We give a sufficient condition for a univalently induced composition operator on the Hardy space H2 to be a Riesz operator. We then establish that every Riesz composition operator has a Koenigs model and explore connections our work has with the model theory and spectral theory of composition operators.

One of the key ingredients of A. Connes’ noncommutative geometry is a generalized Dirac operator which induces a metric(Connes’ distance) on the state space. We generalize such a Dirac operator devised by A. Dimakis et al , whose Connes’ distance recovers the linear distance on a 1D lattice, into 2D lattice. This Dirac operator being “naturally” defined has the “local eigenvalue property” and i...

In [4], Breaz and Breaz gave the univalence conditions of the integral operator Fα,n of the analytic functions belonging to the classes T2, T2,μ and S(p). The purpose of this paper is to generalize the integral operator Fα,n by means of the generalized Al-Oboudi differential operator and investigate univalence conditions of this generalized integral operator considering the classes Tj , Tj,μ an...

It has a wide application in the problem of physics, chemistry, biology, engineering and applied sciences. The theory Bessel functions is intimately connected with certain types differential equations. A detail account applications are given book Watson [26]. In this present paper, we establish generalized extension k-Bessel-Maitland function involving pathway integral operator. obtain composit...

In this article we define some aggregation operators for bipolar-valued hesitant fuzzy sets. These operations include bipolar-valued hesitant fuzzy ordered weighted averaging (BPVHFOWA) operator, bipolar-valued hesitant fuzzy ordered weighted geometric (BPVHFOWG) operator and their generalized forms. We also define hybrid aggregation operators and their generalized forms and solved a decision-m...

We analyze different types of aggregation operators based on the use of probabilities, weighted averages (WAs) and generalized aggregation operators. We present the generalized probabilistic weighted averaging (GPWA) operator. It is a new aggregation operator that unifies the WA and the probability in the same formulation considering the degree of importance that each concept has in the analysi...

A generalized net model of the mutation operator for the genetic algorithm is developed. The apparatus of generalized nets is considered as an appropriate tool for describing the performance of the genetic algorithm. The proposed generalized net model is a realization of the mutation operator for the Breeder genetic algorithm. The resulting GN model can be considered as a separate net, but also...

A bounded linear operator acting on a Hilbert space is a generalized quadratic operator if it has an operator matrix of the form [ aI cT dT ∗ bI ] . It reduces to a quadratic operator if d = 0. In this paper, spectra, norms, and various kinds of numerical ranges of generalized quadratic operators are determined. Some operator inequalities are also obtained. In particular, it is shown that for a...

Given two analytic nonlinear input-output systems represented as Fliess operators, four system interconnections are considered in a unified setting: the parallel connection, product connection, cascade connection and feedback connection. In each case, the corresponding generating series is produced, when one exists, and conditions for convergence of the corresponding Fliess operator are given. ...