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Abstract: An error is pointed out in the paper [J.R. Kang, Y.C. Kwun, J.Y. Park, Controllability of second order differential inclusion in Banach spaces, J. Math. Anal. Appl. 285 (2003) 537-550]. By an additional condition the considered system is controllable. [Copyright &y& Elsevier]

A famous theorem of Coburn says that a nonzero Toeplitz operator on the Hardy space of the unit disk is injective or its adjoint operator is injective. In this paper we study the corresponding problem on the Hardy space of the bidisk. We first show the Coburn type theorem fails generally on the bidisk. But, we show that certain pluriharmonic symbols or product symbols of one variable functions induce Toeplitz operators satisfying the Coburn type theorem. [ABSTRACT FROM AUTHOR]

Abstract: The aim of the paper is to study necessary and sufficient conditions for the existence of the global solution of the one-dimensional semilinear equation appearing in the boundary value problems of gas dynamics. We investigate the Cauchy problem for such equation in the domain where the operator is weakly hyperbolic. We obtain the necessary condition for the existence of the self-similar solutions for the semilinear Gellerstedt-type equation. The approach used in the paper is based on the fundamental solution of the linear Gellerstedt operator and the estimates. [Copyright &y& Elsevier]

Abstract: Degree theory has been developed as a tool for checking the solution existence of nonlinear equations. In his classic paper published in 1983, Browder developed a degree theory for mappings of monotone type , where f is a mapping of class from a bounded open set Ω in a reflexive Banach space X into its dual , and T is a maximal monotone mapping from X into . This breakthrough paved the way for many applications of degree theoretic techniques to several large classes of nonlinear partial differential equations. In this paper we continue to develop the results of Browder on the degree theory for mappings of monotone type . By enlarging the class of maximal monotone mappings and pseudo-monotone homotopies we obtain some new results of the degree theory for such mappings. [Copyright &y& Elsevier]

Abstract: Convoluted C-cosine functions and semigroups in a Banach space setting extending the classes of fractionally integrated C-cosine functions and semigroups are systematically analyzed. Structural properties of such operator families are obtained. Relations between convoluted C-cosine functions and analytic convoluted C-semigroups, introduced and investigated in this paper are given through the convoluted version of the abstract Weierstrass formula which is also proved in the paper. Ultradistribution and hyperfunction sines are connected with analytic convoluted semigroups and ultradistribution semigroups. Several examples of operators generating convoluted cosine functions, (analytic) convoluted semigroups as well as hyperfunction and ultradistribution sines illustrate the abstract approach of the authors. As an application, it is proved that the polyharmonic operator , , acting on with appropriate boundary conditions, generates an exponentially bounded -convoluted cosine function, and consequently, an exponentially bounded analytic -convoluted semigroup of angle , for suitable exponentially bounded kernels and . [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: The present paper is concerned with the problem of weighted best simultaneous approximations in Banach spaces. The weighted best simultaneous approximations to sequences from S- and BS-suns in the Banach space are characterized in view of the Kolmogorov conditions. Applications are provided for weighted best simultaneous approximations from RS-sets and strict RS-sets. Our results obtained in the present paper extend and improve all earlier known results in this direction. [Copyright &y& Elsevier]

Abstract: In this paper, we study the existence of solutions and approximation of the solutions by using a Mann type iterative scheme for variational inequalities in noncompact subsets of Banach spaces. The results presented in this paper generalize the corresponding results of J. Li [J. Li, On the existence of solutions of variational inequalities in Banach spaces, J. Math. Anal. Appl. 295 (2004) 115–126]. [Copyright &y& Elsevier]

Abstract: In this paper the pointwise approximation of Bézier variant of integrated MKZ operators for general bounded functions is studied. Two estimate formulas of this type approximation are obtained. The approximation of functions of bounded variation becomes a special case of the main result of this paper. In the case of functions of bounded variation, Theorem B of the paper corrects the mistake of Theorem 1 of the article [V. Gupta, Degree of approximation to functions of bounded variation by Bézier variant of MKZ operators, J. Math. Anal. Appl. 289 (2004) 292–300]. [Copyright &y& Elsevier]

Abstract: In this paper, we prove the Hyers–Ulam–Rassias stability of homomorphisms in quasi-Banach algebras associated to the Pexiderized Cauchy functional equation. This is applied to investigate homomorphisms between quasi-Banach algebras. The concept of Hyers–Ulam–Rassias stability originated from Th.M. Rassias'' stability theorem that appeared in his paper [Th.M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978) 297–300]. [Copyright &y& Elsevier]

