Results 11 to 20 of about 65 (65)

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, Yasunori Kimura, Wataru Takahashi   +2 more
wiley   +1 more source

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

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
wiley   +1 more source

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

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
wiley   +1 more source

Eigenvalues and ranges for perturbations of nonlinear accretive and monotone operators in Banach spaces

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
wiley   +1 more source

The fixed point index for accretive mapping with K—set contraction perturbation in cones

International Journal of Mathematics and Mathematical Sciences, Volume 19, Issue 2, Page 287-290, 1996., 1994
Let P be cone Banach space E, A, K are two mappings in P, A accretive, K is K—set contraction, then fixed point index defined for mapping −A + K, some fixed point theorems are also deduced.
Yu-Qing Chen
wiley   +1 more source

Iterative solution of unstable variational inequalities on approximately given sets

Abstract and Applied Analysis, Volume 1, Issue 1, Page 45-64, 1996., 1996
The convergence and the stability of the iterative regularization method for solving variational inequalities with bounded nonsmooth properly monotone (i.e., degenerate) operators in Banach spaces are studied. All the items of the inequality (i.e., the operator A, the “right hand side” f and the set of constraints Ω) are to be perturbed. The connection
Y. I. Alber, A. G. Kartsatos, E. Litsyn
wiley   +1 more source

Asymptotic behavior of solutions of nonlinear functional differential equations

International Journal of Mathematics and Mathematical Sciences, Volume 17, Issue 4, Page 703-712, 1994., 1994
Using the properties of almost nonexpansive curves introduced by B. Djafari Rouhani, we study the asymptotic behavior of solutions of nonlinear functional differential equation du(t)/dt + Au(t) + G(u)(t)?f(t), where A is a maximal monotone operator in a Hilbert space H, f?L1(0, 8 : H) and is a given mapping.
Jong Soo Jung, Jong Yeoul Park, Hong Jae Kang   +2 more
wiley   +1 more source

Nonlinear random operator equations and inequalities in Banach spaces

International Journal of Mathematics and Mathematical Sciences, Volume 15, Issue 1, Page 111-118, 1992., 1990
In this paper we give some new existence theorems for nonlinear random equations and inequalities involving operators of monotone type in Banach spaces. A random Hammerstein integral equation is also studied. In order to obtain random solutions we use some results from the existing deterministic theory as well as from the theory of measurable ...
Antonios Karamolegos, Dimitrios Kravvaritis   +1 more
wiley   +1 more source