Fourier series of a generalised function of two variables

In this paper we evaluate certain integrals involving a generalised function of two variables and employ these to establish Fourier series expansions for this function. Results obtained recently by Mac Robert (1959) and (1961), Kesarwani (1966), Bajpai (1969), Parashar (1967) and Shah (1971) can be deduced from our results on specialising the parameters.     

Fractional integration operators of two variables

The object of the present note is to introduce two new fractional integration operators associated with H-function of two variables. Three important properties of these operators are established which generalize the results given earlier by several authors notably by Saxena and Kumbhat,^{11, 12} Saxena and Kalla,⁵ Parashar⁸ and Lowndes.⁶     

On a nonlinear volterra-hammerstein integral equation in two variables

Using a fixed point theorem of Krasnosel'skii type, this article proves the existence of asymptotically stable solutions for a Volterra-Hammerstein integral equation in two variables.     

Laplace invariants for a fourth-order equation with two independent variables

We construct the Laplace invariants for an equation with the leading partial derivative. We write defining equations in terms of the Laplace invariants. We obtain classes of equations admitting four-dimensional Lie algebras.     

A note on a functional equation on groups with involutions in two variables

Aequationes mathematicae - In this paper, we determine the central solutions $$f:Gtimes Grightarrow {{mathbb {C}}}$$ of the functional equation $$begin{aligned} f(x_1sigma y_1,x_2tau...     

The generalised killing equation in finsler space

The infinitesimal deformation of a Finsler space has been studied [3, 4, 5](1) in the general form taking the vector, along which the deformation is considered, as the function of line-elements. The necessary and sufficient condition for the infinitesimal change to become a motion has been obtained in the present paper and is termed as generalised Killing equation. Various alternative forms of this equation which are generalisations of those of Hokari [1], Knebelman [2] and Soo’s [8] have been obtained.     

Fractional non-Archimedean calculus in many variables

Let r ≥ 0 be a real number. We will introduce a notion of r-fold differentiability for functions in many variables over a non-Archimedeanly valued complete field K and then examine properties of theirs such as localness, completeness as a locally convex K-algebra, density of (locally) polynomial functions, closure under composition and, for the dual, under convolution. The definition of a C ^r -function will be given through partial difference quotients and build up on the one-variable case already studied in [8]. In line with [2], we will also show a function on ? _p ^d to be r-times differentiable if and only if its Mahler coefficients obey |a _n ‖n| ^r → 0 as | n| → ∞. As a corollary, a characterization of C ^r -functions f: X → K on open X ? ? _p ^d by partial Taylor-polynomials is obtained.     

On an iteration method for a nonlinear differential-operator equation

We study an iteration method for a first-order differential-operator equation with a nonlinear operator in a separable Hilbert space. The convergence of the iterative process is proved in the strong norms. Convergence estimates are derived. We present an application of the suggested method to the solution of a model initial-boundary value problem for a fourth-order parabolic equation.