Bounds on some new weakly singular Wendroff-type integral inequalities and applications

Some New Nonlinear Weakly Singular Integral Inequalities of Wendroff Type with Applications

On some new weakly singular Volterra integral inequalities with maxima and their applications

*Correspondence: [email protected] Department of Mathematics, Sichuan University for Nationalities, Kangding, Sichuan 626001, P.R. China Abstract In this paper, we consider a general form of nonlinear integral inequalities with the unknown function composed with a given function on the left hand side, more than one distinct nonlinear integrals on its right-hand side, and weakly singular kernels,...

Explicit bounds of unknown function of some new weakly singular retarded integral inequalities for discontinuous functions and their applications

The purpose of the present paper is to establish some new retarded weakly singular integral inequalities of Gronwall-Bellman type for discontinuous functions, which generalize some known weakly singular and impulsive integral inequalities. The inequalities given here can be used in the analysis of the qualitative properties of certain classes of singular differential equations and singular impu...

Some Nonlinear Weakly Singular Integral Inequalities with Two Variables and Applications

Various singular integral inequalities play an important role in the development of the theory of differential equations, functional differential equations, and integral equations. For example, Henry 1 proposed a linear integral inequality with singular kernel to investigate some qualitative properties for a parabolic differential equation, and Sano and Kunimatsu 2 gave a modified version of He...

Some extended Simpson-type inequalities and applications

‎In this paper‎, ‎we shall establish some extended Simpson-type inequalities‎ ‎for differentiable convex functions and differentiable concave functions‎ ‎which are connected with Hermite-Hadamard inequality‎. ‎Some error estimates‎ ‎for the midpoint‎, ‎trapezoidal and Simpson formula are also given‎.