Department Of Mathematics

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https://ir.unilag.edu.ng/handle/123456789/3386
The Department of Mathematics was first established in the School of Mathematical and Physical Sciences in October, 1964 and produced the first set of graduates in 1967. The Department was then composed of two subject areas, namely. Mathematics and Mathematical Physics, and could be taken as two subjects or as one subject. During that period, students in the School of Biological Sciences and the School of Mathematical and Physical Sciences were being examined in three subjects or, in exceptional cases, in one subject in Part III. The Department became part of the newly reconstituted Faculty of Science in 1973. As from 1974, Senate approved a new degree structure based on course units and in 1978, in addition to the Honours Degree Programme in Mathematics, the Department started a combined Honours Degree Programme in Mathematics and Statistics and in 1983, the Department started a Four-Year Degree Programme. The Department started a B.Sc. (Hons) Degree Programme in Industrial Mathematics in 2010/2011.

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Now showing 1 - 20 of 84
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    Open Access
    Abundant Natural Resources, EthnicDiversity, and Inclusive Growth in sub-Saharan Africa: A Mathematical Approach
    (Department of Mathematics, Prairie View A&M University, USA., 2021) Ayoade, A. A.; Adenuga, J. I.; Ajide, K. B.; Odeleye, A. T.
    The sub-Saharan African region is blessed with abundant natural resources and diverse ethnic groups, yet the region is dominated by the largest number of poor people worldwide due to inequitable distribution of national income. Existing statistics forecast decay in the quality of lives over the years compared to the continent of Asia that shares similar history with the region. In this paper, a five-dimensional first-order nonlinear ordinary differential equation was formulated togiveinsightintovariousfactorsthatshapeddynamicsofinclusivegrowthinsub-SaharanAfrica. The validity test was performed based on ample mathematical theorems and the model was found tobevalid.Themodelwasthenstudiedqualitativelyandquantitativelyviastabilitytheoryofnonlinear differential equations which depended on the policy success ratio and classical fourth-order Runge-Kutta scheme implemented in Maple, respectively. The results from the analysis showed that inclusive growth from abundant natural resources and ethnic diversity in sub-Saharan Africa was a function of policy reform whereby an increase in both equitable distribution of national income and accessibility of common man to the goods and services provided by the state to narrow inequality gap was accompanied with a low level of nepotism
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    Open Access
    Application of the ARIMA Models for Predicting Students’ Admissions in the University of Lagos
    (Journal of Scientific Research and Development, 2017) Onyeka-Ubaka, J.N.; Agwuegbo, S.O.N.; Abass, O.
    The objective was to assess the performance of the AutoRegressive Integrated Moving Average (ARIMA) models when occasional level shifts occur in the time series under study. The secondary data on the University of Lagos’ undergraduates’ admissions (1962–2016) were collected and analysed. It is predicted that universities in Nigeria and elsewhere could forecast their enrolment figures and student population growth rate based on the ARIMA models. The Box–Jenkins (B–J) approach provided the theoretical framework for the statistical analysis. The study used the Kalman Filter (KF) algorithm to develop a method using an ARIMA model to overcome and resolve the three main problems of the B–J methodology. The KF estimated the states for dynamic systems in state-variable formulations. Forecasting university admissions is necessary if student population must match the infrastructural provisions on campuses. The best ARIMA models have been selected by using criteria such as Akaike’s Information Criterion (AIC), Schwarz’s Bayesian Criterion (SBC), Absolute Mean Error (AME), Root Mean Square Error (RMSE) and Mean Absolute Percent Error (MAPE). To select the best ARIMA model, the data was split into two periods: estimation period and validation period. The results clearly showed a continual increase in the demand for university education in the University of Lagos and, by extension, other universities in Nigeria.
