Journal of Operators The latest articles from Hindawi © 2017 , Hindawi Limited . All rights reserved. Uncertainty Principles for the Dunkl-Wigner Transforms Tue, 27 Sep 2016 14:32:43 +0000 We prove a version of Heisenberg-type uncertainty principle for the Dunkl-Wigner transform of magnitude ; and we deduce a local uncertainty principle for this transform. Fethi Soltani Copyright © 2016 Fethi Soltani. All rights reserved. Fractals of Generalized -Hutchinson Operator in -Metric Spaces Thu, 28 Jul 2016 13:59:42 +0000 The aim of this paper is to construct a fractal with the help of a finite family of generalized -contraction mappings, a class of mappings more general than contraction mappings, defined in the setup of -metric space. Consequently, we obtain a variety of results for iterated function system satisfying a different set of contractive conditions. Our results unify, generalize, and extend various results in the existing literature. Talat Nazir, Sergei Silvestrov, and Xiaomin Qi Copyright © 2016 Talat Nazir et al. All rights reserved. Convergence Results for a Common Solution of a Finite Family of Equilibrium Problems and Quasi-Bregman Nonexpansive Mappings in Banach Space Thu, 24 Mar 2016 06:37:25 +0000 We introduce an iterative process for finding common fixed point of finite family of quasi-Bregman nonexpansive mappings which is a unique solution of some equilibrium problem. G. C. Ugwunnadi and Bashir Ali Copyright © 2016 G. C. Ugwunnadi and Bashir Ali. All rights reserved. Composition Operators from -Bloch Space to -Bloch Space on the Fourth Cartan-Hartogs Domains Mon, 26 Oct 2015 06:14:49 +0000 We obtain new generalized Hua’s inequality corresponding to , where denotes the fourth Cartan-Hartogs domain in . Furthermore, we introduce the weighted Bloch spaces on and apply our inequality to study the boundedness and compactness of composition operator from to for and . Jianbing Su and Chao Zhang Copyright © 2015 Jianbing Su and Chao Zhang. All rights reserved. Common Fixed Point Theorems of Greguš Type -Weak Contraction for -Weakly Commuting Mappings in 2-Metric Spaces Tue, 20 Oct 2015 11:59:37 +0000 The main purpose of this paper is to establish a common fixed point theorem for set valued mappings in 2-metric spaces by generalizing a theorem of Abd EL-Monsef et al. (2009) and Murthy and Tas (2009) by using -weak contraction in view of Greguš type condition for set valued mappings using -weakly commuting maps. Penumarthy Parvateesam Murthy and Uma Devi Patel Copyright © 2015 Penumarthy Parvateesam Murthy and Uma Devi Patel. All rights reserved. A Generalization of the Fuglede-Putnam Theorem to Unbounded Operators Wed, 25 Mar 2015 12:11:54 +0000 Let be unbounded normal operators in a Hilbert space and let be a closed operator whose domain contains the domain of , and the domain contains the domain of . It is shown that if , then . Fotios C. Paliogiannis Copyright © 2015 Fotios C. Paliogiannis. All rights reserved. On Ordinary, Linear -Difference Equations, with Applications to -Sato Theory Mon, 23 Feb 2015 09:47:49 +0000 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 We present a notion of frame multiresolution analysis on local fields of positive characteristic based on the theory of shift-invariant 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 shift-invariant space theory. Firdous A. Shah Copyright © 2015 Firdous A. Shah. All rights reserved. On Some Algebraic and Operator-Theoretic Properties of -Toeplitz Operators Tue, 06 Jan 2015 08:53:47 +0000 Based on a spectral problem raised by Barría and Halmos, a new class of Hardy-Hilbert space operators, containing the classical Toeplitz operators, is introduced, and some of their Toeplitz-like algebraic and operator-theoretic 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 The aim of this paper is to study a common fixed point theorem for three pairs of self-mappings 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 Ciric-Type Mappings Sun, 23 Nov 2014 00:00:00 +0000 In this short communication the concept of cyclic coupled Kannan-type contractions is generalized using a certain class of Ciric-type mappings. Xavier Udo-utun Copyright © 2014 Xavier Udo-utun. All rights reserved. New Results in the Startpoint Theory for Quasipseudometric Spaces Mon, 17 Nov 2014 12:25:58 +0000 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 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 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 2-particle systems. Victor Chulaevsky Copyright © 2014 Victor Chulaevsky. All rights reserved. On Vector-Valued Generalized Lorentz Difference Sequence Space Sun, 21 Sep 2014 07:10:25 +0000 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 We study some class of Dunkl -multiplier operators; and related to these operators we establish the Heisenberg-Pauli-Weyl uncertainty principle and Donoho-Stark’s uncertainty principle. We give also an application of the theory of reproducing kernels to the Tikhonov regularization on the Sobolev-Dunkl 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 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. Mihai-Gabriel Babuţia, Monteola Ilona Kovács, Mărioara Lăpădat, and Mihail Megan Copyright © 2014 Mihai-Gabriel Babuţia et al. All rights reserved. Cyclic Coupled Fixed Point Result Using Kannan Type Contractions Wed, 02 Jul 2014 11:32:45 +0000 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 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 Operator-Valued Riesz Means Sun, 18 May 2014 10:27:17 +0000 We characterize operator-valued 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 For a new -Kantorovich operator we establish direct approximation theorems in the space via Ditzian-Totik 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 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 finite-dimensional, 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. Sign-Changing Solutions for Nonlinear Operator Equations Thu, 06 Mar 2014 07:53:06 +0000 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 sign-changing 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 Self-Adjoint Operators Sun, 09 Feb 2014 15:48:06 +0000 The paper offers generalizations of the Jensen-Mercer inequality for self-adjoint operators and generally convex functions. The obtained results are applied to define the quasi-arithmetic operator means without using operator convexity. The version of the harmonic-geometric-arithmetic 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 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 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 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 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 Complex-Valued Functions Thu, 24 Oct 2013 13:13:31 +0000 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 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. Marcel-Adrian Şerban Copyright © 2013 Marcel-Adrian Şerban. All rights reserved.