A Study on Common Fixed Point of Joint Generalized Cyclic Weak Nonexpansive Mappings and Generalized Cyclic Contractions in Quasi Metric SpacesRead 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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Chaotic Behaviour and Bifurcation in Real Dynamics of Two-Parameter Family of Functions including Logarithmic Map
The focus of this research work is to obtain the chaotic behaviour and bifurcation in the real dynamics of a newly proposed family of functions , depending on two parameters in one dimension, where assume that is a continuous positive real parameter and is a discrete positive real parameter. This proposed family of functions is different from the existing families of functions in previous works which exhibits chaotic behaviour. Further, the dynamical properties of this family are analyzed theoretically and numerically as well as graphically. The real fixed points of functions are theoretically simulated, and the real periodic points are numerically computed. The stability of these fixed points and periodic points is discussed. By varying parameter values, the plots of bifurcation diagrams for the real dynamics of are shown. The existence of chaos in the dynamics of is explored by looking period-doubling in the bifurcation diagram, and chaos is to be quantified by determining positive Lyapunov exponents.
Dynamic Models of Pollution Penalties and Rewards with Time Delays
In cases of nonpoint pollution sources, the regulator can observe the total emission but unable to distinguish between the firms. The regulator then selects an environmental standard. If the total emission level is higher than the standard, then the firms are uniformly punished, and if lower, then uniformly awarded. This environmental regulation is added to -firm dynamic oligopolies, and the asymptotical behavior of the corresponding dynamic systems is examined. Two particular models are considered with linear and hyperbolic price functions. Without delays, the equilibrium is always (locally) asymptotically stable. It is shown how the stability can be lost if time delays are introduced in the output quantities of the competitors as well as in the firms’ own output levels. Complete stability analysis is presented for the resulting one- and two-delay models including the derivations of stability thresholds, stability switching curves, and directions of the stability switches.
Mathematical Modeling of Public Opinions: Parameter Estimation, Sensitivity Analysis, and Model Uncertainty Using an Agree-Disagree Opinion Model
In this paper, we present a mathematical model that describes agree-disagree opinions during polls. We first present the different compartments of the model. Then, using the next-generation matrix method, we derive thresholds of the stability of equilibria. We consider two sets of data from the Reuters polling system regarding the approval rating of the U.S presidential in two terms. These two weekly polls data track the percentage of Americans who approve and disapprove of the way the President manages his work. To validate the reality of the underlying model, we use nonlinear least-squares regression to fit the model to actual data. In the first poll, we consider only 31 weeks to estimate the parameters of the model, and then, we compare the rest of the data with the outcome of the model over the remaining 21 weeks. We show that our model fits correctly the real data. The second poll data is collected for 115 weeks. We estimate again the parameters of the model, and we show that our model can predict the poll outcome in the next weeks, thus, whether the need for some control strategies or not. Finally, we also perform several computational and statistical experiments to validate the proposed model in this paper. To study the influence of various parameters on these thresholds and to identify the most influential parameters, sensitivity analysis is carried out to investigate the effect of the small perturbation near a parameter value on the value of the threshold. An uncertainty analysis is performed to evaluate the forecast inaccuracy in the outcome variable due to uncertainty in the estimation of the parameters.
Two-Weight, Weak-Type Norm Inequalities for Fractional Integral Operators and Commutators on Weighted Morrey and Amalgam Spaces
Let and be the fractional integral operator of order γ, and let be the linear commutator generated by a symbol function b and , . This paper is concerned with two-weight, weak-type norm estimates for such operators on the weighted Morrey and amalgam spaces. Based on weak-type norm inequalities on weighted Lebesgue spaces and certain -type conditions on pairs of weights, we can establish the weak-type norm inequalities for fractional integral operator as well as the corresponding commutator in the framework of weighted Morrey and amalgam spaces. Furthermore, some estimates for the extreme case are also obtained on these weighted spaces.
Maclaurin Coefficient Estimates for New Subclasses of Bi-univalent Functions Connected with a -Analogue of Bessel Function
In this paper, we introduce new subclasses of the function class of bi-univalent functions connected with a -analogue of Bessel function and defined in the open unit disc. Furthermore, we find estimates on the first two Taylor-Maclaurin coefficients and for functions in these new subclasses.
An Integral Equation for Riemann’s Zeta Function and Its Approximate Solution
Two identities extracted from the literature are coupled to obtain an integral equation for Riemann’s function and thus indirectly. The equation has a number of simple properties from which useful derivations flow, the most notable of which relates anywhere in the critical strip to its values on a line anywhere else in the complex plane. From this, both an analytic expression for , everywhere inside the asymptotic critical strip, as well as an approximate solution can be obtained, within the confines of which the Riemann Hypothesis is shown to be true. The approximate solution predicts a simple, but strong correlation between the real and imaginary components of for different values of σ and equal values of t; this is illustrated in a number of figures.