We show that a càdlàg, local martingale has conditionally independent increments and symmetric jumps if and only if its law is invariant under integral transformations which preserve quadratic variation.

In this paper, stochastic generalizations of some fixed point for operators satisfying random contractively generalized hybrid and some other contractive condition have been proved. We discuss also the existence of a solution to a nonlinear random integral equation in Banah spaces.

In this note we introduce strongly Lipschitz p-integral operators, strongly Lipschitz p-nuclear operators and Lipschitz p-nuclear operators. It is shown that for a linear operator, the Lipschitz p-nuclear norm is the same as its usual p-nuclear norm under certain conditions. We also prove that the Lipschitz 2-dominated operators and the strongly Lipschitz 2-integral operators are the same with ...

We establish sharp L2-Sobolev estimates for classes of pseudodifferential operators with singular symbols [27, 20] whose non-pseudodifferential (Fourier integral operator) parts exhibit two-sided fold singularities. The operators considered include both singular integral operators along curves in R2 with simple inflection points and normal operators arising in linearized seismic imaging in the ...

Abstract In this paper we are presenting the refinements of integral inequalities established for convex functions. Consequently, get several fractional different kinds operators.