## Relative essential spectra involving relative demicompact unbounded linear operators

Published in Acta Mathematica Scientia

Published in Acta Mathematica Scientia

Published in Acta Mathematica Scientia

In this article, we prove a decomposition theorem for I2-convergent double sequences and introduce the notions of I2-Cauchy and I*2)-Cauchy double sequence, and then study their certain properties. Finally, we introduce the notions of regularly (I2,I)-convergence and (I2,I)-Cauchy double sequence.

Published in Acta Mathematica Scientia

Let (M, T) be a smooth closed manifold with a smooth involution T whose fixed point set is a disjoint union of an even-dimensional real projective space and a Dold manifold. In some cases, the equivariant bordism classes of (M, T) are determined.

Published in Acta Mathematica Scientia

The domain of generalized difference matrix B(r, s) in the classical spaces ℓ∞, c, and c0 was recently studied by Kirişçi and Başar in [16]. The main goal of this article is to introduce the paranormed sequence spaces ℓ∞(), c(), and c0(), which are more general and comprehensive than the corresponding consequences of the matrix domain of B(r, s), a...

Published in Acta Mathematica Scientia

The main work of this article is to give a nontrivial method to construct pointed semilattice graded weak Hopf algebra from a Clifford monoid S = [Y;Gα, φα,β] by Ore-extensions, and to obtain a co-Frobenius semilattice graded weak Hopf algebra H(S, n, c, χ, a, b) through factoring At by a semilattice graded weak Hopf ideal.

Published in Acta Mathematica Scientia

This article aims at studying two-direction refinable functions and two-direction wavelets in the setting ℝs, s > 1. We give a sufficient condition for a two-direction refinable function belonging to L2(ℝs). Then, two theorems are given for constructing biorthogonal (orthogonal) two-direction refinable functions in L2(ℝs) and their biorthogonal (or...

Published in Acta Mathematica Scientia

Published in Acta Mathematica Scientia

Recently, Suzuki [T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc. 136 (2008), 1861-1869] proved a fixed point theorem that is a generalization of the Banach contraction principle and characterizes the metric completeness. Paesano and Vetro [D. Paesano and P. Vetro, Suzuki's type c...

Published in Acta Mathematica Scientia

In this article, we introduce the concept of lacunary statistical convergence of order α of real number sequences and give some inclusion relations between the sets of lacunary statistical convergence of order α and strong Nθα(p)-summability. Furthermore, some relations between the spaces NθαSθα are examined.

Published in Acta Mathematica Scientia

The main purpose of this article is to prove a collection of new fixed point theorems for (ws)-compact and so-called 1-set weakly contractive operators under Leray-Schauder boundary condition. We also introduce the concept of semi-closed operator at the origin and obtain a series of new fixed point theorems for such class of operators. As consequen...