Article of the Year 2020
The Role of Control Measures and the Environment in the Transmission Dynamics of CholeraRead 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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Fixed Point Theorems for Set-Valued -Contractions in Branciari Distance Spaces
In this paper, the notion of set-valued -contractions is introduced, and a new fixed point theorem for such contractions is established. An example to illustrate main theorem is given.
Uncertainty Principles for Heisenberg Motion Group
In this article, we will recall the main properties of the Fourier transform on the Heisenberg motion group , where and denote the Heisenberg group. Then, we will present some uncertainty principles associated to this transform as Beurling, Hardy, and Gelfand-Shilov.
Lower Semicontinuity in of a Class of Functionals Defined on with Carathéodory Integrands
We prove lower semicontinuity in for a class of functionals of the form where , is open and bounded, for each satisfies the linear growth condition and is convex in depending only on for a.e. Here, we recall for ; the gradient measure is decomposed into mutually singular measures and . As an example, we use this to prove that is lower semicontinuous in for any bounded continuous and any Under minor addtional assumptions on , we then have the existence of minimizers of functionals to variational problems of the form for the given due to the compactness of in
Fixed Point Results for an Almost Generalized -Admissible -Contraction in the Setting of Partially Ordered b-Metric Spaces
In this paper, we introduce an almost generalized -admissible -contraction with the help of a simulation function and study fixed point results in the setting of partially ordered b-metric spaces. The presented results generalize and unify several related fixed point results in the existing literature. Finally, we verify our results by using two examples. Moreover, one of our fixed point results is applied to guarantee the existence of a solution of an integral equation.
A Note on Derivative of Sine Series with Square Root
Chaundy and Jolliffe proved that if is a nonnegative, nonincreasing real sequence, then series converges uniformly if and only if . The purpose of this paper is to show that if is nonincreasing and , then the series can be differentiated term-by-term on for . However, may not exist.
Existence of Solutions for Superlinear Second-Order System with Noninstantaneous Impulses
Variational methods are used in order to establish the existence of nontrivial weak solution for superlinear second-order system with noninstantaneous impulses. The main result is obtained when a kind of definition of the weak solution for this system is introduced. Meanwhile, an example is presented to illustrate the main result.