Iterative approximation of split feasibility problem in real Hilbert spaces

In this paper, we propose an iterative algorithm for finding solution of split feasibility problem involving a λ−strictly pseudo-nonspreading map and asymptotically nonexpansive semigroups in two real Hilbert spaces. We prove weak and strong convergence theorems using the sequence obtained from the proposed algorithm. Finally, we applied our result to solve a monotone inclusion problem and present a numerical example to support our result.

Stability of Nonlocal Stochastic Volterra Equations

In this paper, we study Ulam-Hyers-Rassias stability of solutions for nonlocal stochastic Volterra equations. Sufficient conditions for the existence and stability of solutions are derived using the Gronwall lemma. The advantage of our model equation is that it allows for additional measurements leading to better results compared to models with local initial conditions. Examples are solved to illustrate the applications of the results.

On Solution of First Order Initial Value Problems using Laplace Transform in Fuzzy Environment

This study aimed at solving a nonhomogeneous linear first order initial value problem by means of Laplace transform method in fuzzy environment. The conditions for a fuzzy function to be H−differentiable and gH−differentiability are well established. Finally, example is constructed to test the applicability or otherwise of the established results.

Optimal Stochastic Forecast Models of Rainfall in South-West Region of Nigeria

Rainfall estimates are important components of water resources applications, especially in agriculture, transport constructing irrigation and drainage systems. This paper aims to stochastically model and forecast the rainfall trend and pattern for a city, each purposively selected in five states of the South-Western Region of Nigeria. The data collected from Nigerian Meteorological Agency (NIMET) website are captured with fractional autoregressive integrated moving average (ARFIMA) and seasonal autoregressive integrated moving average (SARIMA) models. The autocorrelation function (ACF) and partial autocorrelation function (PACF) are used for model identification, the models selected are subjected to diagnostic checks for the models adequacy. Several tests: Augmented Dickey Fuller (ADF), Ljung Box and Jarque Bera tests are used for investigating unit root, serial autocorrelation and normality of residuals, respectively; the mean square error, root mean square error and mean absolute error are employed in validating the optimal stochastic model for each city in all states, in which the model with the lowest error of forecasting of all competing models is suggested as the best. The analyses and findings suggest SARIMA(1,0,1)(1,1,0) [12], SARIMA(3,0,2)(1,0,0) [12], SARIMA(1,0,0)(1,1,0) [12], SARIMA(2,0,2)(2,1,0) [12] and SARIMA(0,0,1)(1,1,0) [12] for (Ibadan) Oyo State, (Ikorodu) Lagos State, (Osogbo) Osun State, (Abeokuta) Ogun State and (Akure) Ondo state, respectively. The seasonal ARIMA (SARIMA) model was proven to be the best optimal stochastic forecast model for forecasting rainfall in the selected cities. The SARIMA model was, therefore, recommended as a veritable technique that will assist decision makers (Government, Farmers, and Policymakers) to establish better strategies “aprior” on the management of rainfall against upcoming weather changes to ensure increase in agricultural yields for the betterment of the citizenry and general economic growth.

Stagnation-Point Flow of Magneto-Williamson Nanofluid over a Stretching Material with Ohmic Heating and Entropy Analysis

This study communicates stagnation-point flow in magneto-Williamson nanofluid along a convectively heated nonlinear stretchable material in a porous medium. The impacts of Joule heating, thermophoresis together with Brownian motion are also checked in this investigation. In addition, thermodynamic second law is applied to develop entropy generation analysis of crucial parameters with identification of parameters capable of minimizing energy loss in the system. The transport equations are simplified into ordinary differential equations and then integrated numerically using Runge-Kutta-Fehlberg with shooting technique. The effects of the emerging parameters on the dimensionless velocity, temperature, concentration and entropy generation number are publicized through tables and graphs with appropriate discussions. In the limiting conditions, the results are found to conform accurately with published studies in the literature. It is found that the viscous drag can be reduced by lowering the magnitude of Weissenberg number, magnetic field and Darcy parameters while heat transfer at the surface improves in the presence of surface convection, temperature ratio and thermal radiation parameters. Besides, the analysis reveals that entropy generation can be minimized by lowering the magnitude of magnetic field, Schmidt number and surface convection parameters. The reduction in these parameters will promote efficient performance of thermal devices. More so, the results obtained in this study can be useful for the construction of appropriate thermal devices for use in energy and electronic devices.

Stability Analysis of Mathematical Model of a Relapse Tuberculosis Incorporating Vaccination

A general SIQRM epidemic model with vaccination and relapse possibility is proposed for analysis in this work. The idea behind the proposed model is to check the effect of immunity obtained from vaccine or treatment, quarantine effect as well as waning effect of immunity on the transmission rate of Tuberculosis within a population that is subjected to proper education without restricted access. Some other infectious diseases in this category include measles and Ebola. Two equilibrium states of the proposed model are obtained as well as the effective reproduction number(Reff). Stability analysis of the model at the Infection Free Equilibrium(I.F.E) state is established on the condition that Reff<1. Numerical simulation for the general SIQRM model was done using specific data for Tuberculosis disease and the result shows that proper education, vaccination and early diagnosis of an infectious individual for quarantining is an efficient way by which the spread of Tuberculosis can be reduced in the population while adequate medical attention yield better result for detected cases

Some new results on the stability and boundedness of solutions of certain class of second order vector differential equations

n this paper, we provide certain conditions that guarantee the stability of the zero solution when P(t, X, Y) = 0 and boundedness of all solutions when P(t, X, Y)# 0 of a certain system of second order differential equation using a suitable Lyapunov function. The results in this paper are quite new and complement those in the literature. Examples are given to demonstrate the correctness of the established results.

On The Closed Form Strategies of an Investor under the CEV and CIR Processes

In this paper, the explicit solutions of the optimal investment plans of an investor with exponential utility function exhibiting constant absolute risk aversion (CARA) under constant elasticity of variance (CEV) and stochastic interest rate is studied. A portfolio comprising of a risk-free asset modelled by the Cox-Ingersoll-Ross (CIR) process and two risky assets modelled by the CEV process is considered, where the instantaneous volatilities of the two risky assets form a 2 x 2 matrix n = {np,q}2x2 such that nnT is positive definite. Using the power transformation and change of variable approach with asymptotic expansion technique, explicit solutions of the optimal investment plans are found. Moreover, numerical simulations are used to study the effects of the interest rate, elasticity parameter, correlation coefficient and the risk averse coefficient on the optimal investment plans.