Some new Hermite--Hadamard type inequalities for geometrically quasi-convex functions on co-ordinates

Abstract

In the paper, the authors introduce a new concept "geometrically quasi-convex function on co-ordinates" and establish some new Hermite-Hadamard type inequalities for geometrically quasi-convex functions on the co-ordinates.

Weighted version of Hermite–Hadamard type inequalities for geometrically quasi-convex functions and their applications

“…Our inequalities are more general and unique in relation to those given in [ 13 ] because of the usage of a weight function, which is assumed to be geometrically symmetric with respect to the geometric mean of the end points of the interval. For further information on quasi-convexity, we refer the reader to [ 1 , 4 , 6 , 7 ], and [ 16 ]. For further information on Hermite–Hadamard type inequalities for different kinds of convexity assumptions, we refer the interested reader to [ 5 , 6 , 9 – 11 ], and [ 1 , 12 , 14 , 15 , 17 ].…”

Some integral inequalities of the Hermite--Hadamard type for log-convex functions on co-ordinates

“…For more and detailed information on this topic, please refer to the newly published papers [2,[6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] and plenty of references therein.…”

Parametrized inequality of Hermite-Hadamard type for functions whose third derivative absolute values are quasi-convex

“…Recently, Guo et al. ( 2015 ) investigated Hermite-Hadamard type inequalities for geometrically quasi-convex functions. Xi and Qi ( 2014 , 2015 ) and Xi et al.…”