Garg, Mukta Das, Ruchi
Published in
Advances in Pure and Applied Mathematics

In this paper, we define various kinds of transitivity of maps on G-spaces. We obtain conditions on G-spaces and on maps for one type of transitivity to imply another type of transitivity. Giving several examples and proving various equivalences, we provide a complete description of the relationships among the different types of transitivities defi...

Anvariyeh, Seid Mohammad Soltani, Samaneh
Published in
Advances in Pure and Applied Mathematics

In this paper, first we introduce the categories of “n-ary hyperstructures” ( HS n {{\mathrm{HS}}_{n}} ) and “n-ary hyperstructures with particular carriers and relations” ( HSP n {{\mathrm{HSP}}_{n}} ), and we prove that the categories of HS n {{\mathrm{HS}}_{n}} and HSP n - 1 {{\mathrm{HSP}}_{n-1}} are isomorphic. Then we prove that the category ...

Monzón, Gabriel
Published in
Advances in Pure and Applied Mathematics

Geometric conditions on general polygons are given in [9] in order to guarantee the error estimate for interpolants built from generalized barycentric coordinates, and the question about identifying sharp geometric restrictions in this setting is proposed. In this work, we address the question when the construction is made by using Wachspress coord...

Khare, Mona Shukla, Anurag
Published in
Advances in Pure and Applied Mathematics

The objective of the present paper is to develop a comprehensive theory of entropy in the realm of a gs-space ( L , p ) {(L,p)} involving the notion of a generalized s-map, and to study dynamics of a p-preserving system ( L , p , ϕ ) {(L,p,\phi)} . It is obtained that the entropy of p-preserving systems is isomorphism invariant, and also entropy of...

Ramakrishnan, Radha Adhikari, Saswata
Published in
Advances in Pure and Applied Mathematics

Recently, a characterization of frames in twisted shift-invariant spaces in L 2 ( ℝ 2 n ) {L^{2}(\mathbb{R}^{2n})} has been obtained in [16]. Using this result, we prove a sampling theorem on a subspace of a twisted shift-invariant space in this paper.

Oğuz, Arzu Denk Topal, Fatma Serap
Published in
Advances in Pure and Applied Mathematics

In this paper, we discuss the existence of symmetric positive solutions for the systems of higher-order boundary value problems on time scales. Our results extend some recent work in the literature. The analysis of this paper mainly relies on the monotone iterative technique.

Selvarangam, Srinivasan Rani, Bose Thandapani, Ethiraju
Published in
Advances in Pure and Applied Mathematics

In this paper, some new sufficient conditions are established for the oscillation of all solutions of the second-order neutral differential equation with mixed neutral terms of the form ( r ( t ) ( x ( t ) + a x ( t - τ ) + b x ( t + σ ) ) ′ ) ′ + p ( t ) x α ( t - k ) + q ( t ) x β ( t + m ) = 0 \bigl{(}r(t)(x(t)+ax(t-\ta...

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...