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    Open Access
    An Approach to the Approximation of Common Coupled Fixed Points of Contractive Maps in Metric-Type Spaces
    (Advanced Fixed Point Theory, 2015) Olaoluwa, H.O.; Olaleru, J.O
    In this research work, some results on the existence and approximation of common coupled fixed points of contractive maps in cone metric spaces are unified and generalized based on a new method
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    Open Access
    An assessment of predictive performance of Zellner’s g-priors in Bayesian model averaging
    (IOS Press, Nieuwe Hemweg 6B 1013 BG Amsterdam The Netherlands., 2018) Ogundeji, Rotimi; Adeleke, Ismaila; Okafor, Ray
    When making predictions and inferences, data analysts are often faced with the challenge of selecting the best model among competing models as a result of large number of regressors that cumulate into large model space. Bayesian model averaging (BMA) is a technique designed to help account for uncertainty inherent in model selection process. In Bayesian analysis, issues of the choice of prior distribution have been quite delicate in data analysis and posterior model probabilities (PMP) in the context of model uncertainty under model selection process are typically sensititve to the specification of prior distribution. This research identified a set of eleven candidate default priors (Zellner’s g-priors) prominent in literature and applicable in Bayesian model averaging. A new robust g-prior specification for regression coefficients in Bayesian Model Averaging is investigated and its predictive performance assessed along with other g-prior structures in literature. The predictive abilities of these g-prior structures are assessed using log predictive scores (LPS) and log maximum likelihood (LML). The sensitivity of posterior results to the choice of these g-prior structures was demonstrated using simulated data and real-life data. The simulated data obtained from multivariate normal distribution were first used to demonstrate the predictive performance of the g-prior structures and later contaminated for the same purpose. Similarly for the same purpose, the real life data were normalized before using the data as obtained. Empirical findings reveal that under different conditions, the new g-prior structure exhibited robust, equally competitive and consistent predictive ability when compared with identified g-prior structures from the literature. The new g-prior offers a sound, fully Bayesian approach that features the virtues of prior input and predictive gains that minimise the risk of misspecification.
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    Open Access
    Bayesian Estimation of Above-Average Performance in Tertiary Institutions: A Case Study of University of Lagos, Akoka, Nigeria.
    (International Organization of Scientific Research, IOSR Journals., 2013) Ogundeji, Rotimi; Lawal, Ganiyu; Arowolo, Olatunji
    Bayesian approach for parameter estimation has the capacity to yield more precise estimates than methods based on sampling theory. There are several common Bayesian models; in this study we applied Empirical Bayes (EB) model called Beta-binomial model. The study is motivated by the need to beam searchlight on universities, faculties or fields of study with graduates who may not be eligible for further educational pursuits. This study provides means of assessment or a basis of evaluation of students’ performances among faculties or fields of study and overall performance of a university. This study uses Bayesian methods of inference to estimate the proportion of above-average performance of graduates from the various faculties in University of Lagos. The model adopted generated results which are of smaller variances compared with variances of sample Proportions, showing that the posterior proportions generated are more efficient estimators. This is further evidenced in narrow widths of the computed confidence intervals. The overall result shows that the proportion of above-average performance of graduates of University of Lagos, who are eligible for further educational pursuits (i.e. higher degrees), is approximately 72% of the university graduates.
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    Open Access
    Best proximity point results for Hardy–Rogers p-proximal cyclic contraction in uniform spaces.
    (Springer Open Journal, 2018) Olisama, V.O.; Olaleru, J.O; Akewe, H
    The Hardy–Rogers p-proximal cyclic contraction, which includes the cyclic, Kannan, Chatterjea and Reich contractions as sub-classes, is developed in uniform spaces. The existence and uniqueness results of best proximity points for these contractions are proved. The results, which are for non-self maps, apart from the fact that they are new in literature, generalise several other similar results in literature. Examples are given to validate the results obtained.
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    Open Access
    Best Proximity Point Results for Some Contractive Mappings in Uniform Spaces
    (Hindawi Publishing Corporation, 2017) Olisama, V.O.; Olaleru, J.O; Akewe, H
    We introduce the concept of 𝐽𝑎V-distance (an analogue of 𝑏-metric), 𝜙𝑝-proximal contraction, and 𝜙𝑝-proximal cyclic contraction for non-self-mappings in Hausdorff uniform spaces. We investigate the existence and uniqueness of best proximity points for these modified contractive mappings. The results obtained extended and generalised some fixed and best proximity points results in literature. Examples are given to validate the main results.
