Journal of Operators http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2014 , Hindawi Publishing Corporation . 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 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 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 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 http://www.hindawi.com/journals/joper/2014/382364/ 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 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 Complex-Valued 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. Marcel-Adrian Şerban Copyright © 2013 Marcel-Adrian Şerban. All rights reserved. The Quasi-Linear 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 quasi-linear 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 well-known 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 Musielak-Orlicz 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 2-Metric 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 2-metric 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 self-mappings 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. Suzuki-Type 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 Suzuki-type 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. Remarks on Some Recent Coupled Coincidence Point Results in Symmetric -Metric Spaces Thu, 16 May 2013 10:52:45 +0000 http://www.hindawi.com/journals/joper/2013/290525/ We use a method of reducing coupled coincidence point results in (ordered) symmetric -metric spaces to the respective results for mappings with one variable, even obtaining (in some cases) more general theorems. Our results generalize, extend, unify, and complement recent coupled coincidence point theorems in this frame, established by Cho et al. (2012), Aydi et al. (2011), and Choudhury and Maity (2011). Also, by using our method several recent tripled coincidence point results in ordered symmetric -metric spaces can be reduced to the coincidence point results with one variable. Stojan Radenović Copyright © 2013 Stojan Radenović. All rights reserved. Evolution of the Minimax Inequality of Ky Fan Thu, 09 May 2013 11:53:02 +0000 http://www.hindawi.com/journals/joper/2013/124962/ There are quite a few generalizations or applications of the 1984 minimax inequality of Ky Fan compared with his original 1972 minimax inequality. In a certain sense, the relationship between the 1984 inequality and several hundreds of known generalizations of the original 1972 inequality has not been recognized for a long period. Hence, it would be necessary to seek such relationship. In this paper, we give several generalizations of the 1984 inequality and some known applications in order to clarify the close relationship among them. Some new types of minimax inequalities are added. Sehie Park Copyright © 2013 Sehie Park. All rights reserved. A Generalization of Prešić Type Mappings in Metric-Like Spaces Mon, 22 Apr 2013 11:20:19 +0000 http://www.hindawi.com/journals/joper/2013/368501/ We generalize the result of Prešić in metric-like spaces by proving some common fixed point theorems for Prešić type mappings in metric-like spaces. An example is given which shows that the generalization is proper. Satish Shukla and Brian Fisher Copyright © 2013 Satish Shukla and Brian Fisher. All rights reserved. On -Tupled Coincidence Point Results in Metric Spaces Sun, 17 Mar 2013 13:31:13 +0000 http://www.hindawi.com/journals/joper/2013/532867/ We prove some n-tupled coincidence point results whenever n is even. We give here several new definitions like n-tupled fixed point, n-tupled coincidence point, and so forth. The main result is supported with the aid of an illustrative example. Mohammad Imdad, Ahmed H. Soliman, Binayak S. Choudhury, and Pradyut Das Copyright © 2013 Mohammad Imdad et al. All rights reserved.