Journal of Function Spaces The latest articles from Hindawi Publishing Corporation © 2016 , Hindawi Publishing Corporation . All rights reserved. -Mixing Tuple of Operators on Banach Spaces Thu, 20 Oct 2016 09:47:17 +0000 We consider the question: what is the appropriate formulation of Godefroy-Shapiro criterion for tuples of operators? We also introduce a new notion about tuples of operators, -mixing, which lies between mixing and weakly mixing. We also obtain a sufficient condition to ensure a tuple of operators to be -mixing. Moreover, we study some new properties of -mixing operators on several concrete Banach spaces. Wei Wang, Yonglu Shu, and Xingzhong Wang Copyright © 2016 Wei Wang et al. All rights reserved. Application of Functionals in Creating Inequalities Wed, 19 Oct 2016 08:28:51 +0000 The paper deals with the fundamental inequalities for convex functions in the bounded closed interval. The main inequality includes convex functions and positive linear functionals extending and refining the functional form of Jensen’s inequality. This inequality implies the Jensen, Fejér, and, thus, Hermite-Hadamard inequality, as well as their refinements. Zlatko Pavić, Shanhe Wu, and Vedran Novoselac Copyright © 2016 Zlatko Pavić et al. All rights reserved. A Cone Measure of Noncompactness and Some Generalizations of Darbo’s Theorem with Applications to Functional Integral Equations Tue, 18 Oct 2016 11:11:38 +0000 We introduce the concept of cone measure of noncompactness and obtain some generalizations of Darbo’s theorem via this new concept. As an application, we establish an existence theorem for a system of integral equations. An example is also provided to illustrate the obtained result. Mohamed Jleli, Mohammad Mursaleen, Kishin Sadarangani, and Bessem Samet Copyright © 2016 Mohamed Jleli et al. All rights reserved. On a Numerical Radius Preserving Onto Isometry on Wed, 12 Oct 2016 14:03:49 +0000 We study a numerical radius preserving onto isometry on . As a main result, when is a complex Banach space having both uniform smoothness and uniform convexity, we show that an onto isometry on is numerical radius preserving if and only if there exists a scalar of modulus 1 such that is numerical range preserving. The examples of such spaces are Hilbert space and spaces for . Sun Kwang Kim Copyright © 2016 Sun Kwang Kim. All rights reserved. The Zeros of the Bergman Kernel for Some Reinhardt Domains Sun, 09 Oct 2016 13:20:41 +0000 We consider the Reinhardt domain We express the explicit closed form of the Bergman kernel for using the exponential generating function for the Stirling number of the second kind. As an application, we show that the Bergman kernel for has zeros if and only if . The study of the zeros of is reduced to some real polynomial with coefficients which are related to Bernoulli numbers. This result is a complete characterization of the existence of zeros of the Bergman kernel for for all positive integers . Jong-Do Park Copyright © 2016 Jong-Do Park. All rights reserved. Function Spaces, Approximation Theory, and Their Applications Tue, 04 Oct 2016 11:30:48 +0000 Carlo Bardaro, Ioan Rasa, Rudolf L. Stens, and Gianluca Vinti Copyright © 2016 Carlo Bardaro et al. All rights reserved. -Berezin Transform on the Weighted Bergman Spaces over the Polydisk Thu, 29 Sep 2016 16:57:15 +0000 We prove that every bounded linear operator on weighted Bergman space over the polydisk can be approximated by Toeplitz operators under some conditions. The main tool here is the so-called -Berezin transform. In particular, our results generalized the results of K. Nam and D. C. Zheng to the case of operators acting on . Ran Li and Yufeng Lu Copyright © 2016 Ran Li and Yufeng Lu. All rights reserved. A Subclass of Harmonic Functions Related to a Convolution Operator Thu, 29 Sep 2016 13:29:22 +0000 We introduce a new subclass of harmonic functions by using a certain linear operator. For this class we derive coefficient bounds, extreme points, and inclusion results and also show that this class is closed under an integral