In this paper,we give a new class of Lipschitz B-(p,r)-invex functions, which is generalizations of B-invex function and(p,r)-invex function.

In this paper the convexity monotonic and correlation theory of functions are studied,are established new inequalities of Hadamard-type for convex functions,Lipschitzian functions and n-time differentiable functions,which generalize some previously known results in the literature.

Two new Hadamard type inequalities for convex functions and Lipschitzian functions are established,which are generalized previously known results in the literature.

For a class of maximal commutators which are the variants of the usual maximal Calderón-Zygmund commutators associated with Calderón-Zygmund operators and Lipschitz functions,their boundedness in Lebesgue spaces is established and some endpoint estimates are obtained.

The boundedness is established of the commutators generated by Calderón-Zygmund operators or fractional integrals with RBMO(μ) functions or Lipschitz functions in Morrey spaces on nonhomogeneous spaces.

In this paper,the continuity for some multilinear operators generated by the singular integral operators with variable Calderón-Zygmund kernel and Lipschitz functions on some Hardy and Herz-type spaces are proved.

A necessary and sufficient condition that Clarke general directional derivative is equals to common directional derivative for locally Lipschitz function is given in this paper.

This paper introduces on spaces homogeneous type Triebel-Lizorkin space β,∞p which is defined by Lipschitz function and Calderon-Zygmund singular integral operator T,and it introduces two commutators Cf,Caf which are decided by fractional integral operator Iαf(x).

Some Properties of Weak Lipschitz Function and It s Generalized Subgradient;