Journal of Operators
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© 2015 , Hindawi Publishing Corporation . All rights reserved.

On Ordinary, Linear Difference Equations, with Applications to Sato Theory
Mon, 23 Feb 2015 09:47:49 +0000
http://www.hindawi.com/journals/joper/2015/824549/
The purpose of this paper is to develop the theory of ordinary, linear difference equations, in particular the homogeneous case; we show that there are many similarities to differential equations. In the second part we study the applications to a analogue of Sato theory. The Schur polynomials act as basis function, similar to Appell polynomials. The Ward addition plays a crucial role as operation for the function argument in the matrix exponential and for the Schur polynomials.
Thomas Ernst
Copyright © 2015 Thomas Ernst. All rights reserved.

Frame Multiresolution Analysis on Local Fields of Positive Characteristic
Mon, 16 Feb 2015 13:58:18 +0000
http://www.hindawi.com/journals/joper/2015/216060/
We present a notion of frame multiresolution analysis on local fields of positive characteristic based on the theory of shiftinvariant spaces. In contrast to the standard setting, the associated subspace of has a frame, a collection of translates of the scaling function of the form , where is the set of nonnegative integers. We investigate certain properties of multiresolution subspaces which provides the quantitative criteria for the construction of frame multiresolution analysis (FMRA) on local fields of positive characteristic. Finally, we provide a characterization of wavelet frames associated with FMRA on local field of positive characteristic using the shiftinvariant space theory.
Firdous A. Shah
Copyright © 2015 Firdous A. Shah. All rights reserved.

On Some Algebraic and OperatorTheoretic Properties of Toeplitz Operators
Tue, 06 Jan 2015 08:53:47 +0000
http://www.hindawi.com/journals/joper/2015/172754/
Based on a spectral problem raised by Barría and Halmos, a new class of HardyHilbert space operators, containing the classical Toeplitz operators, is introduced, and some of their Toeplitzlike algebraic and operatortheoretic properties are studied and explored.
Mehdi Nikpour
Copyright © 2015 Mehdi Nikpour. All rights reserved.

A Fixed Point Theorem for Three Pairs of Mappings Satisfying Contractive Condition of Integral Type in Dislocated Metric Space
Sun, 28 Dec 2014 08:08:49 +0000
http://www.hindawi.com/journals/joper/2014/750427/
The aim of this paper is to study a common fixed point theorem for three pairs of selfmappings satisfying a contractive condition of integral type in the setting of dislocated metric space. We notice that our established theorem generalizes the main result of Branciari (2002) in the context of dislocated metric space.
Mujeeb Ur Rahman and Muhammad Sarwar
Copyright © 2014 Mujeeb Ur Rahman and Muhammad Sarwar. All rights reserved.

Existence of Strong Coupled Fixed Points for Cyclic Coupled CiricType Mappings
Sun, 23 Nov 2014 00:00:00 +0000
http://www.hindawi.com/journals/joper/2014/381685/
In this short communication the concept of cyclic coupled Kannantype contractions is generalized using a certain class of Cirictype mappings.
Xavier Udoutun
Copyright © 2014 Xavier Udoutun. All rights reserved.

New Results in the Startpoint Theory for Quasipseudometric Spaces
Mon, 17 Nov 2014 12:25:58 +0000
http://www.hindawi.com/journals/joper/2014/741818/
We give two generalizations of Theorem 35 proved by Gaba (2014). More precisely, we change the structure of the contractive condition; namely, we introduce a function instead of a simple constant .
Yaé Ulrich Gaba
Copyright © 2014 Yaé Ulrich Gaba. All rights reserved.

Coupled Fixed Point Theorems with New Implicit Relations and an Application
Tue, 11 Nov 2014 06:38:53 +0000
http://www.hindawi.com/journals/joper/2014/389646/
We introduce two new classes of implicit relations and where is a proper subset of , and these classes are more general than the class of implicit relations defined by Altun and Simsek (2010). We prove the existence of coupled fixed points for the maps satisfying an implicit relation in . These coupled fixed points need not be unique. In order to establish the uniqueness of coupled fixed points we use an implicit relation , where . Our results extend the fixed point theorems on ordered metric spaces of Altun and Simsek (2010) to coupled fixed point theorems and generalize the results of Gnana Bhaskar and Lakshimantham (2006). As an application of our results, we discuss the existence and uniqueness of solution of Fredholm integral equation.
G. V. R. Babu and P. D. Sailaja
Copyright © 2014 G. V. R. Babu and P. D. Sailaja. All rights reserved.

