Geodesic
Integral inequalities of Hermite\,--\,Hadamard type for $((\alpha,m), \log)$-convex functions on co--ordinates
Problemy analiza, Tome 4 (2015) no. 2, pp. 73-92

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The convexity of functions is a basic concept in mathematics and it has been generalized in various directions. Establishing integral inequalities of Hermite – Hadamard type for various convex functions is one of main topics in the theory of convex functions and attracts a number of mathematicians for several centuries. Currently there have accumulated an amount of literature on integral inequalities of Hermite – Hadamard type for various convex functions. In the paper, the authors introduce a new concept "$((\alpha,m), \log)$–convex functions on the co–ordinates on the rectangle of the plane" and establish new integral inequalities of the Hermite – Hadamard type for $((\alpha,m),\log)$-convex functions on the co–ordinates on the rectangle of the plane.
Keywords: convex function, \log)$-convex function, co–ordinates, integral inequality of the Hermite – Hadamard type.
Mots-clés : $((\alpha,m) 
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     title = {Integral inequalities of {Hermite\,--\,Hadamard} type for $((\alpha,m), \log)$-convex functions on co--ordinates},
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B.-Ya. Xi; F. Qi. Integral inequalities of Hermite\,--\,Hadamard type for $((\alpha,m), \log)$-convex functions on co--ordinates. Problemy analiza, Tome 4 (2015) no. 2, pp. 73-92. http://geodesic.mathdoc.fr/item/PA_2015_4_2_a6/