Journal of Function Spaces
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A Subclass of Analytic Functions Related to Uniformly Convex and Starlike Functions
Tue, 23 May 2017 00:00:00 +0000
http://www.hindawi.com/journals/jfs/2017/9010964/
We investigate some subclasses of uniformly convex and uniformly starlike functions in open unit disc, which is generalization of class of convex and starlike functions. Some coefficient inequalities, a distortion theorem, the radii of closetoconvexity, and starlikeness and convexity for these classes of functions are studied. The behavior of these classes under a certain modified convolution operator is also discussed.
Saqib Hussain, Akhter Rasheed, Muhammad Asad Zaighum, and Maslina Darus
Copyright © 2017 Saqib Hussain et al. All rights reserved.

Approximation of Functions on a Square by Interpolation Polynomials at Vertices and Few Fourier Coefficients
Mon, 22 May 2017 00:00:00 +0000
http://www.hindawi.com/journals/jfs/2017/9376505/
For a bivariate function on a square, in general, its Fourier coefficients decay slowly, so one cannot reconstruct it by few Fourier coefficients. In this paper we will develop a new approximation scheme to overcome the weakness of Fourier approximation. In detail, we will use Lagrange interpolation and linear interpolation on the boundary of the square to derive a new approximation scheme such that we can use the values of the target function at vertices of the square and few Fourier coefficients to reconstruct the target function with very small error.
Zhihua Zhang
Copyright © 2017 Zhihua Zhang. All rights reserved.

A Note on Reducing Subspaces of Toeplitz Operator on the Weighted Analytic Function Spaces of the Bidisk
Sun, 07 May 2017 09:03:44 +0000
http://www.hindawi.com/journals/jfs/2017/5807909/
We discussed the reducing subspaces of Toeplitz operators on the weighted analytic function spaces of bidisk . The result shows that if the weight is of typeI, the structure of reducing subspaces of on is very simple.
Hongzhao Lin
Copyright © 2017 Hongzhao Lin. All rights reserved.

A New Subclass of Janowski Type Functions Associated with Ruscheweyh Derivative
Wed, 03 May 2017 00:00:00 +0000
http://www.hindawi.com/journals/jfs/2017/6095293/
We introduce and investigate a new subclass of analytic functions using Ruscheweyh derivative. We derive the coefficient inequalities and other interesting properties and characteristics for functions belonging to the general class, which we have introduced and studied in this article. We also observe that this class is preserved under the Bernardi integral transform.
Shahid Mahmood, Sarfraz Nawaz Malik, Saima Mustafa, and S. M. Jawwad Riaz
Copyright © 2017 Shahid Mahmood et al. All rights reserved.

The Embedding Theorem of an Prebarreled Module into Its Random Biconjugate Space
Sun, 30 Apr 2017 07:49:50 +0000
http://www.hindawi.com/journals/jfs/2017/8520797/
We first prove Mazur’s lemma in a random locally convex module endowed with the locally convex topology. Then, we establish the embedding theorem of an prebarreled random locally convex module, which says that if is an prebarreled random locally convex module such that has the countable concatenation property, then the canonical embedding mapping of onto is an linear homeomorphism, where is the strong random biconjugate space of under the locally convex topology.
Xia Zhang and Ming Liu
Copyright © 2017 Xia Zhang and Ming Liu. All rights reserved.

Existence and Multiplicity of Positive Solutions for SchrödingerKirchhoffPoisson System with Singularity
Sun, 23 Apr 2017 00:00:00 +0000
http://www.hindawi.com/journals/jfs/2017/5985962/
We study a singular SchrödingerKirchhoffPoisson system by the variational methods and the Nehari manifold and we prove the existence, uniqueness, and multiplicity of positive solutions of the problem under different conditions.
Mengjun Mu and Huiqin Lu
Copyright © 2017 Mengjun Mu and Huiqin Lu. All rights reserved.

Redefinition of Distance in Metric Spaces
Thu, 20 Apr 2017 00:00:00 +0000
http://www.hindawi.com/journals/jfs/2017/4168486/
The concept of distance was introduced in 2001; on the other hand, that of function was introduced by Lin and Du. Strongly inspired by function, we introduce a new concept, which is a very slight generalization of distance and is more natural than distance. So we could say that we redefine distance in some sense.
Tomonari Suzuki
Copyright © 2017 Tomonari Suzuki. All rights reserved.

Distortion Type Theorems for Functions in the Logarithmic Bloch Space
Sun, 16 Apr 2017 00:00:00 +0000
http://www.hindawi.com/journals/jfs/2017/8694516/
We establish distortion type theorems for locally schlicht functions and for functions having branch points satisfying a normalized Bloch condition in the closed unit ball of the logarithmic Bloch space . As a consequence of our results we have estimations of the schlicht radius for functions in these classes.
Armando J. GarcíaOrtíz, Milton del Castillo Lesmes Acosta, and Julio C. RamosFernández
Copyright © 2017 Armando J. GarcíaOrtíz et al. All rights reserved.