On Partial Charge Transfer Processes in Multiparticle Systems on Graphs
Tue, 21 Oct 2014 10:00:36 +0000
http://www.hindawi.com/journals/joper/2014/373754/
We assess the probability of resonances between sufficiently distant states of an particle disordered quantum system in a combinatorial graph . In the particle configuration space, there are arbitrarily distant pairs of configurations giving rise to pairs of local (random) Hamiltonians which are strongly coupled, so that the eigenvalue concentration (EVC) bounds are difficult to obtain. We extend to any number of particles the efficient EVC bounds, obtained earlier for the 2particle systems.
Victor Chulaevsky
Copyright © 2014 Victor Chulaevsky. All rights reserved.

On VectorValued Generalized Lorentz Difference Sequence Space
Sun, 21 Sep 2014 07:10:25 +0000
http://www.hindawi.com/journals/joper/2014/545346/
We introduce generalized Lorentz difference sequence spaces . Also we study some topologic properties of this space and obtain some inclusion relations.
Birsen Sağır and Oğuz Oğur
Copyright © 2014 Birsen Sağır and Oğuz Oğur. All rights reserved.

Uncertainty Principles and Extremal Functions for the Dunkl Multiplier Operators
Sun, 17 Aug 2014 00:00:00 +0000
http://www.hindawi.com/journals/joper/2014/659069/
We study some class of Dunkl multiplier operators; and related to these
operators we establish the HeisenbergPauliWeyl uncertainty principle and DonohoStark’s uncertainty principle. We give also an application of the theory of reproducing
kernels to the Tikhonov regularization on the SobolevDunkl spaces.
Fethi Soltani
Copyright © 2014 Fethi Soltani. All rights reserved.

Discrete Dichotomy and Remarks on the Boundedness of the Projections
Sun, 06 Jul 2014 11:20:55 +0000
http://www.hindawi.com/journals/joper/2014/196345/
The present paper treats a concept of dichotomy for linear discrete systems. Sufficient conditions for the boundedness of the projection sequences that give the dichotomy are presented and an illustrative example shows the connection between the growth of the system and the bound of the sequence of projections. Thus the growth of the system that is assumed in the theorems is essential.
MihaiGabriel Babuţia, Monteola Ilona Kovács, Mărioara Lăpădat, and Mihail Megan
Copyright © 2014 MihaiGabriel Babuţia et al. All rights reserved.

Cyclic Coupled Fixed Point Result Using Kannan Type Contractions
Wed, 02 Jul 2014 11:32:45 +0000
http://www.hindawi.com/journals/joper/2014/876749/
Putting several existing ideas together, in this paper we define the concept of cyclic coupled Kannan type contraction. We establish a strong coupled fixed point theorem for such mappings. The theorem is supported with an illustrative example.
Binayak S. Choudhury and Pranati Maity
Copyright © 2014 Binayak S. Choudhury and Pranati Maity. All rights reserved.

Properties and in Projective Tensor Products
Tue, 01 Jul 2014 07:39:39 +0000
http://www.hindawi.com/journals/joper/2014/405635/
We give sufficient conditions for a subset of to be relatively weakly compact. A Banach space has property (resp., ) if every subset of is relatively weakly compact (resp., weakly precompact). We prove that the projective tensor product has property (resp., ), when has property (resp., ), has property , and .
Ioana Ghenciu
Copyright © 2014 Ioana Ghenciu. All rights reserved.

Algebra Structure of OperatorValued Riesz Means
Sun, 18 May 2014 10:27:17 +0000
http://www.hindawi.com/journals/joper/2014/923616/
We characterize operatorvalued Riesz means via an algebraic law of composition and establish their functional calculus accordingly. With this aim, we give a new integral expression of the Leibniz derivation rule for smooth functions.
Pedro J. Miana
Copyright © 2014 Pedro J. Miana. All rights reserved.

Approximation by Kantorovich Operators
Thu, 15 May 2014 09:36:06 +0000
http://www.hindawi.com/journals/joper/2014/958656/
For a new Kantorovich operator we establish direct approximation theorems in the space via DitzianTotik modulus of smoothness of second order.
Zoltán Finta
Copyright © 2014 Zoltán Finta. All rights reserved.

