Journal of Function Spaces
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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.

Contraction Mapping Theory and Approach to LMIBased Stability Criteria of TS Fuzzy Impulsive TimeDelays Integrodifferential Equations
Thu, 29 Dec 2016 14:06:11 +0000
http://www.hindawi.com/journals/jfs/2016/5035618/
In this paper, Banach fixed point theorem is employed to derive LMIbased exponential stability of impulsive TakagiSugeno (TS) fuzzy integrodifferential equations, originated from CohenGrossberg Neural Networks (CGNNs). As far as we know, Banach fixed point theorem is rarely employed to derive LMI criteria for TS fuzzy CGNNs, and this inspires our present work. It is worth mentioning that the conditions on the behavior functions are weaker than those of existing results, and the formulated contraction mapping and fixed point technique are different from those of previous literature. Even a corollary of our main result improves one of existing main results due to extending linear function to nonlinear function. Besides, the LMIbased criteria are programmable for computer MATLAB LMI toolbox. Moreover, an analytical table and a numerical example are presented to illustrate the advantage, feasibility, and effectiveness of the proposed methods.
Ruofeng Rao and Shouming Zhong
Copyright © 2016 Ruofeng Rao and Shouming Zhong. All rights reserved.

Certain Geometric Properties of Normalized Wright Functions
Tue, 27 Dec 2016 06:55:46 +0000
http://www.hindawi.com/journals/jfs/2016/1896154/
In this article, we find some geometric properties like starlikeness, convexity of order , closetoconvexity of order , and closetoconvexity of normalized Wright functions with respect to the certain functions. The sufficient conditions for the normalized Wright functions belonging to the classes and are the part of our investigations. We also obtain the conditions on normalized Wright function to belong to the Hardy space .
Mohsan Raza, Muhey U Din, and Sarfraz Nawaz Malik
Copyright © 2016 Mohsan Raza et al. All rights reserved.

On the Boundedness of Biparameter LittlewoodPaley Function
Thu, 22 Dec 2016 13:50:50 +0000
http://www.hindawi.com/journals/jfs/2016/3605639/
Let and let be the biparameter LittlewoodPaley function defined by = , , where is a nonconvolution kernel defined on . In this paper we show that the biparameter LittlewoodPaley function is bounded from to . This is done by means of probabilistic methods and by using a new averaging identity over good double Whitney regions.
Mingming Cao and Qingying Xue
Copyright © 2016 Mingming Cao and Qingying Xue. All rights reserved.

Matrix Quasinorms Induced by Maximal and Minimal Vector Norms
Thu, 15 Dec 2016 06:49:42 +0000
http://www.hindawi.com/journals/jfs/2016/5240218/
In the set of all vector norms in , there exist maximal and minimal complex norms which coincide with the real Euclidean norm in . The purpose of this paper is to introduce new quasinorms defined on complex matrices. These two matrix quasinorms are induced by maximal and minimal complex vector norms. We also prove the dual relation between these two quasinorms.
JongDo Park
Copyright © 2016 JongDo Park. All rights reserved.

Strong Convergence Theorems for an Implicit Iterative Algorithm for the Split Common Fixed Point Problem
Wed, 14 Dec 2016 13:19:23 +0000
http://www.hindawi.com/journals/jfs/2016/4093524/
The aim of this paper is to construct a novel implicit iterative algorithm for the split common fixed point problem for the demicontractive operators , , and , , where , and we obtain the sequence which strongly converges to a solution of this problem, and the solution satisfies the variational inequality. , , where denotes the set of all solutions of the split common fixed point problem.
Huimin He, Sanyang Liu, and Rudong Chen
Copyright © 2016 Huimin He et al. All rights reserved.

A New Nonlinear Contraction Principle in Partial Metric Spaces
Wed, 07 Dec 2016 05:54:54 +0000
http://www.hindawi.com/journals/jfs/2016/8404529/
We present a new nonlinear contraction principle on partial metric spaces and prove the existence of common fixed point. We also give some examples to show our results and apply our results to study the existence of common bounded solution of the system of functional equations.
Yi Zhang and Jiang Zhu
Copyright © 2016 Yi Zhang and Jiang Zhu. All rights reserved.

