Convolution properties for certain classes of multivalent functions

Recently N.E. Cho, O.S. Kwon and H.M. Srivastava [Nak Eun Cho, Oh Sang Kwon, H.M. Srivastava, Inclusion relationships and argument properties for certain subclasses of multivalent functions associated with a family of linear operators, J. Math. Anal. Appl. 292 (2004) 470-483] have introduced the class of multivalent analytic functions and have given a number of results. This class has been defined by means of a special linear operator associated with the Gaussian hypergeometric function. In this paper we have extended some of the previous results and have given other properties of this class. We have made use of differential subordinations and properties of convolution in geometric function theory.     

Some subclasses of analytic functions involving the generalized Noor integral operator

In this paper, we define the generalized Noor integral operator by using convolution. By applying this operator, we introduce some subclasses , and of analytic functions and study their subordinate relations, inclusion relations, the integral operator, the sufficient conditions for a function to be in the class and the radius problems.     

On certain subclasses of close-to-convex and quasi-convex functions with respect to k-symmetric points

In the present paper, the authors introduce two new subclasses of close-to-convex functions and of quasi-convex functions. The integral representations for functions belonging to these classes are provided, the convolution conditions, growth theorems, distortion theorems and covering theorems for these classes are also provided. The results obtained generalize some known results, and some other new results are obtained.     

On certain subclasses of multivalent functions associated with an extended fractional differintegral operator

In the present paper an extended fractional differintegral operator , suitable for the study of multivalent functions is introduced. Various mapping properties and inclusion relationships between certain subclasses of multivalent functions are investigated by applying the techniques of differential subordination. Relevant connections of the definitions and results presented in this paper with those obtained in several earlier works on the subject are also pointed out.     

Operators on the space of vector-valued totally measurable functions

Let L(X,Y) stand for the space of all bounded linear operators between real Banach spaces X and Y, and let Σ be a σ-algebra of sets. A bounded linear operator T from the Banach space B(Σ,X) of X-valued Σ-totally measurable functions to Y is said to be σ-smooth if ‖T(fn)Y_‖→0 whenever a sequence of scalar functions (‖fn(⋅)X_‖) is order convergent to 0 in B(Σ). It is shown that a bounded linear operator is σ-smooth if and only if its representing measure is variationally semi-regular, i.e., as An↓∅ (here stands for the semivariation of m on A∈Σ). As an application, we show that the space Lσs(B(Σ,X),Y) of all σ-smooth operators from B(Σ,X) to Y provided with the strong operator topology is sequentially complete. We derive a Banach-Steinhaus type theorem for σ-smooth operators from B(Σ,X) to Y. Moreover, we characterize countable additivity of measures in terms of continuity of the corresponding operators .     

Univalent polynomials and fractional order differences of their coefficients

Using fractional order differences, we find sufficient conditions on the coefficients of certain polynomials defined on the unit disk such that the zeros of these polynomials does not lie in D.     

Bounded Toeplitz products on the weighted Bergman spaces of the unit ball

Let p>1 and let q denote the number such that (1/p)+(1/q)=1. We give a necessary condition for the product of Toeplitz operators to be bounded on the weighted Bergman space of the unit ball (α>−1), where and , as well as a sufficient condition for to be bounded on . We use techniques different from those in [K. Stroethoff, D. Zheng, Bounded Toeplitz products on Bergman spaces of the unit ball, J. Math. Anal. Appl. 325 (2007) 114-129], in which the case p=2 was proved.     

A unified class of k-uniformly convex functions defined by the Dziok–Srivastava linear operator

The main purpose of this paper is to introduce a new class of functions which are analytic in the open unit disk . We obtain various results including characterization, coefficient estimates, and distortion and covering theorems, for functions belonging to the class .     