Lattice Trace Operators
Mon, 14 Apr 2014 12:16:51 +0000
http://www.hindawi.com/journals/joper/2014/629502/
A bounded linear operator on a Hilbert space is trace class if its singular values are summable. The trace class operators
on form an operator ideal and in the case that is finitedimensional, the trace tr of is given by for any matrix representation of . In applications of trace class operators to scattering theory and representation theory, the subject is complicated by the fact that if is an integral kernel of the operator on the Hilbert space with a finite measure, then may not be defined, because the diagonal may be a set of measure zero. The present note describes a class of linear operators acting on a Banach function space which forms a lattice ideal of operators on , rather than an operator ideal, but coincides with the collection of hermitian positive trace class operators in the case of .
Brian Jefferies
Copyright © 2014 Brian Jefferies. All rights reserved.

SignChanging Solutions for Nonlinear Operator Equations
Thu, 06 Mar 2014 07:53:06 +0000
http://www.hindawi.com/journals/joper/2014/379056/
The existence of six solutions for nonlinear operator equations is obtained by using the topological degree and fixed point index theory. These six solutions are all nonzero. Two of them are positive, the other two are negative, and the fifth and sixth ones are both signchanging solutions. Furthermore, the theoretical results are applied to elliptic partial differential equations.
Yanbin Sang
Copyright © 2014 Yanbin Sang. All rights reserved.

Inequalities of Convex Functions and SelfAdjoint Operators
Sun, 09 Feb 2014 15:48:06 +0000
http://www.hindawi.com/journals/joper/2014/382364/
The paper offers generalizations of the JensenMercer inequality for selfadjoint operators and generally convex functions. The obtained results are applied to define the quasiarithmetic operator means without using operator convexity. The version of the harmonicgeometricarithmetic operator
mean inequality is derived as an example.
Zlatko Pavić
Copyright © 2014 Zlatko Pavić. All rights reserved.

On Approximation by Algebraic Version of the Trigonometric Jackson Integrals in Weighted Integral Metric
Mon, 23 Dec 2013 16:33:38 +0000
http://www.hindawi.com/journals/joper/2013/324630/
We characterize the errors of the algebraic version of trigonometric Jackson integrals in weighted integral metric. We prove direct and strong converse theorem in terms of the weighted functional.
Teodora Zapryanova
Copyright © 2013 Teodora Zapryanova. All rights reserved.

A Survey of Some Topics Related to Differential Operators
Wed, 18 Dec 2013 17:34:20 +0000
http://www.hindawi.com/journals/joper/2013/562963/
This paper is the result of investigations suggested by recent publications and completes the work of Huet, 2010. The topics, which are dealt with, concern some spaces of functions and properties of solutions of linear and nonlinear, stationary and evolution differential equations, namely, existence, spectral properties, resonances, singular perturbations, boundary layers, and inertial manifolds. They are presented in the alphabetical order. The aim of this document and of Huet, 2010, is to be a useful reference for (young) researchers in mathematics and applied sciences.
Denise Huet
Copyright © 2013 Denise Huet. All rights reserved.

A Fixed Point Theorem in Orbitally Complete Partially Ordered Metric Spaces
Wed, 18 Dec 2013 16:33:33 +0000
http://www.hindawi.com/journals/joper/2013/404573/
Let be a partially ordered set and be a mapping. We prove a fixed point theorem for the map satisfying a contractive condition in orbits, when is orbitally complete. Our result extends and generalizes the results of Samet et al. (2013) to partially ordered sets. Also, we generalize the results of Ran and Reurings (2004).
G. V. R. Babu, P. D. Sailaja, and K. T. Kidane
Copyright © 2013 G. V. R. Babu et al. All rights reserved.

Common Fixed Point Theorems for Conversely Commuting Mappings Using Implicit Relations
Sun, 08 Dec 2013 09:13:02 +0000
http://www.hindawi.com/journals/joper/2013/391474/
The object of this paper is to utilize the notion of conversely commuting mappings due to Lü (2002) and prove some common fixed point theorems in Menger spaces via implicit relations. We give some examples which demonstrate the validity of the hypotheses and degree of generality of our main results.
Sunny Chauhan and Huma Sahper
Copyright © 2013 Sunny Chauhan and Huma Sahper. All rights reserved.

Linear Isometries between Real Banach Algebras of Continuous ComplexValued Functions
Thu, 24 Oct 2013 13:13:31 +0000
http://www.hindawi.com/journals/joper/2013/506129/
Let and be compact Hausdorff spaces, and let
and be topological involutions on and , respectively. In 1991,
Kulkarni and Arundhathi characterized linear isometries from a
real uniform function algebra on (, ) onto a real uniform function
algebra on (, ) applying their Choquet boundaries and
showed that these mappings are weighted composition operators.
In this paper, we characterize all onto linear isometries and certain
into linear isometries between and
applying
the extreme points in the unit balls of and .
Davood Alimohammadi and Hadis Pazandeh
Copyright © 2013 Davood Alimohammadi and Hadis Pazandeh. All rights reserved.

