Results 1 to 10 of about 2,787 (187)

Ranges of Operators of Monotone Type in Banach Space

Journal of Mathematical Analysis and Applications, 1993
Let \(X\) be a reflexive Banach space with both \(X\) and \(X^*\) locally uniformly convex. Let \(G\subset X\) be open, bounded, and convex, and \(T: \overline{G}\to X^*\) an operator of monotone type. By means of degree theory of operators of type \((S_ +)\), the author establishes certain range properties of \(T\). He applies the results to the study
Z. Guan
semanticscholar   +3 more sources

Iteration processes for approximating fixed points of operators of monotone type [PDF]

Bulletin of the Australian Mathematical Society, 1998
In this paper, the unique fixed points of multi-valued and single-valued operators of monotone type are approximated by Ishikawa iteration processes or Mann and Ishikawa iteration processes with errors in uniformly smooth Banach spaces. The operators may not satisfy the Lipschitzian conditions and the domain or the range of the operators may not be ...
Shih-sen Chang, K. Tan
semanticscholar   +3 more sources

Nonlinear random equations involving operators of monotone type

Journal of Mathematical Analysis and Applications, 1986
In this paper some new existence theorems for nonlinear random equations with operators of monotone type are presented. In section 3 we treat nonlinear random equations which contain multivalued maximal monotone operators. In section 4 we study a random Hammerstein equation in a Hilbert space involving a linear maximal monotone random operator and a ...
D. Kravvaritis
semanticscholar   +3 more sources

Solvability of semilinear equations with compact perturbations of operators of monotone type [PDF]

Proceedings of the American Mathematical Society, 1994
The solvability of the equation A u − T u + C u = f Au - Tu + Cu = f is studied under various assumptions of monotonicity and compactness on the operators A, T, and C, which map subsets of a reflexive Banach space X into its dual space.
Z. Guan
semanticscholar   +2 more sources

Iteration processes for approximating fixed points of operators of monotone type [PDF]

Proceedings of the American Mathematical Society, 2000
In this paper, the unique fixed points of multi-valued and single-valued operators of monotone type are approximated by Ishikawa and Mann iteration processes with errors in real Banach spaces. The operators may not satisfy the Lipschitzian conditions. The results presented improve and extend some recent results.
G. Feng
semanticscholar   +2 more sources

A Degree Theory for Compact Perturbations of Monotone Type Operators and Application to Nonlinear Parabolic Problem

Abstract and Applied Analysis, 2017
Let X be a real locally uniformly convex reflexive Banach space with locally uniformly convex dual space X⁎. Let T:X⊇D(T)→2X⁎ be maximal monotone, S:X→2X⁎ be bounded and of type (S+), and C:D(C)→X⁎ be compact with D(T)⊆D(C) such that C lies in Γστ (i.e.,
Teffera M. Asfaw
doaj   +2 more sources

On nonlinear mappings of monotone type homotopic to odd operators

Journal of Functional Analysis, 1972
AbstractLet A be a (nonlinear) mapping of monotone type from the real Banach space X into its conjugate space X∗. The solvability of the functional equation Au = 0 in a given open subset of X is investigated under the assumption that A = A0 is homotopic to an odd mapping A1. The same problem is then studied for A of the form A = T + B, with T a maximal
P. Hess
semanticscholar   +3 more sources

Semilinear problems involving nonlinear operators of monotone type

Results in Nonlinear Analysis, 2019
This is a survey article on semilinear problems with a non-symmetric linear part and a nonlinear part of monotone type in real Hilbert spaces. We study the solvability of semilinear inclusions in the nonresonance and resonance cases.
In-Sook Kim
doaj   +2 more sources

Weighted Hardy type inequalities for supremum operators on the cones of monotone functions

Journal of Inequalities and Applications, 2016
The complete characterization of the weighted L p − L r $L^{p}-L^{r}$ inequalities of supremum operators on the cones of monotone functions for all 0 < p , r ≤ ∞ $0< p,r\leq \infty$ is given.
Lars-Erik Persson, Guldarya E Shambilova, Vladimir D Stepanov   +2 more
doaj   +3 more sources

Iterative construction of fixed points for multivalued operators of the monotone type

Journal of Functional Analysis, 1978
AbstractThe fixed points of set valued operators satisfying a condition of the monotonicity type in Hilbert space are approximated by simple recursive averaging processes.
J. Dunn
semanticscholar   +3 more sources