Volume 3, Issue 4

Abstract. In 2009, we have proved a general theorem dealing with summability factors of an infinite series. In this paper, we extend that result by using a quasi-σ-power increasing sequence for some σ (), which is a wider class of sequences, instead of an almost increasing sequence. Some new and known results are also obtained.

Abstract. In this paper we prove the positivity of the transmutation operators associated with a Cherednik type operator on the real line, and we deduce the positivity of the transmutation operators related to the Jacobi–Cherednik operator on ℝ and the Cherednik operator in the one-dimensional case.

Abstract. This paper is concerned with establishing the existence of positive solutions of p -Laplacian singular boundary value problem on time scale where , and is continuous and may be singular at but not at . We establish the existence of at least one positive solution for the p -Laplacian singular boundary value problem on time scales by using the Leray–Schauder degree theory.

Abstract. The harmonic Green and Neumann functions are presented and the related Dirichlet and Neumann problems for the Poisson equation are solved explicitly.

Abstract. Conditions for reconstruction of multivariate homogeneous polynomials from sets of sample values are introduced. In addition, it is shown that one can explicitly obtain the polynomial coefficients from the sample data by considering frames for spaces of symmetric tensors. Further, it is discussed how the reconstruction of homogeneous polynomials can be used to approximate certain smooth functions.