Abstract: In this paper, we study the growth of solutions of a first-order linear differential equation and that of a second-order linear differential equation. From this we obtain some uniqueness theorems of a nonconstant entire function and its first derivative having the same fixed points with the same multiplicities. The results in this paper also improve some known results. Some examples show that the results in this paper are best possible. [Copyright &y& Elsevier]

Abstract: In this paper, the equivalence of the strong convergence between the modified Mann and Ishikawa iterations with errors in two different schemes by Xu [Y.G. Xu, Ishikawa and Mann iteration process with errors for nonlinear strongly accretive operator equations, J. Math. Anal. Appl. 224 (1998) 91–101] and Liu [L.S. Liu, Ishikawa and Mann iterative process with errors for nonlinear strongly accretive mappings in Banach spaces, J. Math. Anal. Appl. 194 (1995) 114–125] respectively is proven for the generalized strongly successively Φ-pseudocontractive mappings without Lipschitzian assumption. Our results generalize the recent results of the papers [Zhenyu Huang, F. Bu, The equivalence between the convergence of Ishikawa and Mann iterations with errors for strongly successively pseudocontractive mappings without Lipschitzian assumption, J. Math. Anal. Appl. 325 (1) (2007) 586–594; B.E. Rhoades, S.M. Soltuz, The equivalence between the convergences of Ishikawa and Mann iterations for an asymptotically nonexpansive in the intermediate sense and strongly successively pseudocontractive maps, J. Math. Anal. Appl. 289 (2004) 266–278; B.E. Rhoades, S.M. Soltuz, The equivalence between Mann–Ishikawa iterations and multi-step iteration, Nonlinear Anal. 58 (2004) 219–228] by extending to the most general class of the generalized strongly successively Φ-pseudocontractive mappings and hence improve the corresponding results of all the references given in this paper by providing the equivalence of convergence between all of these iteration schemes for any initial points , in uniformly smooth Banach spaces. [Copyright &y& Elsevier]

Abstract: In recent papers (cf. [J.L. Arregui, O. Blasco, -Summing sequences, J. Math. Anal. Appl. 274 (2002) 812–827; J.L. Arregui, O. Blasco, -Summing sequences of operators, Quaest. Math. 26 (2003) 441–452; S. Aywa, J.H. Fourie, On summing multipliers and applications, J. Math. Anal. Appl. 253 (2001) 166–186; J.H. Fourie, I. Röntgen, Banach space sequences and projective tensor products, J. Math. Anal. Appl. 277 (2) (2003) 629–644]) the concept of -summing multiplier was considered in both general and special context. It has been shown that some geometric properties of Banach spaces and some classical theorems can be described using spaces of -summing multipliers. The present paper is a continuation of this study, whereby multiplier spaces for some classical Banach spaces are considered. The scope of this research is also broadened, by studying other classes of summing multipliers. Let and be two Banach spaces whose elements are sequences of vectors in X and Y, respectively, and which contain the spaces and of all X-valued and Y-valued sequences which are eventually zero, respectively. Generally spoken, a sequence of bounded linear operators is called a multiplier sequence from to if the linear operator from into which maps onto is bounded with respect to the norms on and , respectively. Several cases where and are different (classical) spaces of sequences, including, for instance, the spaces of almost unconditionally summable sequences in X, are considered. Several examples, properties and relations among spaces of summing multipliers are discussed. Important concepts like R-bounded, semi-R-bounded and weak-R-bounded from recent papers are also considered in this context. [Copyright &y& Elsevier]

Abstract: In this paper we establish the fundamental properties of concentration at a radius for functions in the classical Hardy space on the unit disk. For which is not identically zero and given r, , the concentration is defined via the ratio of the norm of to the norm of . Using the Mahler measure of , we obtain information on the distribution of the zeros of in terms of the concentration ratio. In the last section of the paper, we examine the sharpness of concentration estimates for the Blaschke factor. [Copyright &y& Elsevier]

Abstract: In this paper, we develop an efficient preconditioning method on the basis of the modified hierarchy basis for solving the singular boundary value problem by the Galerkin method. After applying the preconditioning method, we show that the condition number of the linear system arising from the Galerkin method is uniformly bounded. In particular, the condition number of the preconditioned system will be bounded by 2 for the case (see Eq. (1) in the paper). Numerical results are presented to confirm our theoretical results. [Copyright &y& Elsevier]

