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In the case of oscillatory potentials, we give sufficient conditions for the oscillation of the forced nonlinear second order differential equations with delayed argument in the form x″(t)+q(t)x(τ(t))γsgnx(τ(t))=f(t) in the linear (γ=1) and the superlinear (γ>1) cases. [Copyright &y& Elsevier]

In this paper, we study the least squares estimator for sublinear expectations. Under some mild assumptions, we prove the existence and uniqueness of the least squares estimator. The relationship between the least squares estimator and the conditional coherent risk measure (resp. the conditional g -expectation) is also explored. Then some characterizations of the least squares estimator are given. [ABSTRACT FROM AUTHOR]

In this paper, we prove nonexistence of positive supersolutions of a semilinear equation − div ( A ( x ) ∇ u ) + b ( x ) ⋅ ∇ u = f ( u ) in exterior domains in R n ( n ≥ 3 ), where A ( x ) is bounded and uniformly elliptic, b ( x ) = O ( | x | − 1 ) , div b = 0 and f is a continuous and positive function in ( 0 , ∞ ) satisfying f ( u ) ∼ u q as u → 0 with q ≤ n / ( n − 2 ) . Furthermore, we investigate general conditions on b and f for nonexistence of positive supersolutions. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we revisit elliptic estimates invariant under domain expansion. We improve the invariant elliptic estimates in the previous paper [Y. Cho, T. Ozawa, Y. Shim, Calc. Var. PDE 34 (2009) 321–339] via gradient estimate and discuss an application to the Lamé system. [Copyright &y& Elsevier]

Abstract: The paper deals with the equality problem of quasi-arithmetic and Lagrangian means which is to determine all pairs of continuous strictly monotone functions such that, for all , holds. The main result of the paper shows that there are 6 different cases of equality. [Copyright &y& Elsevier]

Abstract: In this paper, we will prove some uniqueness theorems of meromorphic functions whose derivatives share four distinct small functions. The results in this paper improve those given by R. Nevanlinna, L. Yang, G.D. Qiu, and other authors. An example is provided to show that the results in this paper are best possible. [Copyright &y& Elsevier]

Abstract: In this paper the concept of a contraction for multi-valued mappings in a metric space is introduced and the existence theorems for fixed points of such contractions in a complete metric space are proved. Presented results generalize and improve the recent results of Y. Feng, S. Liu [Y. Feng, S. Liu, Fixed point theorems for multi-valued contractive mappings and multi-valued Caristi type mappings, J. Math. Anal. Appl. 317 (2006) 103–112], D. Klim, D. Wardowski [D. Klim, D. Wardowski, Fixed point theorems for set-valued contractions in complete metric spaces, J. Math. Anal. Appl. 334 (2007) 132–139] and several others. The method used in the proofs of our results is new and is simpler than methods used in the corresponding papers. Two examples are given to show that our results are genuine generalization of the results of Feng and Liu and Klim and Wardowski. [Copyright &y& Elsevier]

Abstract: In this paper, the authors consider the limiting problem of the drift-diffusion-Poisson model for semiconductors. Different from previous papers, the model considered involve some special doping profiles D which have the property that the function is allowed to have a jump-discontinuity and sign changing property but is required to be Lipschitz continuous. The existence, uniqueness and large-time asymptotic behavior of the global (in time) solutions are given. [Copyright &y& Elsevier]

Abstract: Basis problems for self-adjoint matrix valued functions are studied. We suggest a new and nonstandard method to solve basis problems both in finite and infinite dimensional spaces. Although many results in this paper are given for operator functions in infinite dimensional Hilbert spaces, but to demonstrate practicability of this method and to present a full solution of basis problems, in this paper we often restrict ourselves to matrix valued functions which generate Rayleigh systems on the n-dimensional complex space . The suggested method is an improvement of an approach given recently in our paper [M. Hasanov, A class of nonlinear equations in Hilbert space and its applications to completeness problems, J. Math. Anal. Appl. 328 (2007) 1487–1494], which is based on the extension of the resolvent of a self-adjoint operator function to isolated eigenvalues and the properties of quadratic forms of the extended resolvent. This approach is especially useful for nonanalytic and nonsmooth operator functions when a suitable factorization formula fails to exist. [Copyright &y& Elsevier]

