Band 38, Heft 3

The purpose of this paper is first to reformulate the fixed point theorem (see Theorem 1 of [J. Brzdȩk, J. Chudziak and Z. Páles, A fixed point approach to stability of functional equations, Nonlinear Anal. 74 2011, 17, 6728–6732]) in β-Banach spaces. We also show that this theorem is a very efficient and convenient tool for proving the hyperstability results of the general linear equation in β-Banach spaces. Our main results state that, under some weak natural assumptions, functions satisfying the equation approximately (in some sense) must be actually solutions to it.

In this short note, we consider piece-wise smooth strictly convex curves in ℝ2{\mathbb{R}^{2}} with prescribed singular angles. Given some geodesic curvature bounds, we give the sharp length estimates.

Srivastava and Panda have studied the simple and multiple generating relations concerning the multivariable H -function. The aim of this paper is to derive the various classes of simple and multiple generating relations involving the multivariable Aleph-function. The generating function is used in the theory of numbers, in physics and other fields of mathematics. We see the particular cases concerning the multivariable I -function, the Aleph-function of two variables and the I -function of two variables.

In the present paper we characterize the compact, invertible, Fredholm and closed range weighted composition operators on Cesàro function spaces. We also make an effort to compute the essential norm of weighted composition operators.