Abstract: Let X be a Banach space and Z a nonempty closed subset of X. Let be an upper semicontinuous function bounded from above. This paper is concerned with the perturbed optimization problem , which is denoted by -sup. We shall prove in the present paper that if Z is a closed boundedly relatively weakly compact nonempty subset, then the set of all for which the problem -sup has a solution is a dense -subset of X. In the case when X is uniformly convex and J is bounded, we will show that the set of all points x in X for which there does not exist such that is a σ-porous subset of X and the set of all points such that there exists a maximizing sequence of the problem -sup which has no convergent subsequence is a σ-porous subset of , where denotes the set of all such that z is in the solution set of -sup. [Copyright &y& Elsevier]

Abstract: Let be a commutative family of nonexpansive mappings of a closed convex subset C of a reflexive Banach space X such that the set of common fixed point is nonempty. In this paper, we suggest and analyze a new viscosity iterative method for a commutative family of nonexpansive mappings. We also prove that the approximate solution obtained by the proposed method converges to a solution of a variational inequality. Our method of proof is simple and different from the other methods. Results proved in this paper may be viewed as an improvement and refinement of the previously known results. [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: This paper deals with a class of boundary value problem of singular differential equations on time scales. The conditions we used here differ from those in the majority of papers as we know. An existence theorem of positive solutions is established by using the Krasnosel''skii fixed point theorem and an example is given to illustrate it. [Copyright &y& Elsevier]

Abstract: Let X be a Banach space and Z a nonempty closed subset of X. Let be a lower semicontinuous function bounded from below. This paper is concerned with the perturbed optimization problem , denoted by -inf for . In the case when X is compactly fully 2-convex, it is proved in the present paper that the set of all points x in X for which there does not exist such that is a σ-porous set in X. Furthermore, if X is assumed additionally to be compactly locally uniformly convex, we verify that the set of all points such that the problem -inf fails to be approximately compact, is a σ-porous set in , where denotes the set of all such that . Moreover, a counterexample to which some results of Ni [R.X. Ni, Generic solutions for some perturbed optimization problem in nonreflexive Banach space, J. Math. Anal. Appl. 302 (2005) 417–424] fail is provided. [Copyright &y& Elsevier]

Abstract: In this paper we use the penalty approach in order to study constrained minimization problems in a Banach space with nonsmooth nonconvex mixed constraints. A penalty function is said to have the exact penalty property [J.-B. Hiriart-Urruty, C. Lemarechal, Convex Analysis and Minimization Algorithms, Springer, Berlin, 1993] if there is a penalty coefficient for which a solution of an unconstrained penalized problem is a solution of the corresponding constrained problem. In this paper we establish sufficient conditions for the exact penalty property. [Copyright &y& Elsevier]

Abstract: Motivated by the accomplishment of the second main theorem with moving targets, many authors studied the moving target problems in value distribution theory and related topics. In this paper, we prove some big Picard''s theorems for holomorphic mappings of several complex variables into with moving hyperplanes, related to Nochka''s little Picard-type theorems. As its application, we give a new quasi-normal criterion for families of meromorphic mappings of several complex variables into with moving hyperplanes. The new results in this paper greatly improve some earlier related results. [Copyright &y& Elsevier]

Abstract: This paper studies the well-posedness of a class of non-autonomous neutral control systems in Banach spaces. We prove that such systems are represented by absolutely regular non-autonomous linear systems in the sense of Schnaubelt [R. Schnaubelt, Feedback for non-autonomous regular linear systems, SIAM J. Control Optim. 41 (2002) 1141–1165]. This paper can be considered as the non-autonomous version of the work presented in [H. Bounit, S. Hadd, Regular linear systems governed by neutral FDEs, J. Math. Anal. Appl. 320 (2006) 836–858]. [Copyright &y& Elsevier]

Abstract: Let E be a real Banach space and let K be a nonempty closed convex subset of E. Let be N strictly pseudocontractive self-maps of K such that , where and let be two real sequence satisfying the conditions: where is common Lipschitz constant of . For , let be new implicit process defined by where , then The results of this paper generalize and improve the results of Osilike in 2004. In this paper, the proof methods of the main results are also different from that of Osilike. [Copyright &y& Elsevier]

Abstract: In this paper we present some results on the question of existence of generalized or measure valued solutions for semilinear impulsive evolution equations on Banach spaces with the nonlinear parts being merely measurable and bounded on bounded sets. This is a far reaching generalization of the previous results of the author and others. It may be interesting to consider extension of the results of this paper to cover impulsive differential inclusions and their potential applications to control theory and uncertain dynamics. [Copyright &y& Elsevier]

Abstract: In this paper it is shown that a relaxation defining the class of generalized d-V-type-I functions leads to a new class of multi-objective problems which preserves the sufficient optimality and duality results in the scalar non-differentiable case, and avoids the major difficulty of verifying that the inequality holds for the same kernel function. The results obtained in this paper generalize and extend the previously known results in this area. [Copyright &y& Elsevier]

