Dongyan Yu's research while affiliated with Beijing University of Posts and Telecommunications and other places

Publications (3)

Article
Full-text available
We introduce the generalized convex function on fractal sets Rα (0<α≤1) of real line numbers and study the properties of the generalized convex function. Based on these properties, we establish the generalized Jensen's inequality and generalized Hermite-Hadamard's inequality. Furthermore, some applications are given.
Article
In the paper, we introduce the generalized convex function on fractal sets and study the properties of the generalized convex function. Based on these properties, we establish the generalized Jensen's inequality and generalized Hermite-Hadamard's inequality on fractal sets. Furthermore, some applications are given .
Article
Let l is an element of N and A = (A(1),..., A(l)) and f = (f(1) , . . ., f(l)) finite collections of functions, where every function Ai has derivatives of order m(i) and, f(1) , ..., f(l) is an element of L-e(infinity)(R-n). Let x is not an element of boolean AND(l)(i=1)Suppf(i). The generalized higher commutator generated by the multilinear fracti...

Citations

... Various extensions of this notion have been reported in the literature in recent years, see [1,4,6,12,13,14,16,17,22,26]. Mo et al. in [20], introduced the following generalized convex function. ...
... The commutator theory for the multilinear fractional integral operators can be found in [5,44], among others. Recently, Mo et al. [28] studied the following generalized commutator of the multilinear fractional integral defined by ...
... Many researchers contemplated the properties of a function on the fractal space and built numerous sorts of fractional calculus by utilizing distinctive approaches, see [25,26]. Mo et al. [27] defined the generalized convex function on fractal sets R (0 < ≤ 1) of real numbers and established generalized Jensen's and Hermite-Hadamard's inequalities for a generalized convex function in the concept of local fractional calculus. In (2017) Sun [28] introduced the concept of harmonic convex function on fractal sets R (0 < ≤ 1) of real numbers and gave some Hermite-Hadamard inequalities for a generalized harmonic function ( ∈ GHK (I)). ...