Hermite–Hadamard-type inequalities for generalized s-convex functions on real linear fractal set $$\mathbb {R}^{\alpha }(0<\alpha <1)$$ R α ( 0 < α < 1 )

Abstract

In this paper, we establish the Hermite-Hadamard-type inequalities for the generalized s-convex functions in the second sense on real linear fractal set R a ð0\a\1Þ:

Certain Ostrowski type inequalities for generalized s-convex functions

“…Recently the fractal theory has received a significant attention (see, e.g., [1,10,5,7,8,9,11,12]). Mo et al [4] proved the following analogue of the Hermite-Hadamard inequality (1.4) for generalized convex functions: Let An analogue in the fractal set R α of the classical Hölder's inequality has been established by Yang [13], which is asserted by the following lemma.…”

“…In [7], Mo and Sui established the following Hermite-Hadamard inequality for generalized s−convex functions on real linear fractal set R α (0 < α < 1) :…”

Generalized Convex Functions and their Applications

“…is known as generalized Hermite-Hadmard's inequality [14]. Many authers paid attention to the study of generalized Hermite-Hadmard's inequality and generalized convex function, see [4,16].…”

Generalized Ostrowski type inequalities for functions whose local fractional derivatives are generalized s-convex in the second sense

“…In recent years, the fractal theory has received significant attention. The calculus on the fractal set can lead to better comprehension for the various real world models from science and engineering [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19].…”

“…In [7], the authors introduced two kinds of generalized s-convex functions on fractal sets R α (0 1) < < α as follows:…”