As the development of singular integral operators, their commutators and multilinear operators have been well studied (see [4, 5, 6, 7, 8, 9, 10]). In [4, 5, 6, 7, 8, 9, 10], the authors prove that the commutators and multilinear operators generated by the singular integral operators and BMO functions are bounded on L(R) for 1 < p <∞; Chanillo (see [2]) proves a similar result when singular int...

It is well known that solutions of inhomogeneous differential and integral equations are represented by integral operators. To investigate the stability of solutions, we often use the continuity of corresponding integral operators in the studied function spaces. For instance, the boundedness of Fourier multiplier operators plays a crucial role in the theory of linear PDE’s, especially in the st...

Many questions concerning the semantics of disjunctive databases and of logic programming systems depend on the fixed points of various multivalued mappings and operators determined by the database or program. We discuss known versions, for multivalued mappings, of the Knaster-Tarski theorem and of the Banach contraction mapping theorem, and formulate a version of the classical fixed-point theo...

We study some integral operators and determine conditions for the univalence of these integral operators.

The extension of mathematical morphology to multivalued images is an important issue. This is particularly true in the context of connected operators based on morphological hierarchies, which aim to provide efficient image filtering and segmentation tools in various application fields, e.g.(bio)medical imaging, remote sensing, or astronomy. In this article, we propose a preliminary study that d...

We show that the general variational inequalities are equivalent to the general WienerHopf equations and use this alterative equivalence to suggest and analyze a new iterative method for finding the common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the general variational inequality involving multivalued relaxed monotone operators. Our results impro...