Volume 7, Issue 3

Using the operatorial approach, we investigate the ultrametric approximate solutions of the following Drygas functional equation: ∑λ∈Φf⁢(x+λ⁢y+aλ)=|Φ|⁢f⁢(x)+∑λ∈Φf⁢(λ⁢y),x,y∈E,$\sum_{\lambda\in\Phi}{f(x+\lambda y+a_{\lambda})=|\Phi|f(x)+\sum_{\lambda\in% \Phi}f(\lambda y)},\quad x,y\in E,$ where 𝕂${\mathbb{K}}$ is an ultrametric valued field of characteristic zero, E is a 𝕂${\mathbb{K}}$-vector space, F is a complete ultrametric space over 𝕂${\mathbb{K}}$, f∈FE${f\in F^{E}}$, Φ is a finite subgroup of the automorphism group of E with order |Φ|${|\Phi|}$, and aλ∈E${a_{\lambda}\in E}$ for all λ∈Φ${\lambda\in\Phi}$.

In this paper, we consider the generalized spherical functions ϕλ${\phi_{\lambda}}$ associated to the root systems of type A in order to provide an estimate in the spectral parameter λ. This estimate generalizes, for the root systems of type A , an estimate obtained by Duistermaat, Kolk and Varadarajan.

The aim of this work is to present a model for coupling the Darcy equations in a porous medium with the Navier–Stokes equations in the cracks. We consider a two- or three-dimensional domain with non-standard condition at the interface, namely the continuity of the pressure. We propose a mixed formulation and establish the existence of a solution for the coupled problem.

In the present paper we characterize, in terms of characters, additive functions and matrix elements of irreducible two-dimensional representations, the continuous solutions of some trigonometric functional equations for mappings defined on an arbitrary group and taking their values in a complex Hilbert space with the Hadamard product. In addition, we investigate a superstability result for these equations.

In the present paper we introduce some applications of I -statistical convergence to form some new spaces of sequences using a sequence of Orlicz functions and matrix transformation over n -normed spaces. We also make an effort to study several properties relevant to the topological and algebraic structure of these spaces. We investigate some inclusion relations involving these spaces.

This paper proposes an iterative method for solving an operator equation on a separable Hilbert space H equipped with a g-frame. We design an algorithm based on the conjugate gradient method and investigate the convergence and optimality of this algorithm.