Abstract: In this paper, using proximal-point mapping technique of P-η-accretive mapping and the property of the fixed-point set of set-valued contractive mappings, we study the behavior and sensitivity analysis of the solution set of a parametric generalized implicit quasi-variational-like inclusion involving P-η-accretive mapping in real uniformly smooth Banach space. Further, under suitable conditions, we discuss the Lipschitz continuity of the solution set with respect to the parameter. The technique and results presented in this paper can be viewed as extension of the techniques and corresponding results given in [R.P. Agarwal, Y.-J. Cho, N.-J. Huang, Sensitivity analysis for strongly nonlinear quasi-variational inclusions, Appl. Math. Lett. 13 (2002) 19–24; S. Dafermos, Sensitivity analysis in variational inequalities, Math. Oper. Res. 13 (1988) 421–434; X.-P. Ding, Sensitivity analysis for generalized nonlinear implicit quasi-variational inclusions, Appl. Math. Lett. 17 (2) (2004) 225–235; X.-P. Ding, Parametric completely generalized mixed implicit quasi-variational inclusions involving h-maximal monotone mappings, J. Comput. Appl. Math. 182 (2) (2005) 252–269; X.-P. Ding, C.L. Luo, On parametric generalized quasi-variational inequalities, J. Optim. Theory Appl. 100 (1999) 195–205; Z. Liu, L. Debnath, S.M. Kang, J.S. Ume, Sensitivity analysis for parametric completely generalized nonlinear implicit quasi-variational inclusions, J. Math. Anal. Appl. 277 (1) (2003) 142–154; R.N. Mukherjee, H.L. Verma, Sensitivity analysis of generalized variational inequalities, J. Math. Anal. Appl. 167 (1992) 299–304; M.A. Noor, Sensitivity analysis framework for general quasi-variational inclusions, Comput. Math. Appl. 44 (2002) 1175–1181; M.A. Noor, Sensitivity analysis for quasivariational inclusions, J. Math. Anal. Appl. 236 (1999) 290–299; J.Y. Park, J.U. Jeong, Parametric generalized mixed variational inequalities, Appl. Math. Lett. 17 (2004) 43–48]. [Copyright &y& Elsevier]

Abstract: In this paper, we deal with the problem of uniqueness and weighted sharing of two meromorphic functions with their first derivatives having the same fixed points with the same multiplicities. The results in this paper improve those given by K. Tohge, Xiao-Min Li and Hong-Xun Yi. [Copyright &y& Elsevier]

Abstract: The paper introduces a new approach to dynamic modeling, using the variation principle, applied to a functional on trajectories of a controlled random process, and its connection to the process'' information functional. In [V.S. Lerner, Dynamic approximation of a random information functional, J. Math. Anal. Appl. 327 (1) (2007) 494–514, available online 5-24-06], we presented the information path functional with the Lagrangian, determined by the parameters of a controlled stochastic equation. In this paper, the solution to the path functional''s variation problem provides both a dynamic model of a random process and the model''s optimal control, which allows us to build a two-level information model with a random process at the microlevel and a dynamic process at the macrolevel. A wide class of random objects, modeled by the Markov diffusion process and a common structure of the process'' information functional, leads to a universal information structure of the dynamic model, which is specified and identified on a particular object with the applied optimal control functions. The developed mathematical formalism, based on classical methods, is aimed toward the solution of problems identification, combined with an optimal control synthesis, which is practically implemented and also demonstrated in the paper''s example. [Copyright &y& Elsevier]

Abstract: In this paper, by means of a series of counterexamples, we study in a systematic way the relationships among (pseudo, quasi) α-preinvexity, (strict, strong, pseudo, quasi) α-invexity and (strict, strong, pseudo, quasi) αη-monotonicity. Results obtained in this paper can be viewed as a refinement and improvement of the results of Noor and Noor [M.A. Noor, K.I. Noor, Some characterizations of strongly preinvex functions, J. Math. Anal. Appl. 316 (2006) 697–706]. [Copyright &y& Elsevier]

Abstract: In this paper we prove the existence of a solution to the scalar equilibrium problem in generalized convex space. As applications, we derive results on the best approximations and simultaneous approximations. The results of this paper generalize some known results in the literature. [Copyright &y& Elsevier]