A New Topological Degree Theory for Perturbations of Demicontinuous Operators and Applications to Nonlinear Equations with Nonmonotone Nonlinearities
Mon, 05 Dec 2016 08:02:02 +0000
http://www.hindawi.com/journals/jfs/2016/3970621/
Let be a real reflexive locally uniformly convex Banach space with locally uniformly convex dual space . Let be maximal monotone of type (i.e., there exist and a nondecreasing function with such that for all , , and be linear, surjective, and closed such that is compact, and be a bounded demicontinuous operator. A new degree theory is developed for operators of the type . The surjectivity of can be omitted provided that is closed, is densely defined and selfadjoint, and , a real Hilbert space. The theory improves the degree theory of Berkovits and Mustonen for , where is bounded demicontinuous pseudomonotone. New existence theorems are provided. In the case when is monotone, a maximality result is included for and . The theory is applied to prove existence of weak solutions in of the nonlinear equation given by , ; , ; and , , where , , , , , is a nonempty, bounded, and open subset of with smooth boundary, and satisfy suitable growth conditions. In addition, a new existence result is given concerning existence of weak solutions for nonlinear wave equation with nonmonotone nonlinearity.
Teffera M. Asfaw
Copyright © 2016 Teffera M. Asfaw. All rights reserved.

TwoWeight Norm Inequality for the OneSided HardyLittlewood Maximal Operators in Variable Lebesgue Spaces
Mon, 05 Dec 2016 07:19:48 +0000
http://www.hindawi.com/journals/jfs/2016/1648281/
The authors establish the twoweight norm inequalities for the onesided HardyLittlewood maximal operators in variable Lebesgue spaces. As application, they obtain the twoweight norm inequalities of variable RiemannLiouville operator and variable Weyl operator in variable Lebesgue spaces on bounded intervals.
Caiyin Niu, Zongguang Liu, and Panwang Wang
Copyright © 2016 Caiyin Niu et al. All rights reserved.

Modeling Sampling in Tensor Products of Unitary Invariant Subspaces
Wed, 30 Nov 2016 06:19:48 +0000
http://www.hindawi.com/journals/jfs/2016/4573940/
The use of unitary invariant subspaces of a Hilbert space is nowadays a recognized fact in the treatment of sampling problems. Indeed, shiftinvariant subspaces of and also periodic extensions of finite signals are remarkable examples where this occurs. As a consequence, the availability of an abstract unitary sampling theory becomes a useful tool to handle these problems. In this paper we derive a sampling theory for tensor products of unitary invariant subspaces. This allows merging the cases of finitely/infinitely generated unitary invariant subspaces formerly studied in the mathematical literature; it also allows introducing the several variables case. As the involved samples are identified as frame coefficients in suitable tensor product spaces, the relevant mathematical technique is that of frame theory, involving both finite/infinite dimensional cases.
Antonio G. García, Alberto Ibort, and María J. MuñozBouzo
Copyright © 2016 Antonio G. García et al. All rights reserved.

About Some Families of Nonexpansive Mappings with respect to Renorming
Mon, 28 Nov 2016 12:10:56 +0000
http://www.hindawi.com/journals/jfs/2016/9310515/
We characterize the family of nonexpansive mappings which are invariant under renormings and we also compare the families of nonexpansive mappings under two equivalent norms.
Juan Rafael AcostaPortilla, Carlos Alberto HernándezLinares, and Víctor PérezGarcía
Copyright © 2016 Juan Rafael AcostaPortilla et al. All rights reserved.

Systems of Inequalities Characterizing Ring Homomorphisms
Thu, 17 Nov 2016 09:24:02 +0000
http://www.hindawi.com/journals/jfs/2016/8069104/
Assume that and are arbitrary mappings between two partially ordered rings and . We study a few systems of functional inequalities which characterize ring homomorphisms. For example, we prove that if and satisfy for all and , then and this mapping is a ring homomorphism. Moreover, we find two other systems for which we obtain analogous assertions.
Włodzimierz Fechner and Andrzej Olbryś
Copyright © 2016 Włodzimierz Fechner and Andrzej Olbryś. All rights reserved.

