of (g, s)-convex function, algebraic and functional properties are presented. In addition, novel functions based on the integral of (g, s)-convex functions in the third sense are created, and inequality relations for these functions are explored and examined under particular conditions. Further, there are also some relationships between (g, s)-convex function and previously defined functions. The (g, s)-convex function and its derivatives will then be used to extend the well-known H-H and Fejer's type inequalities. In order to obtain the previously mentioned conclusions, several special cases from previous literature for extended H-H and Fejer's inequalities are also investigated. The relation between the average (mean) values and newly created H-H and Fejer's inequalities are also examined.

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References

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