Commuting Toeplitz and Hankel Operators on Harmonic Dirichlet Spaces
Thu, 13 Apr 2017 00:00:00 +0000
http://www.hindawi.com/journals/jfs/2017/9627109/
On the harmonic Dirichlet space of the unit disk, the commutativity of Toeplitz and Hankel operators is studied. We obtain characterizations of commuting Toeplitz and Hankel operators and essentially commuting (semicommuting) Toeplitz and Hankel operators with general symbols.
Qian Ding, Yong Chen, and Yufeng Lu
Copyright © 2017 Qian Ding et al. All rights reserved.

On Similarity and Reducing Subspaces of the Shift plus Certain Weighted Volterra Operator
Thu, 13 Apr 2017 00:00:00 +0000
http://www.hindawi.com/journals/jfs/2017/8370139/
Let be an degree polynomial . Inspired by Sarason’s result, we introduce the operator defined by the multiplication operator plus the weighted Volterra operator on the Bergman space. We show that the operator is similar to on some Hilbert space . Then for , by using matrix manipulations, the reducing subspaces of the corresponding operator on the Bergman space are characterized.
Yucheng Li, Hao Chen, and Wenhua Lan
Copyright © 2017 Yucheng Li et al. All rights reserved.

Essential Norms of Volterra Type Operators between Zygmund Type Spaces
Tue, 11 Apr 2017 00:00:00 +0000
http://www.hindawi.com/journals/jfs/2017/1409642/
We investigate the boundedness of some Volterra type operators between Zygmund type spaces. Then, we give the essential norms of such operators in terms of , their derivatives, and the nth power of .
Shanli Ye and Caishu Lin
Copyright © 2017 Shanli Ye and Caishu Lin. All rights reserved.

Global Attractors of the Extensible Plate Equations with Nonlinear Damping and Memory
Tue, 04 Apr 2017 00:00:00 +0000
http://www.hindawi.com/journals/jfs/2017/4896161/
We prove in this paper the existence of a global attractor for the plate equations of Kirchhoff type with nonlinear damping and memory using the contraction function method.
Xiaobin Yao and Qiaozhen Ma
Copyright © 2017 Xiaobin Yao and Qiaozhen Ma. All rights reserved.

Toeplitz Operators, PseudoHomogeneous Symbols, and Moment Maps on the Complex Projective Space
Mon, 03 Apr 2017 07:19:41 +0000
http://www.hindawi.com/journals/jfs/2017/1730920/
Following previous works for the unit ball due to Nikolai Vasilevski, we define quasiradial pseudohomogeneous symbols on the projective space and obtain the corresponding commutativity results for Toeplitz operators. A geometric interpretation of these symbols in terms of moment maps is developed. This leads us to the introduction of a new family of symbols, extended pseudohomogeneous, that provide larger commutative Banach algebras generated by Toeplitz operators. This family of symbols provides new commutative Banach algebras generated by Toeplitz operators on the unit ball.
Miguel Antonio MoralesRamos, Raul QuirogaBarranco, and Armando SanchezNungaray
Copyright © 2017 Miguel Antonio MoralesRamos et al. All rights reserved.

Some New Fixed Point Theorems in Partial Metric Spaces with Applications
Wed, 29 Mar 2017 00:00:00 +0000
http://www.hindawi.com/journals/jfs/2017/1072750/
Recently, a number of fixed point theorems for contraction type mappings in partial metric spaces have been obtained by various authors. Most of these theorems can be obtained from the corresponding results in metric spaces. The purpose of this paper is to present certain fixed point results for single and multivalued mappings in partial metric spaces which cannot be obtained from the corresponding results in metric spaces. Besides discussing some useful examples, an application to Volterra type system of integral equations is also discussed.
Rajendra Pant, Rahul Shukla, H. K. Nashine, and R. Panicker
Copyright © 2017 Rajendra Pant et al. All rights reserved.

Function Spaces, Fixed Points, Approximations, and Applications
Mon, 27 Mar 2017 00:00:00 +0000
http://www.hindawi.com/journals/jfs/2017/2074917/
Giuseppe Marino, Filomena Cianciaruso, Nawab Hussain, and Enrique Llorens Fuster
Copyright © 2017 Giuseppe Marino et al. All rights reserved.

