Remarks on the plancherel and pontryagin theorems

Plancherel Averages: Remarks on a Paper by Stanley

Let Mn stand for the Plancherel measure on Yn, the set of Young diagrams with n boxes. A recent result of R. P. Stanley (arXiv:0807.0383) says that for certain functions G defined on the set Y of all Young diagrams, the average of G with respect to Mn depends on n polynomially. We propose two other proofs of this result together with a generalization to the Jack deformation of the Plancherel me...

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+...

Remarks on the Paper ``Coupled Fixed Point Theorems for Single-Valued Operators in b-Metric Spaces''

In this paper, we improve some recent coupled fixed point resultsfor single-valued operators in the framework of ordered $b$-metricspaces established by Bota et al. [M-F. Bota, A. Petrusel, G.Petrusel and B. Samet, Coupled fixed point theorems forsingle-valued operators in b-metric spaces, Fixed Point TheoryAppl. (2015) 2015:231]. Also, we prove that Perov-type fix...

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...