Abstract: In this paper, we prove Ramanujan''s circular summation formulas previously studied by S.S. Rangachari, S.H. Son, K. Ono, S. Ahlgren and K.S. Chua using properties of elliptic and theta functions. We also derive identities similar to Ramanujan''s summation formula and connect these identities to Jacobi''s and Dixon''s elliptic functions. At the end of the paper, we discuss the connection of our results with the recent thesis of E. Conrad. [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, weak and strong convergence theorems are established for a three-step iterative scheme for asymptotically nonexpansive mappings in Banach spaces. Mann-type and Ishikawa -type iterations are included by the new iterative scheme. The results obtained in this paper extend and improve the recent ones announced by Xu and Noor, Glowinski and Le Tallec, Noor, Ishikawa, and many others. [Copyright &y& Elsevier]

Abstract: In this paper, first a new fixed point theorem is established, and then, by the use of it, the existence theorems of global solutions for nonlinear Volterra type integral equations in Banach spaces are investigated. The results obtained in this paper generalize and improve the results corresponding to those obtained by others. [Copyright &y& Elsevier]

Let X,Y be Banach spaces and M a linear manifold in X×Y={{x,y}∣x∈X, y∈Y}. The central problem which motivates many of the concepts and results of this paper is the problem of characterization and construction of all extremal solutions of a linear inclusion y∈M(x). First of all, concept of metric operator parts and metric generalized inverses for linear manifolds are introduced and investigated, and then, characterizations of the set of all extremal or least extremal solutions in terms of metric operator parts and metric generalized inverses of linear manifolds are given by the methods of geometry of Banach spaces. The principal tool in this paper is the generalized orthogonal decomposition theorem in Banach spaces. [Copyright &y& Elsevier]

The Hermitian monogenic system is an overdetermined system of two Dirac type operators in several complex variables generalizing both the holomorphic system and the real Dirac system. Due to the fact that it is overdetermined, the Cauchy–Kowalevski extension problem only has a solution if the Cauchy data satisfy certain constraints. There is however a subsystem, called Hermitian submonogenic system, for which theses constraints are no longer necessary, while, if the constraints hold, the Cauchy–Kowalevski extension will still be Hermitian monogenic. In this paper we focus on Cauchy–Kowalevski extensions of general polynomials, in the case of the Hermitian submonogenic system, and we compute the corresponding dimensions and reproducing kernels. [ABSTRACT FROM AUTHOR]

The present paper provides an explicit formula for the average intensity of the distribution of complex zeros of a family of random sums of the form S n ( z ) = ∑ j = 0 n η j f j ( z ) , where z is the complex variable x + i y , η j = α j + i β j and { α j } j = 0 n and { β j } j = 0 n are sequences of standard normal independent random variables, and { f j } j = 0 n is a sequence of given analytic functions that are real-valued on the real number line. In addition, the numerical computations of the intensity functions and the empirical distributions for the special cases of random Weyl polynomials, random Taylor polynomials and random truncated Fourier cosine series are included as examples. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we construct an embedding of holomorphic functions in two complex variables into the unit ball in . This leads to a closed subspace of the -functions on the unit sphere spanned by quaternionic polynomials for which we construct orthonormal bases and study the related convergence properties. [Copyright &y& Elsevier]

Abstract: In this paper there are established some analogues of the Hilbert formulas on the unit sphere for the theory of time-harmonic (monochromatic) relativistic Dirac bispinors. The formulas relate a pair of the components of the limit value of a time-harmonic Dirac bispinor in the unit ball to the other pair of components. The obtained results are based on the intimate connection between time-harmonic solutions of the relativistic Dirac equation and the three-dimensional α-hyperholomorphic function theory. Hilbert formulas for α-hyperholomorphic function theory for α being a complex quaternionic number are also presented, such formulas relate a pair of components of the boundary value of an α-hyperholomorphic function in the unit ball to the other pair of components, in an analogy with what is known for the case of the theory of functions of one complex variable. [Copyright &y& Elsevier]

Abstract: In this paper, we first give a new characterization for a domain, , in terms of a quasiconformal extension of a univalent function. As an application, using this characterization, we obtain two more characterizations of such domains by means of some kernel functions introduced recently by Hu and Shen (2012) [9]. [Copyright &y& Elsevier]

Abstract: In this paper we introduce a new weighted energy class of plurisubharmonic functions and show the local property of this class under some extra assumptions on weights. [Copyright &y& Elsevier]

Abstract: In this paper, we give several new necessary and sufficient conditions for the compactness of the composition operator on the Bloch space of the unit ball . [Copyright &y& Elsevier]