Statistical Convergence in Probabilistic Normed Spaces
Sun, 19 Mar 2017 00:00:00 +0000
http://www.hindawi.com/journals/jfs/2017/3154280/
The main objective of the study was to understand the notion of Λconvergence and to study the notion of probabilistic normed spaces. The study has also aimed to define the statistical Λconvergence and statistical ΛCauchy in PNspaces. The concepts of these approaches have been defined by some examples, which have demonstrated the concepts of statistical Λconvergence and statistical ΛCauchy in PNspaces. Previous studies have also been used to understand similar terminologies and notations for the extraction of outcomes.
M. Aldhaifallah, K. S. Nisar, H. M. Srivastava, and M. Mursaleen
Copyright © 2017 M. Aldhaifallah et al. All rights reserved.

A KAM Theorem for Lower Dimensional Elliptic Invariant Tori of Nearly Integrable Symplectic Mappings
Thu, 16 Mar 2017 00:00:00 +0000
http://www.hindawi.com/journals/jfs/2017/3719395/
This paper develops a new KAM theorem for a class of lower dimensional elliptic invariant tori of nearly integrable symplectic mappings with generating functions but without assuming any nondegenerate condition.
Shunjun Jiang
Copyright © 2017 Shunjun Jiang. All rights reserved.

Comment on “On the Frame Properties of Degenerate System of Sines”
Wed, 15 Mar 2017 09:27:36 +0000
http://www.hindawi.com/journals/jfs/2017/9257076/
The proof of Theorem 3.1 of the paper “On the Frame Properties of Degenerate System of Sines” (see (Bilalov and Guliyeva, 2012)) published earlier in this journal contains a gap; the reasoning given there to prove this theorem is not enough to state the validity of the mentioned theorem. To overcome this shortage we state the most general fact on the completeness of sine system which implies in particular the validity of this fact. It is shown in this note that the system , where is an exponential or trigonometric (cosine or sine) systems, becomes complete in the corresponding Lebesgue space or , respectively, whenever belongs to the corresponding Lebesgue space for all indices (under the evident natural condition ). It is also shown that the same conclusion does not remain valid for, in general, any complete or complete orthonormal system . Besides it, the largest class of functions for which the system is complete in space is determined.
Aydin Sh. Shukurov
Copyright © 2017 Aydin Sh. Shukurov. All rights reserved.

Global Hölder Estimates via Morrey Norms for Hypoelliptic Operators with Drift
Sun, 19 Feb 2017 00:00:00 +0000
http://www.hindawi.com/journals/jfs/2017/2805457/
Suppose that are left invariant real vector fields on the homogeneous group with being homogeneous of degree two and homogeneous of degree one. In the paper we study the hypoelliptic operator with drift of the kind where and is a constant matrix satisfying the elliptic condition on . By proving the boundedness of two integral operators on the Morrey spaces with two weights, we obtain global Hölder estimates for .
Yuexia Hou and Pengcheng Niu
Copyright © 2017 Yuexia Hou and Pengcheng Niu. All rights reserved.

Fixed Point Theorems for Manageable Contractions with Application to Integral Equations
Thu, 16 Feb 2017 07:40:56 +0000
http://www.hindawi.com/journals/jfs/2017/7943896/
In this paper we utilize the concept of manageable functions to define multivalued manageable contractions and prove fixed point theorems for such contractions. As applications we deduce certain fixed point theorems which generalize and improve Nadler’s fixed point theorem, MizoguchiTakahashi’s fixed point theorem, and some other wellknown results in the literature. Also, we give an illustrating example showing that our results are a proper generalization of Nadler’s theorem and provide an application to integral equations.
N. Hussain, I. Iqbal, Badriah A. S. Alamri, and M. A. Kutbi
Copyright © 2017 N. Hussain et al. All rights reserved.

New Approach for Common Fixed Point Theorems via Class Functions in Metric Spaces
Thu, 16 Feb 2017 07:40:10 +0000
http://www.hindawi.com/journals/jfs/2017/2624569/
We prove a new approach for some common fixed point results in complete metric spaces for weakly increasing selfmappings satisfying contractions via the concept of class functions. An example is also provided.
A. H. Ansari, M. A. Barakat, and H. Aydi
Copyright © 2017 A. H. Ansari et al. All rights reserved.

Boundedness of Fractional Oscillatory Integral Operators and Their Commutators in Vanishing Generalized Weighted Morrey Spaces
Thu, 16 Feb 2017 00:00:00 +0000
http://www.hindawi.com/journals/jfs/2017/3295376/
In this article, we give the boundedness conditions in terms of Zygmundtype integral inequalities for oscillatory integral operators and fractional oscillatory integral operators on the vanishing generalized weighted Morrey spaces. Moreover, we investigate corresponding commutators.
Bilal Çekiç and Ayşegül Çelik Alabalık
Copyright © 2017 Bilal Çekiç and Ayşegül Çelik Alabalık. All rights reserved.