operator. Saqib Hussain, Akhter Rasheed, and Maslina Darus Copyright © 2016 Saqib Hussain et al. All rights reserved. A Review on Approximation Results for Integral Operators in the Space of Functions of Bounded Variation Mon, 26 Sep 2016 07:08:26 +0000 We present a review on recent approximation results in the space of functions of bounded variation for some classes of integral operators in the multidimensional setting. In particular, we present estimates and convergence in variation results for both convolution and Mellin integral operators with respect to the Tonelli variation. Results with respect to a multidimensional concept of -variation in the sense of Tonelli are also presented. Laura Angeloni and Gianluca Vinti Copyright © 2016 Laura Angeloni and Gianluca Vinti. All rights reserved. Convergence Theorems for Bregman K-Mappings and Mixed Equilibrium Problems in Reflexive Banach Spaces Sun, 18 Sep 2016 09:45:51 +0000 We introduce a new mixed equilibrium problem with a relaxed monotone mapping in a reflexive Banach space and prove the existence of solution of the equilibrium problem. Using Bregman distance, we introduce the concept of Bregman -mapping for a finite family of Bregman quasiasymptotically nonexpansive mappings and show the fixed point set of the Bregman -mapping is the set of common fixed points of . Using the Bregman -mapping, we introduce an iterative sequence for finding a common point in the set of a common fixed points of the finite family of Bregman quasiasymptotically nonexpansive mappings and the set of solutions of some mixed equilibrium problems. Strong convergence of the iterative sequence is proved. Our results generalise and improve many recent results in the literature. Bashir Ali and M. H. Harbau Copyright © 2016 Bashir Ali and M. H. Harbau. All rights reserved. A New Extension of Hardy-Hilbert’s Inequality in the Whole Plane Thu, 08 Sep 2016 07:02:55 +0000 By the use of weight coefficients and Hermite-Hadamard’s inequality, a new extension of Hardy-Hilbert’s inequality in the whole plane with multiparameters and a best possible constant factor is given. The equivalent forms, the operator expressions, and a few particular inequalities are considered. Bicheng Yang and Qiang Chen Copyright © 2016 Bicheng Yang and Qiang Chen. All rights reserved. A Half-Discrete Hilbert-Type Inequality in the Whole Plane with Multiparameters Wed, 07 Sep 2016 12:04:52 +0000 By the use of weight functions and technique of real analysis, a new half-discrete Hilbert-type inequality in the whole plane with multiparameters and the best possible constant factor is given. Furthermore, the equivalent forms, two kinds of particular inequalities, and the operator expressions with the norm are considered. Qunwei Ma, Bicheng Yang, and Leping He Copyright © 2016 Qunwei Ma et al. All rights reserved. Growth of Meromorphic Function Sharing Functions and Some Uniqueness Problems Mon, 05 Sep 2016 12:04:50 +0000 Estimating the growth of meromorphic solutions has been an important topic of research in complex differential equations. In this paper, we devoted to considering uniqueness problems by estimating the growth of meromorphic functions. Further, some examples are given to show that the conclusions are meaningful. Jianming Qi, Fanning Meng, and Wenjun Yuan Copyright © 2016 Jianming Qi et al. All rights reserved. Partial Differential Equations and Function Spaces Thu, 01 Sep 2016 10:34:00 +0000 Shijun Zheng, Simone Secchi, Huoxiong Wu, and Nguyen Cong Phuc Copyright © 2016 Shijun Zheng et al. All rights reserved. Mappings of Type Special Space of Sequences Sun, 28 Aug 2016 16:47:51 +0000 We give sufficient conditions on a special space of sequences defined by Mohamed and Bakery (2013) such that the finite rank operators are dense in the complete space of operators whose approximation numbers belong to this sequence space. Hence, under a few conditions, every compact operator would be approximated by finite rank operators. We apply it on the sequence space defined by Tripathy and Mahanta (2003). Our results match those