461 research outputs found
A Recession Notion for a Class of Monotone Bivariate Functions
Using monotone bifunctions, we introduce a recession concept
for general equilibrium problems relying on a variational convergence notion. The interesting purpose is to extend some results of P. L. Lions on
variational problems. In the process we generalize some results by H. Brezis
and H. Attouch relative to the convergence of the resolvents associated with
maximal monotone operators
Ergodic Convergence to a Zero of the Extended Sum
In this note we show that the splitting scheme of Passty [7] as well as the barycentric-proximal method of Lehdili & Lemaire [4] can be used to approximate a zero of the extended sum of maximal monotone operators. When the extended sum is maximal monotone, we extend the convergence result obtained by Lehdili & Lemaire for convex functions to the case of maximal monotone operators. Moreover, we recover the main convergence results by Passty and Lehdili & Lemaire when the pointwise sum of the involved operators is maximal monotone
Closedness type regularity conditions for surjectivity results involving the sum of two maximal monotone operators
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 , where and and are maximal monotone operators on
the reflexive Banach space . Then, this is used to obtain sufficient
conditions for the surjectivity of and for the situation when belongs
to the range of . Several special cases are discussed, some of them
delivering interesting byproducts.Comment: 11 pages, no figure
An algorithm with strong convergence for the split common fixed point problem of total asymptotically strict pseudocontraction mappings
Composite viscosity methods for common solutions of general mixed equilibrium problem, variational inequalities and common fixed points
Algorithms of common solutions for a variational inequality, a split equilibrium problem and a hierarchical fixed point problem
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