Properties of Weighted Composition Operators on Some Weighted Holomorphic Function Classes in the Unit Ball

In this paper, we introduce NK-type spaces of holomorphic functions in the unit ball of C n by the help of a non-decreasing function K: (0,∞) → [0,∞). Several important properties of these spaces in the unit ball are provided. The results are applied to characterize boundedness and compactness of weighted composition operators Wu,φ from NK (B) spaces into Beurling-type classes. We also find the essential norm estimates for Wu,φ from NK(B) spaces into Beurling-type classes

Properties of Weighted Composition Operators on Some Weighted Holomorphic Function Classes in the Unit Ball

In this paper, we introduce NK-type spaces of holomorphic functions in the unit ball of C n by the help of a non-decreasing function K: (0,∞) → [0,∞). Several important properties of these spaces in the unit ball are provided. The results are applied to characterize boundedness and compactness of weighted composition operators Wu,φ from NK (B) spaces into Beurling-type classes. We also find the essential norm estimates for Wu,φ from NK(B) spaces into Beurling-type classes

Certain Classes of Operators on Some Weighted Hyperbolic Function Spaces

In this paper, some classes of concerned multiplication operators consisting of analytic and hyperbolic functions are defined and considered. Furthermore, some properties such as boundedness and compactness of the new operators are discussed. Finally, a general class of weighted hyperbolic Bloch functions is characterized by metric spaces

A New Technique for Solving a Nonlinear Integro-Differential Equation with Fractional Order in Complex Space

This work aims to explore the solution of a nonlinear fractional integro-differential equation in the complex domain through the utilization of both analytical and numerical approaches. The demonstration of the existence and uniqueness of a solution is established under certain appropriate conditions with the use of Banach fixed point theorems. To date, no research effort has been undertaken to look into the solution of this integro equation, particularly due to its fractional order specification within the complex plane. The validation of the proposed methodology was performed by utilizing a novel strategy that involves implementing the Rationalized Haar wavelet numerical method with the application of the Bernoulli polynomial technique. The primary reason for choosing the proposed technique lies in its ability to transform the solution of the given nonlinear fractional integro-differential equation into a representation that corresponds to a linear system of algebraic equations. Furthermore, we conduct a comparative analysis between the outcomes obtained from the suggested method and those derived from the rationalized Haar wavelet method without employing any shared mathematical methodologies. In order to evaluate the precision and effectiveness of the proposed method, a series of numerical examples have been developed