known for -absolutely summable sequences of reals. Awad A. Bakery Copyright © 2016 Awad A. Bakery. All rights reserved. Some Fixed Points Results of Quadratic Functions in Split Quaternions Tue, 23 Aug 2016 09:47:34 +0000 We attempt to find fixed points of a general quadratic polynomial in the algebra of split quaternion. In some cases, we characterize fixed points in terms of the coefficients of these polynomials and also give the cardinality of these points. As a consequence, we give some simple examples to strengthen the infinitude of these points in these cases. We also find the roots of quadratic polynomials as simple consequences. Young Chel Kwun, Mobeen Munir, Waqas Nazeer, and Shin Min Kang Copyright © 2016 Young Chel Kwun et al. All rights reserved. Multiple Positive Solutions of Third-Order BVP with Advanced Arguments and Stieltjes Integral Conditions Mon, 22 Aug 2016 14:11:41 +0000 We consider the following third-order boundary value problem with advanced arguments and Stieltjes integral boundary conditions: and , where , , is continuous, for , and for . Under some suitable conditions, by applying a fixed point theorem due to Avery and Peterson, we obtain the existence of multiple positive solutions to the above problem. An example is also included to illustrate the main results obtained. Jian Chang, Jian-Ping Sun, and Ya-Hong Zhao Copyright © 2016 Jian Chang et al. All rights reserved. Adjoining a Constant Function to -Dimensional Chebyshev Space Wed, 17 Aug 2016 09:10:49 +0000 This paper is concerned with extending a Chebyshev system of continuous nonconstant functions into a set of functions including a constant function. Necessary and sufficient conditions for the new set to be a Chebyshev system are discussed and some results are obtained. Mansour Alyazidi-Asiry Copyright © 2016 Mansour Alyazidi-Asiry. All rights reserved. Approximation by First-Order Linear Differential Equations with an Initial Condition Mon, 15 Aug 2016 12:50:58 +0000 We will consider a continuously differentiable function satisfying the inequality for all and for some and some . Then we will approximate by a solution of the linear equation with . Jaiok Roh and Soon-Mo Jung Copyright © 2016 Jaiok Roh and Soon-Mo Jung. All rights reserved. Ulam’s Type Stability and Fixed Points Methods 2016 Mon, 08 Aug 2016 16:39:38 +0000 Janusz Brzdęk, Liviu Cădariu, Krzysztof Ciepliński, Ajda Fošner, Zbigniew Leśniak, and Bing Xu Copyright © 2016 Janusz Brzdęk et al. All rights reserved. Survey on Recent Ulam Stability Results Concerning Derivations Mon, 08 Aug 2016 10:00:13 +0000 This is a survey presenting the most significant results concerning approximate (generalized) derivations, motivated by the notions of Ulam and Hyers-Ulam stability. Moreover, the hyperstability and superstability issues connected with derivations are discussed. In the section before the last one we highlight some recent outcomes on stability of conditions defining (generalized) Lie derivations. Janusz Brzdęk, Liviu Cădariu, Krzysztof Ciepliński, Ajda Fošner, and Zbigniew Leśniak Copyright © 2016 Janusz Brzdęk et al. All rights reserved. On the Hyers-Ulam Stability of the First-Order Difference Equation Thu, 04 Aug 2016 12:24:30 +0000 We prove Hyers-Ulam stability of the first-order difference equation of the form , where is a given function with some moderate features. Moreover, we introduce some conditions for the function under which the difference equation is not stable in the sense of Hyers and Ulam. Soon-Mo Jung and Young Woo Nam Copyright © 2016 Soon-Mo Jung and Young Woo Nam. All rights reserved. On the Theory of Multilinear Singular Operators with Rough Kernels on the Weighted Morrey Spaces Thu, 04 Aug 2016 12:22:53 +0000 We study some multilinear operators with rough kernels. For the multilinear fractional integral operators and the multilinear fractional maximal integral operators , we obtain their boundedness on weighted Morrey spaces with two weights when or . For the multilinear singular integral operators and the multilinear maximal singular integral