Corrigendum to “Filling Disks of Hayman Type of Meromorphic Functions”
Mon, 14 Nov 2016 11:18:05 +0000
http://www.hindawi.com/journals/jfs/2016/2131260/
Nan Wu and Zuxing Xuan
Copyright © 2016 Nan Wu and Zuxing Xuan. All rights reserved.

Complex Convexity of Orlicz Modular Sequence Spaces
Thu, 10 Nov 2016 12:48:00 +0000
http://www.hindawi.com/journals/jfs/2016/5917915/
The concepts of complex extreme points, complex strongly extreme points, complex strict convexity, and complex midpoint locally uniform convexity in general modular spaces are introduced. Then we prove that, for any Orlicz modular sequence space , is complex midpoint locally uniformly convex. As a corollary, is also complex strictly convex.
Lili Chen, Deyun Chen, and Yang Jiang
Copyright © 2016 Lili Chen et al. All rights reserved.

Argument Properties for a Class of Analytic Functions Involving Libera Transform
Thu, 03 Nov 2016 13:12:39 +0000
http://www.hindawi.com/journals/jfs/2016/8908705/
The purpose of this paper is to find sufficient argument properties, such that the images of some subclasses of functions by the Libera transform have bounded arguments.
Badr S. Alkahtani, Teodor Bulboacă, Rakesh Kumar, and Rubayyi Alqahtani
Copyright © 2016 Badr S. Alkahtani et al. All rights reserved.

A New Approach to the Study of Fixed Point Theorems with Distances via Functions
Tue, 01 Nov 2016 10:16:12 +0000
http://www.hindawi.com/journals/jfs/2016/6978439/
We introduce some new generalization of fixed point theorems in complete metric spaces endowed with distances via functions. Our results extend many of known fixed point theorems such as Reich type contraction, Geraghty contraction, MeirKeeler contraction, and contraction. In addition, the result and corollaries show that our approach has a constructive attitude and many known and unknown results can be constructed in such way.
Farzad Zarinfar, Farshid Khojasteh, and Seyyed Mansour Vaezpour
Copyright © 2016 Farzad Zarinfar et al. All rights reserved.

Boundedness of Type Calderón–Zygmund Operators and Commutators in the Generalized Weighted Morrey Spaces
Mon, 31 Oct 2016 11:17:32 +0000
http://www.hindawi.com/journals/jfs/2016/1309348/
We first introduce some new Morrey type spaces containing generalized Morrey space and weighted Morrey space as special cases. Then, we discuss the strongtype and weaktype estimates for a class of Calderón–Zygmund type operators in these new Morrey type spaces. Furthermore, the strongtype estimate and endpoint estimate of commutators formed by and are established. Also, we study related problems about twoweight, weaktype inequalities for and in the Morrey type spaces and give partial results.
Hua Wang
Copyright © 2016 Hua Wang. All rights reserved.

Solvability of Conjugate Boundary Value Problems with Integral Boundary Conditions at Resonance
Mon, 31 Oct 2016 05:57:25 +0000
http://www.hindawi.com/journals/jfs/2016/3454879/
We investigate a conjugate boundary value problem with integral boundary conditions. By using Mawhin continuation theorem, we study the solvability of this boundary value problem at resonance. It is shown that the boundary value problem , , , , , has at least one solution under some suitable conditions.
Qiao Sun and Yujun Cui
Copyright © 2016 Qiao Sun and Yujun Cui. All rights reserved.

A New Approach for the Approximations of Solutions to a Common Fixed Point Problem in Metric Fixed Point Theory
Thu, 27 Oct 2016 12:03:31 +0000
http://www.hindawi.com/journals/jfs/2016/6759320/
We provide sufficient conditions for the existence of a unique common fixed point for a pair of mappings , where is a nonempty set endowed with a certain metric. Moreover, a numerical algorithm is presented in order to approximate such solution. Our approach is different to the usual used methods in the literature.
Ishak Altun, Nassir Al Arifi, Mohamed Jleli, Aref Lashin, and Bessem Samet
Copyright © 2016 Ishak Altun et al. All rights reserved.