Blower, Gordon Doust, Ian
Published in
Advances in Pure and Applied Mathematics

Let A be the generator of a strongly continuous cosine family ( cos ( t A ) ) t ∈ ℝ {(\cos(tA))_{t\in\mathbb{R}}} on a complex Banach space E. The paper develops an operational calculus for integral transforms and functions of A using the generalized harmonic analysis associated to certain hypergroups. It is shown that characters of hypergroups...

Majumder, Sujoy Mandal, Rajib
Published in
Advances in Pure and Applied Mathematics

The purpose of the paper is to study uniqueness problems of certain types of differential-difference polynomials sharing a nonzero polynomial of certain degree under relaxed sharing hypotheses. We not only point out some gaps in the proof of the main results in [17], but also rectify the errors, and present our main results in a more compact way.

Hassine, Kods
Published in
Advances in Pure and Applied Mathematics

The main goal of this paper is to develop a potential theoretical approach to study the Dunkl Laplacian Δ k {\Delta_{k}} , which is a standard example of differential-difference operators. Introducing the Green kernel relative to Δ k {\Delta_{k}} , we prove that the Dunkl Laplacian generates a Balayage space and we investigate the associated family...

Abdellatif, Nahla Bernardi, Christine Touihri, Moncef Yakoubi, Driss
Published in
Advances in Pure and Applied Mathematics

The aim of this work is the numerical study of a nonlinear equation, which models the water flow in a partially saturated underground porous medium under the surface. We propose a discretization of this equation that combines Euler’s implicit scheme in time and spectral methods in space. We prove optimal error estimates between the continuous and d...

Alomari, Mohammad W. Hussain, Sabir Liu, Zheng
Published in
Advances in Pure and Applied Mathematics

In this paper, new inequalities connected with the celebrated Steffensen’s integral inequality are proved.

Hssini, EL Miloud Tsouli, Najib Haddaoui, Mustapha
Published in
Advances in Pure and Applied Mathematics

In this paper, based on the mountain pass theorem and Ekeland’s variational principle, we show the existence of solutions for a class of non-homogeneous and nonlocal problems in Orlicz–Sobolev spaces.

Benavente, Ana Favier, Sergio Levis, Fabián
Published in
Advances in Pure and Applied Mathematics

Given an Orlicz space L φ {L^{\varphi}} , we give very relaxed sufficient conditions on φ to ensure that there exists a best φ-approximation from any finite dimensional bounded linear subspace S ⊂ L φ {S\subset L^{\varphi}} . In addition, given an operator T, defined from L φ {L^{\varphi}} into itself, we give necessary and sufficient conditions on...

Haseeb, Abdul Siddiqi, Mohammad Danish Shahid, Mohammad Hasan
Published in
Advances in Pure and Applied Mathematics

The objective of the present paper is to study some new results on quasi-conformal curvature tensor in a Kenmotsu manifold with respect to a semi-symmetric non-metric connection.

Kok, Johan Sudev, Naduvath K. Chithra, Kaithavalappil P. Mary, Augustine
Published in
Advances in Pure and Applied Mathematics

In this paper, we introduce the notion of an energy graph G of order n ∈ ℕ ${n\in\mathbb{N}}$ . Energy graphs are simple, connected and finite directed graphs. The vertices, labelled u 1 , u 2 , … , u n ${u_{1},u_{2},\dots,u_{n}}$ , are such that ( u i , u j ) ∉ A ( G ) ${(u_{i},u_{j})\notin A(G)}$ for all arcs ( u i , u j ) ${(u_{i},u_{j})}$ wit...

Au-Yeung, Enrico
Published in
Advances in Pure and Applied Mathematics

We propose a new class of random matrices that enables the recovery of signals with sparse representation in a known basis with overwhelmingly high probability. To construct a matrix in this class, we begin with a fixed non-random matrix that satisfies two very general conditions. Then we decompose the matrix into pieces of sparse matrices. A rando...