Abstract: The concept of weak contraction from the case of single-valued mappings is extended to multi-valued mappings and then corresponding convergence theorems for the Picard iteration associated to a multi-valued weak contraction are obtained. The main results in this paper extend, improve and unify a multitude of classical results in the fixed point theory of single and multi-valued contractive mappings and also improve recent results from the paper [P.Z. Daffer, H. Kaneko, Fixed points of generalized contractive multi-valued mappings, J. Math. Anal. Appl. 192 (1995), 655–666]. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce a class of P-η-accretive mappings, an extension of η-m-accretive mappings [C.E. Chidume, K.R. Kazmi, H. Zegeye, Iterative approximation of a solution of a general variational-like inclusion in Banach spaces, Int. J. Math. Math. Sci. 22 (2004) 1159–1168] and P-accretive mappings [Y.-P. Fang, N.-J. Huang, H-accretive operators and resolvent operator technique for solving variational inclusions in Banach spaces, Appl. Math. Lett. 17 (2004) 647–653], in real Banach spaces. We prove some properties of P-η-accretive mappings and give the notion of proximal-point mapping, termed as P-η-proximal-point mapping, associated with P-η-accretive mapping. Further, using P-η-proximal-point mapping technique, we prove the existence of solution and discuss the convergence analysis of iterative algorithm, for multi-valued variational-like inclusions in real Banach space. The theorems presented in this paper extend and improve many known results in the literature. [Copyright &y& Elsevier]

Abstract: In this paper we complete a distributional Fourier analysis developed by Howell in a serie of papers. We investigate convolution operators in the corresponding distribution spaces. [Copyright &y& Elsevier]

Abstract: In this paper, we suggest and analyze a new inexact proximal point method for solving general variational inequalities, which can be considered as an implicit predictor–corrector method. An easily measurable error term is proposed with further relaxed error bound and an optimal step length is obtained by maximizing the profit-function and is dependent on the previous points. Our results include several known and new techniques for solving variational inequalities and related optimization problems. Results obtained in this paper can be viewed as an important improvement and refinement of the previously known results. Preliminary numerical experiments are included to illustrate the advantage and efficiency of the proposed method. [Copyright &y& Elsevier]

Abstract: In the first part of this paper, we introduce the notions of upper weight, lower weight and weight of subsequences of natural numbers and investigate some new estimations about Banach limits by using some results from Sucheston [L. Sucheston, On existence of finite invariant measures, Math. Z. 86 (1964) 327–336; L. Sucheston, Banach limit, Amer. Math. Monthly 74 (1967) 308–311]. In the second part of this paper, we study the connections between weights and densities of subsequences of natural numbers, and give a familiar formula to find some values of Banach limits on almost convergent sequences. [Copyright &y& Elsevier]

Abstract: In this paper we investigate the distributional Chébli–Trimèche transforms. We use the so-called kernel method and we are inspired by the papers of Dube and Pandey [L.S. Dube, J.N. Pandey, On the Hankel transform of distributions, Tôhoku Math. J. 27 (1975) 337–354] and Koh and Zemanian [E.L. Koh, A.H. Zemanian, The complex Hankel and I-transformations of generalized functions, SIAM J. Appl. Math. 16 (1968) 945–957] about distributional Hankel transforms. We note that our procedure, supported in a representation of the elements in the corresponding dual spaces, is simpler than the methods described in the above mentioned papers. Some applications of our distributional theory are presented. [Copyright &y& Elsevier]

Abstract: The purpose of this paper is to study the weak and strong convergence of implicit iteration process with errors to a common fixed point for a finite family of asymptotically nonexpansive mappings and nonexpansive mappings in Banach spaces. The results presented in this paper extend and improve the corresponding results of [H. Bauschke, The approximation of fixed points of compositions of nonexpansive mappings in Hilbert space, J. Math. Anal. Appl. 202 (1996) 150–159; B. Halpern, Fixed points of nonexpansive maps, Bull. Amer. Math. Soc. 73 (1967) 957–961; P.L. Lions, Approximation de points fixes de contractions, C. R. Acad. Sci. Paris, Ser. A 284 (1977), 1357–1359; S. Reich, Strong convergence theorems for resolvents of accretive operators in Banach spaces, J. Math. Anal. Appl. 75 (1980) 287–292; Z.H. Sun, Strong convergence of an implicit iteration process for a finite family of asymptotically quasi-nonexpansive mappings, J. Math. Anal. Appl. 286 (2003) 351–358; R. Wittmann, Approximation of fixed points of nonexpansive mappings, Arch. Math. 58 (1992) 486–491; H.K. Xu, M.G. Ori, An implicit iterative process for nonexpansive mappings, Numer. Funct. Anal. Optimiz. 22 (2001) 767–773; Y.Y. Zhou, S.S. Chang, Convergence of implicit iterative process for a finite family of asymptotically nonexpansive mappings in Banach spaces, Numer. Funct. Anal. Optimiz. 23 (2002) 911–921]. [Copyright &y& Elsevier]

