We present a new sufficient condition under which a maximal monotone operator T : X ⇉ X∗ admits a unique maximal monotone extension to the bidual T̃ : X∗∗ ⇉ X∗. For non-linear operators this condition is equivalent to uniqueness of the extension. The class of maximal monotone operators which satisfy this new condition includes class of Gossez type D maximal monotone operators, previously defined...

In this paper, we consider LC–functions, a class of special convex functions from the product of a reflexive Banach space and its dual into ]−∞,∞]. Using Fitzpatrick functions, we will show that the theory of LC–functions is a proper extension of the theory of maximal monotone sets. Various versons of the Fenchel duality theorem lead to a number of results on maximal monotonicity, some of them ...

We use representations of maximal monotone operators for studying recession (or asymptotic) operators associated to maximal monotone operators. Such a concept is useful for dealing with unboundedness. Dedicated to Alfred Auslender on the occasion of his sixty-fifth birthday

We introduce and study a new system of nonlinear variational-like inclusions involving sG, η maximal monotone operators, strongly monotone operators, η-strongly monotone operators, relaxed monotone operators, cocoercive operators, λ, ξ -relaxed cocoercive operators, ζ, φ, g-relaxed cocoercive operators and relaxed Lipschitz operators in Hilbert spaces. By using the resolvent operator technique ...

In this paper, we study an elliptic obstacle problem with a generalized fractional Laplacian and multivalued operator which is described by gradient. Under quite general assumptions on the data, employ surjectivity theorem for mappings generated sum of maximal monotone bounded pseudomonotone mapping to prove that set weak solutions nonempty, closed. Then, introduce sequence penalized problems w...

The question whether or not the sum of two maximal monotone operators is maximal monotone under Rockafellar’s constraint qualification— that is, whether or not “the sum theorem” is true— is themost famous open problem inMonotone Operator Theory. In his 2008monograph “From Hahn-Banach to Monotonicity”, Stephen Simons asked whether or not the sum theorem holds for the special case of a maximal mo...