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    Open Access
    Block method for numerical solution of differential-algebraic equations with hessenberg index-3
    (2014) OA Akinfenwa, SA Okunuga
    A Block Second Derivative Formula (BSDF) of order seven for the numerical solution of Hessenberg Differential Algebraic Equations (DAEs) of index 3 is presented. This is achieved by constructing a Continuous Second Derivative Formula (CSDF) used to obtain the main and additional methods which are combined to form a single block of methods that simultaneously provide the approximate solutions for the Hessenberg DAEs of index 3. The error constant and stability properties of the BSDF are discussed. The performance of the method is demonstrated on some numerical examples to show the accuracy and efficiency of the method.
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    Open Access
    Budget Deficits, External Debt and Economic Growth in Nigeria
    (World Scientific Publishing Company, 2010-09) Osinubi, T.S; Dauda, R.O.S; Olaleru, O.E
    The necessity for governments to borrow in order to finance deficit budgets has led to the development of external debt. This study examines how the use of budget deficits as an instrument of stabilization leads to the accumulation of external debt with the attending effects on growth in Nigeria between 1970 and 2003. By synthesizing a relationship between budget deficits and external debt the study shows the implications on economic growth of conducting a fiscal policy within the contexts of debt stabilization and debt sustainability. The results of the econometric analysis confirm the existence of the debt Laffer curve and the nonlinear effects of external debt on growth in Nigeria. The study concludes that if debt-financed budget deficits are operated in order to stabilize the debt ratio at the optimum sustainable level debt overhang problems would be avoided and the benefits of external borrowing would be maximized.
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    Open Access
    Common fixed point theorems for pairs of hybrid maps in G-symmetric spaces
    (Academic Publications, Limited, 2015) Eke, K.S; Olaleru, J.O
    The existence of the common fixed points for some pairs of hybrid maps(i.e. singled-valued and set-valued maps) satisfying some generalized contractive conditions in G-symmetric spaces are proved. The results extend and improve some results in literature
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    Open Access
    Common Fixed Point Results for Occasionally Weakly Compatible Maps in G-Symmetric Spaces
    (Scientific Research, 2014-03-05) Eke, K.S; Olaleru, J
    The notion of a G-symmetric space is introduced and the common fixed points for some pairs of occasionally weakly compatible maps satisfying some contractive conditions in a G-symmetric space are proved. The results extend and improve some results in literature.
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    Open Access
    Common Fixed Point Results for Occasionally Weakly Compatible Maps in G-Symmetric Spaces
    (Science Research, 2014) Eke, K.S.; Olaleru, J.O
    The notion of a G-symmetric space is introduced and the common fixed points for some pairs of occasionally weakly compatible maps satisfying some contractive conditions in a G-symmetric space are proved. The results extend and improve some results in literature.
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    Open Access
    Common Fixed Point Theorems for Pairs of Hybrid Maps in G-Symmetric Spaces
    (International Journal of Pure and Applied Mathematics, 2015) Eke, K.S.; Olaleru, J.O
    The existence of the common fixed points for some pairs of hybrid maps(i.e. singled-valued and set-valued maps) satisfying some generalized contractive conditions in G-symmetric spaces are proved. The results extend and improve some results in literature.
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    Open Access
    Common Fixed Points of a Three-Step Iteration with errors of Asymptotically Quasi-Nonexpansive Nonself-Mappings in the Intermediate sense in Banach spaces
    (F a s c i c u l i M a t h e m a t i c i, 2014) Okeke, G.A.; Olaleru, J.O
    In this paper, we extend the results of Inprasit and Wattanataweekul [7] to the class of asymptotically quasi-nonexpansive nonself-mappings in the intermediate sense. We prove some strong convergence theorems for asymptotically quasi-nonexpansive nonself-mappings in the intermediate sense using a three-step iterative method for finding a common element of the set of solutions of a generalized mixed equilibrium problem and the set of common fixed points of a finite family of nonexpansive mappings in a real Hilbert space. Our results extends, improves, unifies and generalizes the results of [13], [25] and [27].
