Remarks on Theorems of Muntz-Szasz Type

Muntz - Szasz Type Approximation and the Angular Growth of Lacunary Integral Functions

We consider analogues of the Miintz-Szasz theorem, as in Ll5j and [4j, for functions regular in an angle. This yields necessary and sufficient conditions for the existence of integral functions which are bounded in an angle and have gaps of a very regular nature in their power series expansion. In the case when the gaps are not so regular, similar results hold for formal power series which conv...

Some Remarks on Liouville Type Theorems

The goal of this note is to present elementary proofs of statements related to the Liouville theorem.

Remarks on Recent Fixed Point Theorems

Remarks on Certain Selected Fixed Point Theorems

Theorem 1. Let A, S, I, and J be self-mappings of a complete metric space (X,d) such that the pairs (A,I) and (S,J) are commuting and A(X)⊂ J(X) and S(X)⊂ I(X) such [ 1+pd(Ax,Sy)]d(Ix,Jy) ≤ pmax{d(Ix,Ax)·d(Sy,Jy),d(Ix,Sy)·d(Jy,Ax)} +φ(d(Ax,Sy),d(Ix,Ax),d(Sy,Jy),d(Ix,Sy),d(Jy,Ax)), (1) for all x,y ∈ X where p ≥ 0 and φ ∈ Ψ . Then A, S, I, and J have a unique common fixed point provided one of th...

Some theorems and remarks on interpolation

Throughout this paper x"'), x-"1 ,. . ., x~,' will denote the roots of the n-th Chebyshev polynomial T " (x) [T " (cosh) = cos nJ]. f(x) will denote a function continuous in [-1, +1] and L,(f(x)) will denote the Lagrange interpolation polynomial of f(x) taken at the points xi(") (i = 1, 2,. . ., n) ; in other words, L,(f(x)) is a polynomial of degree not greater than (n-1) for which') L " (f(x+...