Results 21 to 30 of about 129 (117)
The sum theorem for maximal monotone operators in reflexive Banach spaces revisited
, 2021 The goal of this note is to present a new shorter proof for the maximal monotonicity of the Minkowski sum of two maximal monotone multi-valued operators defined in a reflexive Banach space under the classical interiority condition involving their domains.
VOISEI, Mircea D.
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Some results on variational inequalities and generalized equilibrium problems with applications [PDF]
, 2010 An iterative algorithm is considered for variational inequalities, generalized equilibrium problems and fixed point problems. Strong convergence of the proposed iterative algorithm is obtained in the framework Hilbert spaces.
Xiaolong Qin +5 more
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Nonlinear Fokker-Planck equations with time-dependent coefficients [PDF]
, 2022 An operatorial based approach is used here to prove the existence and uniqueness of a strong solution $u$ to the time-varying nonlinear Fokker--Planck equation $u_t(t,x)-\Delta(a(t,x,u(t,x))u(t,x))+{\rm div}(b(t,x,u(t,x))u(t,x))=0$ in $(0,\infty)\times
Barbu, Viorelc +4 more
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Strong convergence of an iterative sequence for maximal monotone operators in a Banach space
Abstract and Applied Analysis, Volume 2004, Issue 3, Page 239-249, 2004., 2004 We first introduce a modified proximal point algorithm for maximal monotone operators in a Banach space. Next, we obtain a strong convergence theorem for resolvents of maximal monotone operators in a Banach space which generalizes the previous result by Kamimura and Takahashi in a Hilbert space.
Fumiaki Kohsaka, Wataru Takahashi
wiley +1 more source
Abstract and Applied Analysis, Volume 2003, Issue 1, Page 19-31, 2003., 2003 The notions of relaxed submonotone and relaxed monotone mappings in Banach spaces are introduced and many of their properties are investigated. For example, the Clarke subdifferential of a locally Lipschitz function in a separable Banach space is relaxed submonotone on a residual subset.
Tzanko Donchev, Pando Georgiev
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Convergence theorems for generalized projections and maximal monotone operators in Banach spaces
Abstract and Applied Analysis, Volume 2003, Issue 10, Page 621-629, 2003., 2003 We study a sequence of generalized projections in a reflexive, smooth, and strictly convex Banach space. Our result shows that Mosco convergence of their ranges implies their pointwise convergence to the generalized projection onto the limit set. Moreover, using this result, we obtain strong and weak convergence of resolvents for a sequence of maximal ...
Takanori Ibaraki +2 more
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Convergence theorems and stability results for Lipschitz strongly pseudocontractive operators
International Journal of Mathematics and Mathematical Sciences, Volume 31, Issue 10, Page 611-617, 2002., 2002 Suppose that X is an arbitrary real Banach space and T : X → X is a Lipschitz strongly pseudocontractive operator. It is proved that under certain conditions the Ishikawa iterative method with errors converges strongly to the fixed point of T and this iteration procedure is stable with respect to T.
Zeqing Liu, Lili Zhang, Shin Min Kang
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Topological degree and application to a parabolic variational inequality problem
International Journal of Mathematics and Mathematical Sciences, Volume 25, Issue 4, Page 273-287, 2001., 2001 We are interested in constructing a topological degree for operators of the form F = L + A + S, where L is a linear densely defined maximal monotone map, A is a bounded maximal monotone operators, and S is a bounded demicontinuous map of class (S+) with respect to the domain of L.
A. Addou, B. Mermri
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A G‐KKM type theorem and its applications to minimax inequalities on G‐convex spaces
International Journal of Stochastic Analysis, Volume 11, Issue 4, Page 493-505, 1998., 1998 A G‐KKM type theorem is obtained on G‐convex spaces. As application, a generalization of Ky Fan′s minimax inequality to non‐compact sets on G‐convex spaces is first obtained. As special cases of this minimax inequality, some new minimax inequalites are obtained. Four fixed point theorems and four equivalent formulations of the second minimax inequality
Mohammad S. R. Chowdhury
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Abstract and Applied Analysis, Volume 2, Issue 3-4, Page 197-205, 1997., 1997 Various eigenvalue and range results are given for perturbations of m‐accretive and maximal monotone operators. The eigenvalue results improve and extend some recent results by Guan and Kartsatos, while the range theorem gives an affirmative answer to a recent problem of Kartsatos.
Zhou Haiyun, Athanassios G. Kartsatos
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