Abstract: In this paper and in a forthcoming one, we study difference equations in of the types which are linked to families of conics, cubics and quartics, respectively. These equations generalize Lyness'' one studied in several papers, whose behavior was completely elucidated in [G. Bastien, M. Rogalski, in press] through methods which are transposed in the present paper for the study of (1) and (2), and in the forthcoming one for (3). In particular we prove in the present paper a form of chaotic behavior for solutions of difference equations (1) and (2), and find all the possible periods for these solutions. [Copyright &y& Elsevier]

In this paper we generalize a version of the classical Calderón–Zygmund theorem on principle value integrals in generalized Lebesgue spaces proved in [J. Reine Angew. Math. 563 (2003) 197–220], to kernels, which do not satisfy standard estimates on . This result will be used in part II of this paper to prove the classical theorem on halfspace estimates of Agmon, Douglis, and Nirenberg [Comm. Pure Appl. Math. 12 (1959) 623–727] for generalized Lebesgue spaces . [Copyright &y& Elsevier]

The paper presents a formula for the γ-interior of a set under special conditions for γ :expX→expX, more general than those in the previous paper [Acta Math. Hungar. 80 (1998) 89–93]. There are also some applications. [Copyright &y& Elsevier]

In this paper, we first establish collective fixed points theorems for a family of multivalued maps with or without assuming that the product of these multivalued maps is Φ-condensing. As an application of our collective fixed points theorem, we derive the coincidence theorem for two families of multivalued maps defined on product spaces. Then we give some existence results for maximal elements for a family of LS-majorized multivalued maps whose product is Φ-condensing. We also prove some existence results for maximal elements for a family of multivalued maps which are not LS-majorized but their product is Φ-condensing. As applications of our results, some existence results for equilibria of abstract economies are also derived. The results of this paper are more general than those given in the literature. [Copyright &y& Elsevier]

We consider the null controllability problem for thermoelastic plates, defined on a two dimensional domain Ω, and subject to hinged, clamped or free boundary conditions. The uncontrolled partial differential equation system generates an analytic semigroup on the space of finite energy. Consequently, the concept of null controllability is indeed appropriate for consideration here. It is shown that all finite energy states can be driven to zero by means of just one L2((0,T)×Ω) control be it either mechanical or thermal. The singularity, as T↓0, of the associated minimal energy function is the main object studied in the paper. Singularity and blow-up rates for minimal energy function are not only of interest in their own right but are also of critical importance in Stochastic PDEs. In this paper, we establish the optimal blow-up rate O(T-5/2) for this function. It is shown that the rate of singularity is the same as for finite-dimensional truncations of the model. In view of sharp estimates available in the finite dimensional setting [Math. Control Signals Systems 9 (1997) 327], the singularity rates provided in this paper are optimal. [Copyright &y& Elsevier]

Wavelets of Haar type of higher order m on self-similar fractals were introduced by the author in J. Fourier Anal. Appl. 4 (1998) 329–340. These are piecewise polynomials of degree m instead of piecewise constants. It was shown that for certain totally disconnected fractals, spaces of functions defined on the fractal may be characterized by means of the magnitude of the wavelet coefficients of the functions. In this paper, the study of these wavelets is continued. It is shown that also in the case when the fractals are not totally disconnected, the wavelets can be used to study regularity properties of functions. In particular, the self-similar sets considered can be, e.g., an interval in R or a cube in Rn. It turns out that it is natural to use Haar wavelets of higher order also in these classical cases, and many of the results in the paper are new also for these sets. [Copyright &y& Elsevier]

The idea of statistical convergence was first introduced by Fast (1951) but the rapid developments were started after the papers of Sˇala´t (1980) and Fridy (1985). Now a days it has become one of the most active area of research in the field of summability. In this paper we define and study statistical analogue of convergence and Cauchy for double sequences. We also establish the relation between statistical convergence and strongly Cesa`ro summable double sequences. [Copyright &y& Elsevier]

This paper is concerned with a time-periodic reaction–diffusion equation. It is known that typical trajectories approach periodic solutions with possibly longer period than that of the equation. Such solutions are called subharmonic solutions. In this paper, for any domain Ω, time-period τ>0 and integer n⩾2, we construct an example of a time-periodic reaction–diffusion equation on Ω with a minimal period τ which possesses a stable solution of minimal period nτ. [Copyright &y& Elsevier]

