Results 31 to 40 of about 434 (146)
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
An intermediate value theorem for monotone operators in ordered Banach spaces [PDF]
, 2012 We consider a monotone increasing operator in an ordered Banach space having u− and u+ as a strong super- and subsolution, respectively. In contrast with the well-studied case u+
V. Kostrykin, A. Oleynik
semanticscholar +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
wiley +1 more source
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
core +1 more source
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
wiley +1 more source
A note on ‘A best proximity point theorem for Geraghty-contractions’
, 2013 In Caballero et al. (Fixed Point Theory Appl. (2012). doi:10.1186/1687-1812-2012-231), the authors prove a best proximity point theorem for Geraghty nonself contraction.
Jingling Zhang +2 more
semanticscholar +1 more source
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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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
wiley +1 more source
, 2015 In this article, we first introduce the concept of T-mapping of a finitefamily of strictly pseudononspreading mapping , and we show that the fixed point set of theT-mapping is the set of common fixed points of and T is a quasi-nonexpansive mapping.Based ...
Hai-tao Che, Mei-xia Li
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Semilinear systems with a multi-valued nonlinear term
Open Mathematics, 2017 Introducing a topological degree theory, we first establish some existence results for the inclusion h ∈ Lu − Nu in the nonresonance and resonance cases, where L is a closed densely defined linear operator on a Hilbert space with a compact resolvent and ...
Kim In-Sook, Hong Suk-Joon
doaj +1 more source