operators , we show they are bounded on weighted Morrey spaces with two weights if and bounded on weighted Morrey spaces with one weight if for . Sha He and Xiangxing Tao Copyright © 2016 Sha He and Xiangxing Tao. All rights reserved. Explicit Bounds and Sharp Results for the Composition Operators Preserving the Exponential Class Wed, 03 Aug 2016 14:11:14 +0000 Let be a quasiconformal mapping whose Jacobian is denoted by and let be the space of exponentially integrable functions on . We give an explicit bound for the norm of the composition operator : and, as a related question, we study the behaviour of the norm of in the exponential class. The property of is the counterpart in higher dimensions of the area distortion formula due to Astala in the plane and it is the key tool to prove the sharpness of our results. Fernando Farroni and Raffaella Giova Copyright © 2016 Fernando Farroni and Raffaella Giova. All rights reserved. On the Stability of Alternative Additive Equations in Multi--Normed Spaces Mon, 01 Aug 2016 07:19:39 +0000 We introduce the notion of multi--normed space () and study the stability of the alternative additive functional equation of two forms in this type of space. Xiuzhong Yang, Jing Ma, and Guofen Liu Copyright © 2016 Xiuzhong Yang et al. All rights reserved. Fixed Point Theorems for Generalized Mizoguchi-Takahashi Graphic Contractions Sun, 31 Jul 2016 13:48:11 +0000 Remarkable feature of contractions is associated with the concept Mizoguchi-Takahashi function. For the purpose of extension and modification of classical ideas related with Mizoguchi-Takahashi contraction, we define generalized Mizoguchi-Takahashi -contractions and establish some generalized fixed point theorems regarding these contractions in this paper. Some applications to the construction of a fixed point of multivalued mappings in -chainable metric space are also discussed. Nawab Hussain, Jamshaid Ahmad, and Marwan Amin Kutbi Copyright © 2016 Nawab Hussain et al. All rights reserved. Existence Results for Fuzzy Partial Differential Inclusions Sun, 31 Jul 2016 06:00:18 +0000 We discuss the existence of solution of a certain type of fuzzy partial differential inclusions with local conditions of integral types. Nayyar Mehmood and Akbar Azam Copyright © 2016 Nayyar Mehmood and Akbar Azam. All rights reserved. New Inner Product Quasilinear Spaces on Interval Numbers Tue, 26 Jul 2016 14:42:05 +0000 Primarily we examine the new example of quasilinear spaces, namely, “ interval space.” We obtain some new theorems and results related to this new quasilinear space. After giving some new notions of quasilinear dependence-independence and basis on quasilinear functional analysis, we obtain some results on interval space related to these concepts. Secondly, we present , and quasilinear spaces and we research some algebraic properties of these spaces. We obtain some new results and provide an important contribution to the improvement of quasilinear functional analysis. Hacer Bozkurt and Yılmaz Yilmaz Copyright © 2016 Hacer Bozkurt and Yılmaz Yilmaz. All rights reserved. Riesz Transform Characterization of Weighted Hardy Spaces Associated with Schrödinger Operators Tue, 26 Jul 2016 13:45:18 +0000 We characterize the weighted local Hardy spaces related to the critical radius function and weights by localized Riesz transforms ; in addition, we give a characterization of weighted Hardy spaces via Riesz transforms associated with Schrödinger operator , where is a Schrödinger operator on () and is a nonnegative function satisfying the reverse Hölder inequality. Hua Zhu Copyright © 2016 Hua Zhu. All rights reserved. Stability of a Quartic Functional Equation in Restricted Domains Tue, 26 Jul 2016 10:03:53 +0000 Let be a real normed space and a Banach space and . We prove the Ulam-Hyers stability theorem for the quartic functional equation in restricted domains. As a consequence we consider a measure zero stability problem of the above inequality when . Jaeyoung Chung and Yu-Min Ju Copyright © 2016 Jaeyoung Chung and Yu-Min Ju. All rights reserved.