Three extremal problems for trigonometric polynomials are studied in this paper. The first was initiated by Maiorov. It relates to the trigonometric polynomials with n nonzero harmonics. The Lp-norm of the Weyl derivative is compared with the Lq-norm of the polynomial. The other two problems have appeared in the recent paper by Oswald. They deal with the polynomials of degree n. The minimum of Lp-norm with respect to the choice of phases is compared with lq-norm of its coefficients. [Copyright &y& Elsevier]

Different from the existing mathematical models for switched systems, where the switching from one subsystem to another subsystem is finished instantly, in this paper it is assumed that the switching is a transfer process. Moreover, there exists a basic transfer subsystem such that in the transfer process, the transfer subsystem is active. Based on the model of switched systems under constrained switching, this paper studies the controllability of such systems with time delay in the control function. A necessary and sufficient condition for controllability of such systems is established. Finally, an example is given to illustrate the utility of our results. [Copyright &y& Elsevier]

In this paper, we are interested in the first eigenvalue of p-Laplacian and the relation between the first eigenvalue and the existence (or nonexistence) of nontrivial (positive) solution for quasilinear elliptic obstacle problems. Utilizing the fact that obstacle problem have consanguineous relations with corresponding equation, we get a simple approach to study the properties of solutions of obstacle problems, such as existence and nonexistence, regularity and stability, etc. In this paper we are mainly concerned with the existence and nonexistence. [Copyright &y& Elsevier]

With q a positive real number, the nonlinear partial differential equation in the title of the paper arises in the study of the growth of surfaces. In that context it is known as the generalized deterministic KPZ equation. The paper is concerned with the initial-value problem for the equation under the assumption that the initial-data function is bounded and continuous. Results on the existence, uniqueness, and regularity of solutions are obtained. [Copyright &y& Elsevier]

Using the idea of weighted sharing of values, we study the problem of uniqueness of meromorphic functions that share three values. The results in this paper improve all theorems given by Lahiri in Nagoya Math. J. 161 (2001) 193–206. Examples are provided to show that some results in this paper are sharp. [Copyright &y& Elsevier]

In this paper, we establish existence results for positive solutions for the (n−1,1) three-point boundary value problems consisting of the equation u(n)+λa(t)fu(t)=0, t∈(0,1), with one of the following boundary value conditions: u(0)=αu(η), u(1)=βu(η), u(i)(0)=0 for i=1,2,…,n−2, and u(n−2)(0)=αu(n−2)(η), u(n−2)(1)=βu(n−2)(η), u(i)(0)=0 for i=0,1,…,n−3, where η∈(0,1), α⩾0, β⩾0, and a :(0,1)→R may change sign and R=(−∞,+∞). f(0)>0, λ>0 is a parameter. Our approach is based on the Leray–Schauder degree theory. This paper is motivated by Eloe and Henderson (Nonlinear Anal. 28 (1997) 1669–1680). [Copyright &y& Elsevier]

The paper considers systems of the form − div ( | ∇ u | n − 2 ∇ u ) = | ∇ u | n − 2 Ω ⋅ ∇ u on a bounded domain in R n with u ∈ W 1 , n , a matrix Ω ∈ L n (depending on u ) and some additional structural assumptions on Ω. We prove that if a sequence of solutions of the above system converges weakly, the limit itself is also a solution. The class of systems considered includes the n -harmonic system and the presented reasoning is a generalization of C. Wang's proof for n -harmonic maps. [ABSTRACT FROM AUTHOR]

In this paper, we study the initial and boundary value problem of the Navier–Stokes equations in the half-space. We prove the existence of weak solution u ∈ L α q ( 0 , ∞ ; L p ( R + n ) ) , α = 1 2 ( 1 − n p − 2 q ) ≥ 0 , n < p < ∞ with ∇ u ∈ L loc q 2 ( 0 , ∞ ; L loc p 2 ( R + n ) ) for the solenoidal initial data h ∈ B ˙ p q − 1 + n p ( R + n ) and the boundary data g ∈ L α q ( 0 , ∞ ; B ˙ p p − 1 p ( R n − 1 ) ) when ‖ h ‖ B ˙ p q − 1 + n p ( R + n ) + ‖ g ‖ L α q ( 0 , ∞ ; B ˙ p p − 1 p ( R n − 1 ) ) is small enough. Moreover, the solution is unique in the class L α q ( 0 , T ; L p ( R + n ) ) for any T ≤ ∞ if α > 0 and for some T < ∞ if α = 0 . [ABSTRACT FROM AUTHOR]