Abstract: Let be a Hermite operator, where Δ is the Laplacian on . In this paper, we first characterize the Hardy spaces associated with L by a new version of area integral. Then, we use it to prove the boundedness of Riesz transforms , for L on . Moreover, we characterize the Hardy space by . This gives a negative answer to a question asked by Thangavelu. [Copyright &y& Elsevier]

Abstract: The generalized Grötzsch function has numerous applications in geometric function theory and analytic number theory and its properties have been investigated by many authors. In this paper we study the concavity of the generalized Grötzsch function with respect to Hölder means. [Copyright &y& Elsevier]

Abstract: This paper is devoted to studying the relationship between an entire function and its derivative when they share one small function. We generalize some previous results of Gundersen and Yang [G. Gundersen, L.Z. Yang, Entire functions that share one value with one or two of their derivatives, J. Math. Anal. Appl. 223 (1998) 85–95], Chang and Zhu [J. Chang, Y. Zhu, Entire functions that share a small function with their derivatives, J. Math. Anal. Appl. 351 (2009) 491–496]. [Copyright &y& Elsevier]

Abstract: Let be a fixed number. A function is said to be a-shift-generating (a-SG) if for every , is a totally positive sequence and it does not coincide with a sequence of the form , where and . In this paper, we describe all a-SG functions and obtain a new characterization of totally positive functions in the terms of a-SG functions. In addition, using characteristic properties of a-SG functions, we generalize the famous Jacobian identity in theory of elliptic functions. [Copyright &y& Elsevier]

Abstract: Suppose that X, Y, A and B are Banach spaces such that X is isomorphic to and Y is isomorphic to . Are X and Y necessarily isomorphic? In this generality, the answer is no, as proved by W.T. Gowers in 1996. In the present paper, we provide a very simple necessary and sufficient condition on the 10-tuples in with , , , , and or or or , which guarantees that X is isomorphic to Y whenever these Banach spaces satisfy Namely, or , divides and divides , where is the characteristic number of the 4-tuple and is the discriminant of the 6-tuple . We conjecture that this result is in some sense a maximal extension of the classical Pełczyński''s decomposition method in Banach spaces: the case . [Copyright &y& Elsevier]

Abstract: In this paper we characterize the relation between two entire functions which are permutable and satisfy certain algebraic differential equations. [Copyright &y& Elsevier]

Abstract: In this paper, we will study the isometric extension problem for -spaces and prove that every surjective isometry from the unit sphere of onto that of a Banach space E can be extended to a linear surjective isometry from onto E. Moreover, we introduce the approximate isometric extension problem and show that, if E and F are Banach spaces and E satisfies the property (m) (special cases are , and ), then every bijective ϵ-isometry between the unit spheres of E and F can be extended to a bijective 5ϵ-isometry between their closed unit balls. At last, we will give an example to show that the surjectivity assumption cannot be omitted. Using this, we solve the non-surjective isometric extension problem in the negative. [Copyright &y& Elsevier]

Abstract: This paper considers two problems on the Fock type spaces (). Firstly, it is shown that on the space (), the identity representation of is a boundary representation for the Banach subalgebra , while on the space , it is not. Secondly, it is shown that all the submodules of are rigid. [Copyright &y& Elsevier]

Abstract: In this paper we consider the solutions of micropolar fluid equations in space dimension two with periodic boundary condition. We show that the strong solutions are analytic in time with values in an appropriate Gevrey class of function, provided that external forces and moments are time-independent and are in a Gevrey class. [Copyright &y& Elsevier]

Abstract: In this paper a new concept for a block operator matrix is studied on a Banach space. It is shown that, under certain conditions, it defines a closable operator and its essential spectra are determined. Application to transport operators in -space is given. [Copyright &y& Elsevier]

Abstract: A subset Y of a dual Banach space is said to have the property if for every -compact subset H of Y. The purpose of this paper is to give a characterization of the property for subsets of a dual Banach space , and to study the behavior of the property with respect to additions, unions, products, whether the closed linear hull has the property when Y does, etc. We show that the property is stable under all these operations in the class of -analytic subsets of . [Copyright &y& Elsevier]

Abstract: In this paper we study the distribution of zeros of each entire function of the sequence , which approaches the Riemann zeta function for , and is closely related to the solutions of the functional equations . We determine the density of the zeros of on the critical strip where they are situated by using almost-periodic functions techniques. Furthermore, by using a theorem of Kronecker, we also establish a formula for the number of zeros of inside certain rectangles in the critical strip. [Copyright &y& Elsevier]