Journal of Function Spaces The latest articles from Hindawi © 2017 , Hindawi Limited . All rights reserved. Global Hölder Estimates via Morrey Norms for Hypoelliptic Operators with Drift Sun, 19 Feb 2017 00:00:00 +0000 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 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, Mizoguchi-Takahashi’s fixed point theorem, and some other well-known 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 We prove a new approach for some common fixed point results in complete -metric spaces for weakly increasing self-mappings 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 In this article, we give the boundedness conditions in terms of Zygmund-type 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 Explicit formulae for the -functional for the general couple , where is a compatible couple of quasi-normed 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 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. Shan-He Wu, Imran Abbas Baloch, and İmdat İşcan Copyright © 2017 Shan-He 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 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 Quasi-Variational Problems with -Prox-Regular Data in Banach Spaces Mon, 30 Jan 2017 00:00:00 +0000 In this paper, we propose an extension of quasi-equilibrium problems from the convex case to the nonconvex case and from Hilbert spaces to Banach spaces. The proposed problem is called quasi-variational 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 Segal-Bargmann Transform on Fractional Hermite-Sobolev Spaces Thu, 19 Jan 2017 00:00:00 +0000 Let and . We prove that the Segal-Bargmann transform is a bounded operator from fractional Hermite-Sobolev spaces to fractional Fock-Sobolev spaces . Hong Rae Cho, Hyunil Choi, and Han-Wool Lee Copyright © 2017 Hong Rae Cho et al. All rights reserved. Certain Subclasses of Multivalent Functions Defined by Higher-Order Derivative Tue, 17 Jan 2017 00:00:00 +0000 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 Calderón-Zygmund Operators on Nonhomogeneous Metric Measure Spaces Mon, 09 Jan 2017 09:29:28 +0000 Let be a nonhomogeneous metric measure space. In this paper, the boundedness for commutators generated by bilinear -type Calderón-Zygmund 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 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 matrix-valued 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 LMI-Based Stability Criteria of T-S Fuzzy Impulsive Time-Delays Integrodifferential Equations Thu, 29 Dec 2016 14:06:11 +0000 In this paper, Banach fixed point theorem is employed to derive LMI-based exponential stability of impulsive Takagi-Sugeno (T-S) fuzzy integrodifferential equations, originated from Cohen-Grossberg Neural Networks (CGNNs). As far as we know, Banach fixed point theorem is rarely employed to derive LMI criteria for T-S 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 LMI-based 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 In this article, we find some geometric properties like starlikeness, convexity of order , close-to-convexity of order , and close-to-convexity 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 Littlewood-Paley -Function Thu, 22 Dec 2016 13:50:50 +0000 Let and let be the biparameter Littlewood-Paley -function defined by = ,  ,   where is a nonconvolution kernel defined on . In this paper we show that the biparameter Littlewood-Paley 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 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. Jong-Do Park Copyright © 2016 Jong-Do 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 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 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 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 self-adjoint, 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. Two-Weight Norm Inequality for the One-Sided Hardy-Littlewood Maximal Operators in Variable Lebesgue Spaces Mon, 05 Dec 2016 07:19:48 +0000 The authors establish the two-weight norm inequalities for the one-sided Hardy-Littlewood maximal operators in variable Lebesgue spaces. As application, they obtain the two-weight norm inequalities of variable Riemann-Liouville 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 The use of unitary invariant subspaces of a Hilbert space is nowadays a recognized fact in the treatment of sampling problems. Indeed, shift-invariant 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. Muñoz-Bouzo 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 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 Acosta-Portilla, Carlos Alberto Hernández-Linares, and Víctor Pérez-García Copyright © 2016 Juan Rafael Acosta-Portilla et al. All rights reserved. Systems of Inequalities Characterizing Ring Homomorphisms Thu, 17 Nov 2016 09:24:02 +0000 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 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 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 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 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, Meir-Keeler 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 We first introduce some new Morrey type spaces containing generalized Morrey space and weighted Morrey space as special cases. Then, we discuss the strong-type and weak-type estimates for a class of Calderón–Zygmund type operators in these new Morrey type spaces. Furthermore, the strong-type estimate and endpoint estimate of commutators formed by and are established. Also, we study related problems about two-weight, weak-type 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 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 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.