In this paper we prove that spectral synthesis holds for a variety on an Abelian group if spectral analysis holds on it and the residue ring of the annihilator of the variety is a Noether ring. This extends the fundamental result of M. Lefranc about spectral synthesis on finitely generated Abelian groups. [ABSTRACT FROM AUTHOR]

This paper addresses the properties of the C 0 -semigroup generated by the reparable system with finite repair time. In particular, it can be shown that the C 0 -semigroup is eventually differentiable and eventually compact, which is not true for the case when the repair time is infinite, as discussed in [9] and [11] . [ABSTRACT FROM AUTHOR]

This paper is concerned with Wold-type decomposition for regular operators whose orbits under any vector satisfy some growth conditions. Several results on left invertible operators close to isometries are extended. We also give numerous results on the Moore–Penrose inverse for regular operators in this particular setting. [ABSTRACT FROM AUTHOR]

In this paper, we study the Cauchy problem of the Camassa–Holm equation. We present a well-posedness result and a blow-up criterion of solutions in the inhomogeneous Triebel–Lizorkin spaces. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we provide an existence result of periodic solutions to planar systems having a repulsive singularity on both the axes. We require a nonresonance assumption, related to the spectrum of the periodic problem associated to the Steen's planar system which is isochronous (see [15]). As a particular case we obtain the existence of periodic solutions to a periodically perturbed Steen's planar system. [Copyright &y& Elsevier]

Abstract: A celebrated theorem of Coburn asserts that, on the setting of the Hardy space, if a Toeplitz operator is nonzero, then either it is one-to-one or its adjoint operator is one-to-one. In this paper, we show that an analogous result holds for Toeplitz operators acting on the Dirichlet space. [Copyright &y& Elsevier]

Abstract: Periodic travelling wave solutions of reaction–diffusion equations were studied by many authors. The type reaction–diffusion system is a notable special model that admits explicit periodic travelling wave solutions and was introduced by Kopell and Howard in 1973. There are now similar systems which are investigated by means of autonomous dynamics. In contrast, there are few papers which are concerned with non-autonomous cases. For this reason, we apply Mawhin’s continuation theorem to derive the existence of periodic travelling wave solutions for non-autonomous systems, and we describe the ‘disappearance’ of periodic travelling wave solutions under special situations. Our main result is also illustrated by examples. [Copyright &y& Elsevier]

Abstract: In this note, at first we will point out a fact which is implicitly contained in the original paper of John and Nirenberg [Comm. Pure Appl. Math. 14 (1961) 415–426]. If a function f satisfies (obviously if the value of left term is finite it must be zero), then there holds where is the nondecreasing rearrangement of f. As a consequence, we get the following inequality By this inequality, the bilinear estimates in BMO in [Math. Z. 235 (2000) 173–194] can be easily improved. These bilinear estimates are crucial for the main results in that paper. [Copyright &y& Elsevier]

Abstract: In this paper, we give new characterization of the classical Morrey space. Complementary global Morrey-type spaces are introduced. It is proved that for particular values of parameters these spaces give new pre-dual space of the classical Morrey space. We also show that our new pre-dual space of the Morrey space coincides with known pre-dual spaces. [Copyright &y& Elsevier]

Abstract: The main aim of this paper is the investigation of conditions under which a locally convex quasi ⁎-algebra attains sufficiently many -continuous ⁎-representations in , to separate its points. Having achieved this, a usual notion of bounded elements on rises. On the other hand, a natural order exists on related to the topology τ, that also leads to a kind of bounded elements, which we call “order bounded”. What is important is that under certain conditions the latter notion of boundedness coincides with the usual one. Several nice properties of order bounded elements are extracted that enrich the structure of locally convex quasi ⁎-algebras. [Copyright &y& Elsevier]

Abstract: In this paper, we establish a necessary and sufficient condition for the convexity of the complete elliptic integrals of the first kind with respect to Hölder means. [Copyright &y& Elsevier]

Abstract: The aim of this paper is to study the connection between the (non)uniform exponential dichotomy of a non(uniform) exponentially bounded, strongly continuous evolution family and the admissibility of some function spaces. Thus, there are extended recent results established by L. Barreira and C. Valls (2010, 2011) in and . [Copyright &y& Elsevier]

Abstract: In this paper, the property of linearly dependence of solutions and for higher order linear differential equation where () are entire periodic coefficients and () is the dominant coefficient, is investigated. [Copyright &y& Elsevier]