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Fej\'{e}r type inequalities for Harmonically-convex functions with applications |
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| Authors: | Muhammad Amer Latif Sever Silvestru Dragomir and Ebrahim Momoniat |
| Institution: | School of Computer Science and Applied Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, Johannesburg, South Africa,School of Computer Science and Applied Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, Johannesburg, South Africa;School of Engineering and Science, Victoria University, PO Box 14428 Melbourne City, MC 8001, Australia and School of Computer Science and Applied Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, Johannesburg, South Africa |
| Abstract: | In this paper, a new weighted identity involving harmonically symmetric functions and differentiable functions is established. By using the notion of harmonic symmetricity, harmonic convexity and some auxiliary results, some new Fej\''{e}r type integral inequalities are presented. Applications to special means of positive real numbers are given as well. |
| Keywords: | Hermite-Hadamard''s inequality Fej\''{e}r''s inequality convex function harmonically-convex function H\"{o}lder''s inequality power mean inequality |
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