General Holmstedt’s Formulae for the Functional
Tue, 14 Feb 2017 06:15:16 +0000
http://www.hindawi.com/journals/jfs/2017/4958073/
Explicit formulae for the functional for the general couple , where is a compatible couple of quasinormed spaces, are proved. As a consequence, the corresponding reiteration theorems are derived.
Irshaad Ahmed, Georgi E. Karadzhov, and Ali Raza
Copyright © 2017 Irshaad Ahmed et al. All rights reserved.

On Harmonically Preinvex Functions
Tue, 31 Jan 2017 09:09:19 +0000
http://www.hindawi.com/journals/jfs/2017/2148529/
We define a new generalized class of harmonically preinvex functions named harmonically preinvex functions, which includes harmonic preinvex functions, harmonic preinvex functions, harmonic preinvex functions, and convex functions as special cases. We also investigate the properties and characterizations of harmonically preinvex functions. Finally, we establish some integral inequalities to show the applications of harmonically preinvex functions.
ShanHe Wu, Imran Abbas Baloch, and İmdat İşcan
Copyright © 2017 ShanHe Wu et al. All rights reserved.

Fixed Point Theorems for Multivalued Nonself Almost Contractions in Banach Spaces Endowed with Graphs
Tue, 31 Jan 2017 00:00:00 +0000
http://www.hindawi.com/journals/jfs/2017/7053849/
In this paper, we prove some fixed point theorems for multivalued nonself almost contractions in Banach spaces with a directed graph and give some examples to illustrate our main results. The main results in this paper extend and generalize many known results in the literature therein.
J. Tiammee, P. Charoensawan, and S. Suantai
Copyright © 2017 J. Tiammee et al. All rights reserved.

Iterative Schemes for Nonconvex QuasiVariational Problems with ProxRegular Data in Banach Spaces
Mon, 30 Jan 2017 00:00:00 +0000
http://www.hindawi.com/journals/jfs/2017/8708065/
In this paper, we propose an extension of quasiequilibrium problems from the convex case to the nonconvex case and from Hilbert spaces to Banach spaces. The proposed problem is called quasivariational problem. We study the convergence of some algorithms to solutions of the proposed nonconvex problems in Banach spaces.
M. Bounkhel and Dj. Bounekhel
Copyright © 2017 M. Bounkhel and Dj. Bounekhel. All rights reserved.

Boundedness of the SegalBargmann Transform on Fractional HermiteSobolev Spaces
Thu, 19 Jan 2017 00:00:00 +0000
http://www.hindawi.com/journals/jfs/2017/9176914/
Let and . We prove that the SegalBargmann transform is a bounded operator from fractional HermiteSobolev spaces to fractional FockSobolev spaces .
Hong Rae Cho, Hyunil Choi, and HanWool Lee
Copyright © 2017 Hong Rae Cho et al. All rights reserved.

Certain Subclasses of Multivalent Functions Defined by HigherOrder Derivative
Tue, 17 Jan 2017 00:00:00 +0000
http://www.hindawi.com/journals/jfs/2017/5739196/
In this paper, we define and study some subclasses of multivalent analytic functions of higher order in the unit disc. These classes generalize some classes previously studied. We obtain coefficient inequalities, distortion theorems, extreme points, and integral mean inequalities. We derive some results as special cases.
Xiaofei Li, Deng Ding, Liping Xu, Chuan Qin, and Songbo Hu
Copyright © 2017 Xiaofei Li et al. All rights reserved.

Boundedness for Commutators of Bilinear Type CalderónZygmund Operators on Nonhomogeneous Metric Measure Spaces
Mon, 09 Jan 2017 09:29:28 +0000
http://www.hindawi.com/journals/jfs/2017/3690452/
Let be a nonhomogeneous metric measure space. In this paper, the boundedness for commutators generated by bilinear type CalderónZygmund operators and functions on is obtained.
Rulong Xie, Lisheng Shu, and Aiwen Sun
Copyright © 2017 Rulong Xie et al. All rights reserved.

A Method for a Class of Constrained Minimized Problems of Maximum Eigenvalue Functions
Mon, 02 Jan 2017 06:46:55 +0000
http://www.hindawi.com/journals/jfs/2017/5309698/
In this paper, we apply the algorithm to solve the constrained minimization problem of a maximum eigenvalue function which is the composite function of an affine matrixvalued mapping and its maximum eigenvalue. Here, we convert the constrained problem into its equivalent unconstrained problem by the exact penalty function. However, the equivalent problem involves the sum of two nonsmooth functions, which makes it difficult to apply algorithm to get the solution of the problem. Hence, our strategy first applies the smooth convex approximation of maximum eigenvalue function to get the approximate problem of the equivalent problem. Then the approximate problem, the space decomposition, and the Lagrangian of the object function at a given point will be addressed particularly. Finally, the algorithm will be presented to get the approximate solution of the primal problem by solving the approximate problem.
Wei Wang, Ming Jin, Shanghua Li, and Xinyu Cao
Copyright © 2017 Wei Wang et al. All rights reserved.