A note on multivalued monotone operators.

Bipotentials for non monotone multivalued operators: fundamental results and applications

This is a survey of recent results about bipotentials representing multivalued operators. The notion of bipotential is based on an extension of Fenchel’s inequality, with several interesting applications related to non associated constitutive laws in non smooth mechanics, such as Coulomb frictional contact or non-associated Drücker-Prager model in plasticity. Relations betweeen bipotentials and...

Some results on pre-monotone operators

‎In this paper‎, ‎some properties of pre-monotone operators are proved‎. ‎It is shown that in a reflexive Banach space‎, ‎a full domain multivalued $sigma$-monotone operator with sequentially norm$times$weak$^*$ closed graph is norm$times$weak$^*$ upper semicontinuous‎. ‎The notion of $sigma$-convexity is introduced and the‎ ‎relations between the $sigma$-monotonicity and $sigma$-convexity is i...

On the Multivalued Poincaré Operators

By Poincaré operators we mean the translation operator along the trajectories of the associated differential system and the first return (or section) map defined on the cross section of the torus by means of the flow generated by the vector field. The translation operator is sometimes also called as Poincaré–Andronov or Levinson or, simply, T -operator. In the classical theory (see [K], [W], [Z...

A note on multivalued Wλ0 pseudomonotone map

This paper is concerned with a class of Wλ0 pseudomonotone maps given by Kasyanov et al. (2010, 2006) [2,15]. We indicate that its main character of passing to a subsequence in classical definition is meaningless. Then, we show that Wλ0 pseudomonotone map is the same as a class of known pseudomonotone maps (Theorem 2) rather than its generalization (cf. Kasyanov et al. (2010) [2] lines 2–3, p. ...

A Note on Weighted Composition Operators on L^p-Spaces