Sahand Communications in Mathematical Analysis
Volume:1 Issue: 1, Winter-Spring 2014

In this paper, we show that in each finite dimensional Hilbert space, a frame of subspaces is an ultra Bessel sequence of subspaces. We also show that every frame of subspaces in a finite dimensional Hilbert space has frameness bound.

Minkowski type inequalities for the seminormed fuzzy integrals on abstract spaces are studied in a rather general form. Also related inequalities to Minkowski type inequality for the semi-normed fuzzy integrals on abstract spaces are studied. Several examples are given to illustrate the validity of theorems. Some results on Chebyshev and Minkowski type inequalities are obtained.

This work concerns the study of existence and uniqueness to heat equation with fractional Laplacian differentiation in extended Colombeau algebra.

This paper deals with the boundary value problem involving the differential equationly≔-y^''+qy=λy subject to the standard boundary conditions along with the following discontinuity conditions at a point aϵ(0,π) y(a+0)=a_1 y(a-0), y^'' (a+0)=a_1^(-1) y^'' (a-0)+a_2 y(a-0), where q(x), a_1, a_2 are real, q∈L^2 (0,π) and λ is a parameter independent of x. We develop the Hochestadt''s result based on the transformation operator for inverse Sturm-Liouville problem when there are discontinuous conditions. Furthermore, we establish a formula for q(x)-q ̃(x) in the finite interval where q(x) and q ̃(x) are analogous functions.

Motivating the perturbations of frames in Hilbert and Banach spaces, in this paper we introduce the invariance of Frechet frames under perturbation. Also we show that for any Frechet spaces, there is a Frechet frame and any element in these spaces has a series expansion.

In the present paper, we prove subordination, superordination and sandwich-type properties of a certain integral operators for univalent functions on open unit disc, moreover the special behavior of this class is investigated.

In this paper, we study the multiplicity of positive solutions for the Laplacian systems with sign-changing weight functions. Using the decomposition of the Nehari manifold, we prove that an elliptic system has at least two positive solutions.