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    Open Access
    A Comparison of Mann and Ishikawa iterations of quasi-contraction operators
    (World Congress on Engineering, 2007) Olaleru, J.O
    It is generally conjectured that the Mann iteration converges faster than the Ishikawa iteration for any operator defined on an arbitrary closed convex subset of a Banach space. The recent result of Babu et al [1] shows that this conjecture can be proved for a class of quasi-contractive operators called the Zamfirescu operators[10]. In this paper it is shown that the proof can indeed be generalised to that of quasi-contraction maps.
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    Open Access
    A comparison of Picard and Mann Iterations for Quasi-Contraction Maps
    (Fixed Point Theory Journal, 2007) Olaleru, J.O
    For a class of quasi-contractive operators defined on an arbitrary Banach space, it has been shown that the Picard iteration technique converges faster than the Mann iteration technique. In this paper we make a comparison of the Picard and Mann iterations with respect to their convergence rate for a more general class of operators called quasi-contractions in metrizable topological vector spaces. It was observed that the Picard iteration converges faster than the Mann iteration for this class of maps. This answers the question posed by Berinde in his paper.
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    Open Access
    Continuous block backward differentiation formula for solving stiff ordinary differential equations.
    (Elsevier, 2013-04) Akinfenwa, O.A; Jator, S.N; Yao, N.M
    In this paper, we consider an implicit Continuous Block Backward Differentiation formula (CBBDF) for solving Ordinary Differential Equations (ODEs). A block of p new values at each step which simultaneously provide the approximate solutions for the ODEs is derived, where p is the number of points. A performance comparison of the continuous block methods is made with existing methods. Numerical results indicate that the CBBDF is more efficient in improving the number of integration steps with better accuracy.
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    Open Access
    Convergence of a Modified Multi-Step Iterative Scheme for P- Nearly Uniformly L-Lipschitzian Asymptotically Pseudocontrative Mappings
    (International Journal of Analysis and Applications, 2014) Olisama, V.O.; Mogbademu, A.A.; Olaleru, J.O
    In this paper, it is shown that the modified multi-step iteration converges strongly to the common fixed point of a finite family of nearly uniformly L- Lipschitzian asymptotically pseudo contractive mappings. The main result is an improvement and extension of well known results in the literature.
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    Open Access
    Convergence Theorems for Asymptotically Pseudocontractive Mappings in the Intermediate Sense for the Modified Noor Iterative Scheme
    (International Journal of Mathematical Modelling & Computations, 2015) Okeke, G.A.; Olaleru, J.O
    We study the convergence of the modified Noor iterative scheme for the class of asymptotically pseudocontractive mappings in the intermediate sense which is not necessarily Lipschitzian. Our results improves, extends and unifies the results of [Schu, Iterative construction of fixed points of asymptotically nonexpansive mappings, Mathematical Analysis and Applications, 158 (2) (1991) 407-413] and [Qin et al.Convergence theorems on asymptotically pseudocontractive mappings in the intermediate sense, Fixed Point Theory and Applications,2010, Article ID 186874, 14 pages, (2010)].
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    Open Access
    Convergence Theorems on Asymptotically Generalized Φ-Hemicontractive Mappings in the Intermediate Sense
    (Hikari Ltd, 2013) Olaleru, J.O; Okeke, G.A; Akewe, H
    In this study, we introduce two classes of nonlinear mappings, the class of asymptotically generalized Φ-hemicontractive mappings in the intermediate sense and asymptotically generalized Φ-pseudocontractive mappings in the intermediate sense; and prove the convergence of Mann type iterative scheme with errors to their fixed points. Our results generalize the results of Chang et al. [4], Chidume and Chidume [5] and Kim et al. [8] among others.