Polynomial almost periodic solutions for a class of Riemann-Hilbert problems with triangular symbols

Let with α,β∈]0,1[ such that α+β<1, αβ⁻¹∉Q and a,b,c∈C?{0}. In this paper the existence of almost-periodic polynomial (APP) solutions to the equation (with and ) is studied. The natural space in which to seek a solution to the above problem is the space of almost periodic functions with spectrum in the group αZ+βZ+Z. Due to the difficulty in dealing with the problem in that generality, solutions are sought with spectrum in the group αZ+βZ. Several interesting and totally new results are obtained. It is shown that, if 1∉αZ+βZ, no polynomial solutions exist, i.e., almost periodic polynomial solutions exist only if αZ+βZ=αZ+βZ+Z. Keeping to this setting, it is shown that APP solutions exist if and only if the function satisfies the simple spectral condition α+β>1/2. The proof of this result is nontrivial and has a number-theoretic flavour. Explicit formulas for the solution to the above problem are given in the final section of the paper. The derivation of these formulas is to some extent a byproduct of the proof of the result on the existence of APP solutions.     

Positive solutions of a system of non-autonomous fractional differential equations

Existence of positive solutions for the following system of fractional differential equations:

     

A higher rank version of Kitai's theorem

We prove that each linear action of on an infinite-dimensional Banach space generated by compact operators cannot be hypercyclic. This result generalizes a theorem of Kitai for the case of Z₊ actions. Contrary to the case of infinite dimension, a hypercyclic action of on C is given.     

On the parallel computation of the biconnected and strongly connected co-components of graphs

In this paper, we consider the problems of co-biconnectivity and strong co-connectivity, i.e., computing the biconnected components and the strongly connected components of the complement of a given graph. We describe simple sequential algorithms for these problems, which work on the input graph and not on its complement, and which for a graph on n vertices and m edges both run in optimal O(n+m) time. Our algorithms are not data structure-based and they employ neither breadth-first-search nor depth-first-search.Unlike previous linear co-biconnectivity and strong co-connectivity sequential algorithms, both algorithms admit efficient parallelization. The co-biconnectivity algorithm can be parallelized resulting in an optimal parallel algorithm that runs in time using processors. The strong co-connectivity algorithm can also be parallelized to yield an -time and O(m^1.188/logn)-processor solution. As a byproduct, we obtain a simple optimal O(logn)-time parallel co-connectivity algorithm.Our results show that, in a parallel process environment, the problems of computing the biconnected components and the strongly connected components can be solved with better time-processor complexity on the complement of a graph rather than on the graph itself.     

On some classes of p-valent functions involving Carlson-Shaffer operator

Let , be a class of functions analytic in the open unit disc E. We use Carlson-Shaffer operator for p-valent functions to define and study certain classes of analytic functions. Inclusion results, a radius problem and some other interesting properties are discussed.     

On the norm of a Hilbert's type linear operator and applications

In this paper, the norm of a Hilbert's type linear operator is given. As applications, a new operator inequality and the equivalent forms with the norm are obtained, and particularly some new extended Hilbert's type inequalities and the equivalent forms with the best constant factors are established.     

On Bernardi's integral operator and the Briot-Bouquet differential subordination

Let A,B,D,E∈[−1,1]. Conditions on A,B,D and E are determined so that

     

Duality techniques for certain integral transforms to be starlike

For β<1, let denote the class of all normalized analytic functions f such that

     

New applications of Besov-type and Triebel-Lizorkin-type spaces

In this paper, the authors prove that Besov-Morrey spaces are proper subspaces of Besov-type spaces and that Triebel-Lizorkin-Morrey spaces are special cases of Triebel-Lizorkin-type spaces . The authors also establish an equivalent characterization of when τ∈[0,1/p). These Besov-type spaces and Triebel-Lizorkin-type spaces were recently introduced to connect Besov spaces and Triebel-Lizorkin spaces with Q spaces. Moreover, for the spaces and , the authors investigate their trace properties and the boundedness of the pseudo-differential operators with homogeneous symbols in these spaces, which generalize the corresponding classical results of Jawerth and Grafakos-Torres by taking τ=0.