Qinghua Feng

Some nonlinear delay integral inequalities on time scales arising in the theory of dynamics equations

In this paper, some new nonlinear delay integral inequalities on time scales are established, which provide a handy tool in the research of boundedness of unknown functions in delay dynamic equations on time scales. The established results generalize some of the results in Lipovan [J. Math. Anal. Appl. 322, 349-358 (2006)], Pachpatte [J. Math. Anal. Appl. 251, 736-751 (2000)], Li [Comput. Math. Appl. 59, 1929-1936 (2010)], and Sun [J. Math. Anal. Appl. 301, 265-275 (2005)].MSC 2010: 26E70; 26D15; 26D10.

Some new Gronwall-Bellman type nonlinear dynamic inequalities containing integration on infinite intervals on time scales

In this paper, some new Gronwall-Bellman-type nonlinear dynamic inequalities containing integration on infinite intervals on time scales are established, which provides new bounds on unknown functions and can be used as a handy tool in the qualitative analysis of solutions of certain dynamic equations on time scales.MSC:26E70, 26D15, 26D10.

Some new Gronwall-type inequalities arising in the research of fractional differential equations

In this paper, some new Gronwall-type inequalities, which can be used as a handy tool in the qualitative and quantitative analysis of the solutions to certain fractional differential equations, are presented. The established results are extensions of some existing Gronwall-type inequalities in the literature. Based on the inequalities established, we investigate the boundedness, uniqueness, and continuous dependence on the initial value and parameter for the solution to a certain fractional differential equation.MSC:26D10.

Generalized Ostrowski type inequalities for multiple points on time scales involving functions of two independent variables

In this article, we establish some new Ostrowski type integral inequalities on time scales involving functions of two independent variables for k2 points, which on one hand unify continuous and discrete analysis, on the other hand extend some known results in the literature. The established results can be used in the estimate of error bounds for some numerical integration formulae, and some of the results are sharp.Mathematical Subject Classification 2010: 26E70; 26D15; 26D10.

Generalized Gronwall-Bellman-type discrete inequalities and their applications

In this paper, some new nonlinear Gronwall-Bellman-type discrete inequalities are established, which can be used as a handy tool in the research of qualitative and quantitative properties of solutions of certain difference equations. The established results generalize some of the recent results obtained by Cheung and Ma, respectively.Mathematics Subject Classification (2010) 26D15

Some new finite difference inequalities arising in the theory of difference equations

AbstractIn this work, some new finite difference inequalities in two independent variables are established, which can be used in the study of qualitative as well as quantitative properties of solutions of certain difference equations. The established results extend some existing results in the literature. MSC 2010: 26D15

Some Delay Integral Inequalities on Time Scales and Their Applications in the Theory of Dynamic Equations

We establish some delay integral inequalities on time scales, which on one hand provide a handy tool in the study of qualitative as well as quantitative properties of solutions of certain delay dynamic equations on time scales and on the other hand unify some known continuous and discrete results in the literature.

New Ostrowski-Grüss type inequalities with the derivatives bounded by functions

In this paper, we establish some new Ostrowski-Grüss type inequalities involving multiple interior points with the first-order derivative bounded by functions instead of constants, some of which provide sharp bounds. Then we establish a new 2D Ostrowski-Grüss type inequality involving multiple interior points with the second mixed partial derivative bounded by functions. For illustrating the applications of the Ostrowski-Grüss type inequalities established, we apply them to derive error bounds for some numerical integration formulae.MSC:26D10, 26D20.

Some new nonlinear integral inequalities and their applications in the qualitative analysis of differential equations

In this paper, some new nonlinear integral inequalities are established, which provide a handy tool for analyzing the global existence and boundedness of solutions of differential and integral equations. The established results generalize the main results in Sun (J. Math. Anal. Appl. 301, 265-275, 2005), Ferreira and Torres (Appl. Math. Lett. 22, 876-881, 2009), Xu and Sun (Appl. Math. Comput. 182, 1260-1266, 2006) and Li et al. (J. Math. Anal. Appl. 372, 339-349 2010).MSC 2010: 26D15; 26D10

Some New Delay Integral Inequalities in Two Independent Variables on Time Scales

Some new Gronwall-Bellman-type delay integral inequalities in two independent variables on time scales are established, which can be used as a handy tool in the research of boundedness of solutions of delay dynamic equations on time scales. Some of the established results are 2D extensions of several known results in the literature, while some results unify existing continuous and discrete analysis.