Fejér type integral inequalities related with geometrically-arithmetically convex functions with applications

  • S. S. Dragomir School of Engineering and Science, Victoria University, PO Box 14428 Melbourne City, MC 8001, Australia; School of Computational and Applied Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, Johannesburg, South Africa
  • M. A. Latif Department of Basic Sciences, Deanship of Preparatory Year, University of Hail, Hail 2440
  • E. Momoniat Department of Pure and Applied Mathematics, University of Johannesburg, P.O. Box 524, Auckland Park 2006
Keywords: Hermite–Hadamard inequality, Fejér inequality, convex function, GA-convex function, Hölder inequality, power mean inequality


A new identity involving a geometrically symmetric function and a differentiable function is established. Some new Fejér type integral inequalities, connected with the left part of Hermite–Hadamard type inequalities for geometrically-arithmetically convex functions, are presented by using the Hölder integral inequality and the notion of geometrically-arithmetically convexity. Applications of our results to special means of positive real numbers are given.


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