Topologically Transitive and Mixing Properties of Set-Valued Dynamical SystemsRead the full article
Abstract and Applied Analysis publishes research with an emphasis on important developments in classical analysis, linear and nonlinear functional analysis, ordinary and partial differential equations, optimisation theory, and control theory.
Chief Editor, Dr Wong, is an associate professor at Nanyang Technological University, Singapore. Her research interests include differential equations, difference equations, integral equations, and numerical mathematics.
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Controlled Continuous ---Frames for Hilbert -Modules
Frame theory has a great revolution for recent years. This theory has been extended from Hilbert spaces to Hilbert -modules. In this paper, we define and study the new concept of controlled continuous ---frames for Hilbert -modules and we establish some properties.
Equivalent Characterization on Besov Space
In this paper, we give an equivalent characterization of the Besov space. This reveals the equivalent relation between the mixed derivative norm and single-variable norm. Fourier multiplier, real interpolation, and Littlewood-Paley decomposition are applied.
New Solutions for the Generalized BBM Equation in terms of Jacobi and Weierstrass Elliptic Functions
The Jacobi elliptic function method is applied to solve the generalized Benjamin-Bona-Mahony equation (BBM). Periodic and soliton solutions are formally derived in a general form. Some particular cases are considered. A power series method is also applied in some particular cases. Some solutions are expressed in terms of the Weierstrass elliptic function.
The Multiple -Riemann Integral
The aim of this paper is to extend the notion of -Riemann integrability of functions defined over to functions defined over a rectangular box of . As a generalization of step functions, we introduce a notion of -step functions which allows us to give an equivalent definition of the -Riemann integrable functions.
Boundary Value Problem for Nonlinear Implicit Generalized Hilfer-Type Fractional Differential Equations with Impulses
This article deals with some existence, uniqueness, and Ulam-Hyers-Rassias stability results for a class of boundary value problem for nonlinear implicit fractional differential equations with impulses and generalized Hilfer Fractional derivative. The results are obtained using the Banach contraction principle and Krasnoselskii’s and Schaefer’s fixed-point theorems.
A Common Fixed Point Theorem for Generalised -Kannan Mapping in Metric Space with Applications
This paper is aimed at proving a common fixed point theorem for -Kannan mappings in metric spaces with an application to integral equations. The main result of the paper will extend and generalise the recent existing fixed point results in the literature. We also provided illustrative examples and some applications to integral equation, nonlinear fractional differential equation, and ordinary differential equation for damped forced oscillations to support the results.