scholarly journals FACTORIZATION OF OPERATORS THROUGH SUBSPACES OF -SPACES

2016 ◽  
Vol 103 (3) ◽  
pp. 313-328
Author(s):  
J. M. CALABUIG ◽  
J. RODRÍGUEZ ◽  
E. A. SÁNCHEZ-PÉREZ
Keyword(s):  
Banach Spaces ◽  
Vector Measure ◽  
Special Cases ◽  
Finite Measures ◽  
Scalar Integral

We analyze domination properties and factorization of operators in Banach spaces through subspaces of$L^{1}$-spaces. Using vector measure integration and extending classical arguments based on scalar integral bounds, we provide characterizations of operators factoring through subspaces of$L^{1}$-spaces of finite measures. Some special cases involving positivity and compactness of the operators are considered.

scholarly journals On Stable Perturbations of the Generalized Drazin Inverses of Closed Linear Operators in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Qianglian Huang ◽  
Lanping Zhu ◽  
Xiaoru Chen ◽  
Chang Zhang
Keyword(s):  
Banach Spaces ◽  
Null Space ◽  
Linear Operators ◽  
Special Cases ◽  
Stable Perturbation ◽  
Closed Linear Operators

We investigate the stable perturbation of the generalized Drazin inverses of closed linear operators in Banach spaces and obtain some new characterizations for the generalized Drazin inverses to have prescribed range and null space. As special cases of our results, we recover the perturbation theorems of Wei and Wang, Castro and Koliha, Rakocevic and Wei, Castro and Koliha and Wei.

scholarly journals An iterative algorithm for generalized nonlinear variational inclusions with relaxed strongly accretive mappings in Banach spaces

2004 ◽  
Vol 2004 (20) ◽  
pp. 1035-1045 ◽  
Author(s):  
A. H. Siddiqi ◽  
Rais Ahmad
Keyword(s):  
Banach Spaces ◽  
Iterative Algorithm ◽  
Resolvent Operator ◽  
Existence Of Solutions ◽  
Operator Technique ◽  
Variational Inclusions ◽  
Special Cases ◽  
Accretive Mappings ◽  
Resolvent Operator Technique ◽  
The Resolvent Operator

We use Nadler's theorem and the resolvent operator technique form-accretive mappings to suggest an iterative algorithm for solving generalized nonlinear variational inclusions with relaxed strongly accretive mappings in Banach spaces. We prove the existence of solutions for our inclusions without compactness assumption and the convergence of the iterative sequences generated by the algorithm in real Banach spaces. Some special cases are also discussed.

scholarly journals Common Fixed Points of Multistep Noor Iterations with Errors for a Finite Family of Generalized Asymptotically Quasi-Nonexpansive Mappings

2009 ◽  
Vol 2009 ◽  
pp. 1-14 ◽  
Author(s):  
S. Imnang ◽  
S. Suantai
Keyword(s):  
Fixed Points ◽  
Banach Spaces ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Iteration Scheme ◽  
Finite Family ◽  
Special Cases

We introduce a general iteration scheme for a finite family of generalized asymptotically quasi-nonexpansive mappings in Banach spaces. The new iterative scheme includes the multistep Noor iterations with errors, modified Mann and Ishikawa iterations, three-step iterative scheme of Xu and Noor, and Khan and Takahashi scheme as special cases. Our results generalize and improve the recent ones announced by Khan et al. (2008), H. Fukhar-ud-din and S. H. Khan (2007), J. U. Jeong and S. H. Kim (2006), and many others.

scholarly journals Strongly Convex Functions of Higher Order Involving Bifunction

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1028 ◽  
Author(s):  
Bandar B. Mohsen ◽  
Muhammad Aslam Noor ◽  
Khalida Inayat Noor ◽  
Mihai Postolache
Keyword(s):  
Banach Spaces ◽  
Convex Functions ◽  
Higher Order ◽  
Strongly Convex Functions ◽  
Strongly Convex ◽  
New Concepts ◽  
Special Cases ◽  
Novel Applications

Some new concepts of the higher order strongly convex functions involving an arbitrary bifuction are considered in this paper. Some properties of the higher order strongly convex functions are investigated under suitable conditions. Some important special cases are discussed. The parallelogram laws for Banach spaces are obtained as applications of higher order strongly affine convex functions as novel applications. Results obtained in this paper can be viewed as refinement and improvement of previously known results.

