The main purpose of this paper is to detemine the fine spectrum of the generalized difference operator Delta_{uv} over the sequence space c0. These results are more general than the fine spectrum of the generalized difference operator Delta_{uv} of Srivastava and Kumar.

We present an AXIOM environment called JET for geometric computations with partial dierential equations within the framework of the jet bundle formalism. This comprises especially the completion of a given dierential equation to an involutive one according to the Cartan-Kuranishi Theorem and the setting up of the determining system for the generators of classical and non-classical Lie symmetrie...

some necessary and sufficient conditions are given for the existence of a g-positive (g-repositive) solution to adjointable operator equations $ax=c,axa^{left( astright) }=c$ and $axb=c$ over hilbert $c^{ast}$-modules, respectively. moreover, the expressions of these general g-positive (g-repositive) solutions are also derived. some of the findings of this paper extend some known results in the...

The Steklov averages (Steklov or integral means) are used in approximation theory of functions different aspects. This article concerns the by using operator cosine function framework. offers a counterpart translation operator, which forms basic concept for modulus continuity and some processes as well. We will show that allows to define very general an abstract Banach space. properties these g...

We investigate the generalized convergence and sums of series of the form P n≥0 anT P (x), where P ∈ R[x], an ∈ R, ∀n ≥ 0, and T : R[x] → R[x] is a linear operator that commutes with the differentiation d dx : R[x]→ R[x]. CONTENTS 1. The main result 1 2. Some applications 3 References 9 1. THE MAIN RESULT We consider series of the form ∑ n≥0 anT P (x), (†) where P ∈ R[x], and T : R[x]→ R[x] is ...

In this paper we study translation surfaces with the non-degenerate third fundamental form in Lorentz- Minkowski space $mathbb{L}^{3}$. As a result, we classify translation surfaces satisfying an equation in terms of the position vector field and the Laplace operator with respect to the third fundamental form $III$ on the surface.

In this paper, several direct and inverse theorems in terms of the best approximations functions moduli smoothness are proved concerning approximation from space $$\mathbb {L}_{2}^{(\alpha ,\beta )}$$ by partial sums Jacobi-Dunkl series. For purpose, we use generalized translation operator which was defined Vinogradov.

‎in this paper‎, ‎we study translation invariant surfaces in the‎ ‎3-dimensional heisenberg group $rm nil_3$‎. ‎in particular‎, ‎we‎ ‎completely classify translation invariant surfaces in $rm nil_3$‎ ‎whose position vector $x$ satisfies the equation $delta x = ax$‎, ‎where $delta$ is the laplacian operator of the surface and $a$‎ ‎is a $3 times 3$-real matrix‎.

‎In this paper‎, ‎we study translation invariant surfaces in the‎ ‎3-dimensional Heisenberg group $rm Nil_3$‎. ‎In particular‎, ‎we‎ ‎completely classify translation invariant surfaces in $rm Nil_3$‎ ‎whose position vector $x$ satisfies the equation $Delta x = Ax$‎, ‎where $Delta$ is the Laplacian operator of the surface and $A$‎ ‎is a $3 times 3$-real matrix‎.