Fibre Contraction Principle with respect to an Iterative Algorithm
Mon, 30 Sep 2013 13:31:23 +0000
http://www.hindawi.com/journals/joper/2013/408791/
We apply the fibre contraction principle in the case of a general iterative algorithm to approximate the fixed point of triangular operator using the admissible perturbation. A simple example and an application to a functional equation with parameter are given in order to illustrate the abstract results and to show the role of admissible perturbations.
MarcelAdrian Şerban
Copyright © 2013 MarcelAdrian Şerban. All rights reserved.

The QuasiLinear Operator Outer Generalized Inverse with Prescribed Range and Kernel in Banach Spaces
Sun, 04 Aug 2013 08:28:20 +0000
http://www.hindawi.com/journals/joper/2013/204587/
Let and be Banach spaces, and let be a bounded linear operator. In this paper, we first define and characterize the quasilinear operator (resp., out) generalized inverse (resp., ) for the operator , where and are homogeneous subsets. Then, we further investigate the perturbation problems of the generalized inverses and . The results obtained in this paper extend some wellknown results for linear operator generalized inverses with prescribed range and kernel.
Jianbing Cao and Yifeng Xue
Copyright © 2013 Jianbing Cao and Yifeng Xue. All rights reserved.

Some Properties of the Sequence Space
Wed, 26 Jun 2013 13:12:08 +0000
http://www.hindawi.com/journals/joper/2013/904838/
We introduce the sequence space defined by a MusielakOrlicz function . We also study some topological properties and prove some inclusion relations involving this space.
Kuldip Raj and Sunil K. Sharma
Copyright © 2013 Kuldip Raj and Sunil K. Sharma. All rights reserved.

Unified Metrical Common Fixed Point Theorems in 2Metric Spaces via an Implicit Relation
Thu, 20 Jun 2013 14:15:00 +0000
http://www.hindawi.com/journals/joper/2013/186910/
We prove some common fixed point theorems for two pairs of weakly compatible mappings in 2metric spaces via an implicit relation. As an application to our main result, we derive Bryant's type generalized fixed point theorem for four finite families of selfmappings which can be utilized to derive common fixed point theorems involving any finite number of mappings. Our results improve and extend a host of previously known results. Moreover, we study the existence of solutions of a nonlinear integral equation.
Sunny Chauhan, Mohammad Imdad, and Calogero Vetro
Copyright © 2013 Sunny Chauhan et al. All rights reserved.

SuzukiType Generalization of Chatterjea Contraction Mappings on
Complete Partial Metric Spaces
Wed, 12 Jun 2013 11:47:16 +0000
http://www.hindawi.com/journals/joper/2013/923843/
Motivated by Suzuki (2008), we prove a Suzukitype fixed point theorem employing Chatterjea contraction on partial metric spaces.
Mohammad Imdad and Ali Erduran
Copyright © 2013 Mohammad Imdad and Ali Erduran. All rights reserved.

Some Common Fixed Point Results for Rational Type Contraction Mappings in Complex Valued Metric Spaces
Mon, 03 Jun 2013 17:34:09 +0000
http://www.hindawi.com/journals/joper/2013/813707/
We prove some common fixed point theorems for two pairs of weakly compatible mappings satisfying a rational type contractive condition in the framework of complex valued metric spaces. The proved results generalize and extend some of the known results in the literature.
Sumit Chandok and Deepak Kumar
Copyright © 2013 Sumit Chandok and Deepak Kumar. All rights reserved.

Weighted Composition Operators from the Bloch Space and the Analytic Besov Spaces into the Zygmund Space
Sun, 19 May 2013 15:35:44 +0000
http://www.hindawi.com/journals/joper/2013/154029/
We provide several characterizations of the bounded and the compact weighted composition operators from the Bloch space and the analytic Besov spaces (with ) into the Zygmund space . As a special case, we show that the bounded (resp., compact) composition operators from , , and to coincide. In addition, the boundedness and the compactness of the composition operator can be characterized in terms of the boundedness (resp., convergence to 0, under the boundedness assumption of the operator) of the Zygmund norm of the powers of the symbol.
Flavia Colonna and Songxiao Li
Copyright © 2013 Flavia Colonna and Songxiao Li. All rights reserved.