Contributions to the spectral theory for nonlinear operators in Banach spaces

1978 ◽  
Vol 118 (1) ◽  
pp. 229-294 ◽  
Author(s):  
M. Furi ◽  
M. Martelli ◽  
A. Vignoli
Keyword(s):  
Banach Spaces ◽  
Spectral Theory ◽  
Nonlinear Operators

scholarly journals Fejér monotonicity and fixed point theorems with applications to a nonlinear integral equation in complex valued Banach spaces

2020 ◽  
Vol 21 (1) ◽  
pp. 135
Author(s):  
Godwin Amechi Okeke ◽  
Mujahid Abbas
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Banach Spaces ◽  
Nonlinear Integral Equation ◽  
Metric Spaces ◽  
Banach Algebras ◽  
Cone Metric Spaces ◽  
Nonlinear Operators ◽  
Complex Valued ◽  
Cone Metric

It is our purpose in this paper to prove some fixed point results and Fej´er monotonicity of some faster fixed point iterative sequences generated by some nonlinear operators satisfying rational inequality in complex valued Banach spaces. We prove that results in complex valued Banach spaces are valid in cone metric spaces with Banach algebras. Furthermore, we apply our results in solving certain mixed type VolterraFredholm functional nonlinear integral equation in complex valued Banach spaces.

scholarly journals Strong Convergence Theorems for a Common Fixed Point of a Family of Asymptoticallyk-Strict Pseudocontractive Mappings

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
H. Zegeye ◽  
N. Shahzad
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
Iterative Process ◽  
Finite Family ◽  
Important Class ◽  
Convergence Theorems ◽  
Nonlinear Operators ◽  
Pseudocontractive Mappings

We provide an iterative process which converges strongly to a common fixed point of finite family of asymptoticallyk-strict pseudocontractive mappings in Banach spaces. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear operators.

scholarly journals Systems of Variational Inequalities with Nonlinear Operators

Mathematics ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 338 ◽  
Author(s):  
Lu-Chuan Ceng ◽  
Qing Yuan
Keyword(s):  
Fixed Point ◽  
Variational Inequalities ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
General System ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Nonlinear Operators ◽  
Pseudocontractive Mappings ◽  
Common Fixed Point Problem

In this work, we concern ourselves with the problem of solving a general system of variational inequalities whose solutions also solve a common fixed-point problem of a family of countably many nonlinear operators via a hybrid viscosity implicit iteration method in 2 uniformly smooth and uniformly convex Banach spaces. An application to common fixed-point problems of asymptotically nonexpansive and pseudocontractive mappings and variational inequality problems for strict pseudocontractive mappings is also given in Banach spaces.

scholarly journals Forward-Backward Splitting Methods for Accretive Operators in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-25 ◽  
Author(s):  
Genaro López ◽  
Victoria Martín-Márquez ◽  
Fenghui Wang ◽  
Hong-Kun Xu
Keyword(s):  
Banach Spaces ◽  
Nonlinear Problems ◽  
Split Feasibility Problem ◽  
Splitting Methods ◽  
Feasibility Problem ◽  
Nonlinear Operator Equation ◽  
Accretive Operators ◽  
Nonlinear Operators ◽  
Constrained Convex Minimization Problem ◽  
The Split Feasibility Problem

Splitting methods have recently received much attention due to the fact that many nonlinear problems arising in applied areas such as image recovery, signal processing, and machine learning are mathematically modeled as a nonlinear operator equation and this operator is decomposed as the sum of two (possibly simpler) nonlinear operators. Most of the investigation on splitting methods is however carried out in the framework of Hilbert spaces. In this paper, we consider these methods in the setting of Banach spaces. We shall introduce two iterative forward-backward splitting methods with relaxations and errors to find zeros of the sum of two accretive operators in the Banach spaces. We shall prove the weak and strong convergence of these methods under mild conditions. We also discuss applications of these methods to variational inequalities, the split feasibility problem, and a constrained convex minimization problem.

$B$-spectral theory of linear relations in complex Banach spaces

2017 ◽  
Vol 91 (3-4) ◽  
pp. 455-466
Author(s):  
Marcel Roman ◽  
Adrian Sandovici
Keyword(s):  
Banach Spaces ◽  
Spectral Theory ◽  
Linear Relations

scholarly journals A new spectral theory for nonlinear operators and its applications

1997 ◽  
Vol 2 (1-2) ◽  
pp. 163-183 ◽  
Author(s):  
W. Feng
Keyword(s):  
Spectral Theory ◽  
The Other ◽  
Linear Case ◽  
Nonlinear Operators ◽  
Definition Of ◽  
Mapping Theory

In this paper, by applying(p,k)-epi mapping theory, we introduce a new definition of spectrum for nonlinear operators which contains all eigenvalues, as in the linear case. Properties of this spectrum are given and comparison is made with the other definitions of spectra. We also give applications of the new theory.

Some spectral theory for nonlinear operators

1997 ◽  
Vol 30 (5) ◽  
pp. 3135-3146 ◽  
Author(s):  
Jürgen Appell
Keyword(s):  
Spectral Theory ◽  
Nonlinear Operators

scholarly journals Five short lemmas in Banach spaces

2016 ◽  
Vol 32 (1) ◽  
pp. 131-140
Author(s):  
QINGPING ZENG ◽  
Keyword(s):  
Banach Spaces ◽  
Spectral Theory ◽  
Commutative Diagram ◽  
Spectral Properties ◽  
Linear Operators ◽  
General Question ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Local Spectral Theory

Consider a commutative diagram of bounded linear operators between Banach spaces...with exact rows. In what ways are the spectral and local spectral properties of B related to those of the pairs of operators A and C? In this paper, we give our answers to this general question using tools from local spectral theory.

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