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Fixed points, eigenvalues and surjectivity for (ws)-compact operators on unbounded convex sets

100%

Amar A.

Open Mathematics

2013

tom 11

nr 1

85-93

The paper studies the existence of fixed points for some nonlinear (ws)-compact, weakly condensing and strictly quasibounded operators defined on an unbounded closed convex subset of a Banach space. Applications of the newly developed fixed point theorems are also discussed for proving the existence of positive eigenvalues and surjectivity of quasibounded operators in similar situations. The main condition in our results is formulated in terms of axiomatic measures of weak noncompactness.

Closedness type regularity conditions for surjectivity results involving the sum of two maximal monotone operators

88%

Ioan Boţ R., Grad S.-M.

Open Mathematics

2011

tom 9

nr 1

162-172

In this note we provide regularity conditions of closedness type which guarantee some surjectivity results concerning the sum of two maximal monotone operators by using representative functions. The first regularity condition we give guarantees the surjectivity of the monotone operator S(· + p) + T(·), where p ɛ X and S and T are maximal monotone operators on the reflexive Banach space X. Then, this is used to obtain sufficient conditions for the surjectivity of S + T and for the situation when 0 belongs to the range of S + T. Several special cases are discussed, some of them delivering interesting byproducts.

Ograniczanie wyników

2 Open Mathematics

1 Amar A.

1 Grad S.-M.

1 Ioan Boţ R.

1 2013

1 2011

Wyniki wyszukiwania

Fixed points, eigenvalues and surjectivity for (ws)-compact operators on unbounded convex sets

Closedness type regularity conditions for surjectivity results involving the sum of two maximal monotone operators