The implicit midpoint rule for nonexpansive mappings in 2-uniformly convex hyperbolic spaces

2019 ◽  
Vol 26 (1/2) ◽  
pp. 95-105
Author(s):  
H. Fukhar-ud-din ◽  
A.R. Khan
Keyword(s):  
Banach Spaces ◽  
Hilbert Spaces ◽  
Nonexpansive Mappings ◽  
Hyperbolic Spaces ◽  
Uniformly Convex ◽  
Convergence Theorems ◽  
Implicit Midpoint Rule ◽  
Midpoint Rule ◽  
Uniformly Convex Banach Spaces ◽  
Special Cases

The purpose of this paper is to introduce the implicit midpoint rule (IMR) of nonexpansive mappings in 2- uniformly convex hyperbolic spaces and study its convergence. Strong and △-convergence theorems based on this algorithm are proved in this new setting. The results obtained hold concurrently in uniformly convex Banach spaces, CAT(0) spaces and Hilbert spaces as special cases.

scholarly journals Strong convergence theorems for fixed points of pseudo-contractive semigroup

2007 ◽  
Vol 76 (3) ◽  
pp. 441-452 ◽  
Author(s):  
Xue-Song Li ◽  
Nan-Jing Huang
Keyword(s):  
Fixed Points ◽  
Banach Spaces ◽  
Common Fixed Points ◽  
Nonexpansive Semigroup ◽  
Uniformly Smooth ◽  
Uniformly Convex Banach Spaces ◽  
Special Cases ◽  
Uniformly Smooth Banach Spaces ◽  
Iteration Processes ◽  
Implicit Iteration

We study some convergence of two kinds of implicit iteration processes for approximating common fixed points of a pseudo-contractive semigroup in uniformly convex Banach spaces with uniformly Gateaux differential norms. As special cases, we get some convergence of the implicit iteration processes for approximating common fixed points of a nonexpansive semigroup in uniformly smooth Banach spaces and give a positive answer to an open problem proposed by Xu in Bull. Austral. Math. Soc. (2005). The results presented in this paper generalise some corresponding results from Osilike in Panamer. Math. J. (2004), Suzuki in Proc. Amer. Math. Soc. (2002) and Xu in Bull. Austral. Math. Soc. (2005).

scholarly journals ON A DIRICHLET PROBLEM WITH p-LAPLACIAN AND SET-VALUED NONLINEARITY

2011 ◽  
Vol 86 (1) ◽  
pp. 83-89 ◽  
Author(s):  
S. A. MARANO
Keyword(s):  
Fixed Point ◽  
Dirichlet Problem ◽  
Banach Spaces ◽  
Differential Inclusion ◽  
Existence Of Solutions ◽  
Type Theorem ◽  
Special Cases ◽  
Homogeneous Dirichlet Problem ◽  
Point Type

AbstractThe existence of solutions to a homogeneous Dirichlet problem for a p-Laplacian differential inclusion is studied via a fixed-point type theorem concerning operator inclusions in Banach spaces. Some meaningful special cases are then worked out.

Uniformly bounded projections and semi-groups of operators

1974 ◽  
Vol 75 (2) ◽  
pp. 199-217
Author(s):  
G. O. Okikiolu
Keyword(s):  
Banach Spaces ◽  
Characteristic Functions ◽  
Semi Group ◽  
Trans Form ◽  
Fourier Trans ◽  
Special Cases ◽  
Dirichlet Integrals ◽  
Multiplier Operators ◽  
Uniformly Bounded

Classes of operators called uniformly bounded projections defined on Banach spaces have been formally introduced (see for example (2), 8·9·28; 8·9·92), and their connexions with semi-groups of operators considered. Notable cases of such operators include the Dirichlet integrals which are connected with the semi-group of Poisson operators in Lp In the main conclusions of this paper, there is an exposition of the connexion between classes of uniformly bounded projections and semi-groups of operators. In particular, it is shown that certain uniformly bounded analytic semi-groups of operators give rise to classes of uniformly bounded projections. Various of the known special cases in Lp are also considered as Fourier trans form multiplier operators with characteristic functions of intervals as multipliers.

scholarly journals Moments of probability measures on a group

1981 ◽  
Vol 4 (1) ◽  
pp. 1-37 ◽  
Author(s):  
Herbert Heyer
Keyword(s):  
Topological Group ◽  
Banach Spaces ◽  
Lie Groups ◽  
Finite Groups ◽  
Lie Group ◽  
Probability Measures ◽  
Moment Conditions ◽  
New Developments ◽  
Large Numbers ◽  
Special Cases

New developments and results in the theory of expectatiors and variances for random variables with range in a topological group are presented in the following order (i) Introduction (2) Basic notions (3) The three series theorem in Banach spaces (4) Moment Conditions (5) Expectations and variances (6) A general three series theorem (7) The special cases of finite groups and Lie groups (8)The strong laws of large numbers on a Lie group (9) Further studies on moments of probability measures.

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