ABSTRACT Let E be a uniformly convex and uniformly smooth real Banach space and E ∗ be its dual. Let A : E → 2 E∗ be a bounded maximal monotone map. Assume that A−1 (0) 6= ∅. A new iterative sequence is constructed which converges strongly to an element of A−1 (0). The theorem proved, complements results obtained on strong convergence of the proximal point algorithm for approximating an element of A−1 (0) (assuming existence) and also resolves an important open question. Further...
INTRODUCTION Questions about controllability and stability arise in almost every dynamical system problem. As a result, controllability and stability are one of the most extensively studied subjects in system theory. A departure point of control theory is the dierential equation
The cardinal goal to the study of theory of Partial Differential Equations (PDEs) is to insure or find out properties of solutions of PDE that are not directly attainable by direct analytical means. Certain function spaces have certain known properties for which solutions of PDEs can be classified. As a result, this work critically looked into some function spaces and their properties. We consider extensively, L p − spaces, distribution theory and sobolev spaces. The emphasis is made on sob...
ABSTRACT Let E be a real normed space with dual space E ∗ and let A : E → 2 E∗ be any map. Let J : E → 2 E∗ be the normalized duality map on E. A new class of mappings, J-pseudocontractive maps, is introduced and the notion of J-fixed points is used to prove that T := (J − A) is J-pseudocontractive if and only if A is monotone. In the case that E is a uniformly convex and uniformly smooth real Banach space with dual E ∗ , T : E → 2 E∗ is a bounded J-pseudocontractive map wi...
The exploitation of nature's propensity offers us ample opportunities to achieve or deal with an optimal objective concerning constrained shape, volume, time, velocity, energy or gain. This vivifies the need to study Optimization Theory and related topics. In order to make the concepts clear, let us recall some keywords. Given a nonempty set X and a function f : X → R which is bounded below, computing the number
Abstract The goal of this thesis is to extend the notion of integration with respect to a measure to Lattice spaces. To do so the paper is first summarizing the notion of integration with respect to a measure on R. Then, a construction of an integral on Banach spaces called the Bochner integral is introduced and the main focus which is integration on lattice spaces is lastly addressed.
ABSTRACT The work of Osilike and Isiogugu, Nonlinear Analysis, 74 (2011), 1814-1822 on weak and strong convergence theorems for a new class of k-strictly pseudononspreading mappings in real Hilbert spaces is reviewed. We studied in detail this new class of mappings which is more general than the class of nonspreading mappings studied by Kurokawa and Takahashi, Nonlinear Analysis 73 (2010) 1562-1568. Many incisive examples establishing the relationship of the class of k-strictly pseudononspre...
Abstract Stochastic calculus has been applied to the problems of pricing financial derivatives since 1973 when Black and Scholes published their famous paper ”The pricing of options and corporate liabilities” in the journal of political economy. In this work, we introduce basic concepts of probability theory which gives a better understanding in the study of stochastic processes, such as Markov process, Martingale and Brownian motion. We then construct the Itˆo’s integral under stocha...
ABSTRACT The asset price returns are multi-period (that is multi-fractal dimensional) market depending on market scenarios which are the measure points. In this research work, a number of continuous time stochastic models were formulated, for the measurement of random behaviour of equity returns, using multi-fractal measures which examine power law behaviours at different time scales. Fractal exponent was first derived followed by a seemingly Black-Scholes parabolic equation. The solution to...
ABSTRACT The subgradient extragradient method is considered an improvement of the extragradient method for variational inequality problem for the class of monotone and Lipschitz continuous mappings in the setting of Hilbert spaces. In this Thesis, we proposed an improved subgradient extragradient method for variational inequality problem for the class of monotone and Lipschitz continuous mappings in the setting of real Banach spaces.
ABSTRACT The major goal of this research work is to determine the dynamic buckling load of a viscously damped imperfect quadratic-cubic elastic model structure, which is modeled by a nonlinear differential equation containing a load parameter. For a structure with small imperfections and subjected to step loading , the equation contains two small independent parameters, upon which asymptotic expansions are initiated. The nonlinearity is quadratic-cubic in nature and multiple-scaling two-timi...
CHAPTER ONE INTRODUCTION 1.1 BACKGROUND OF THE STUDY Linear Programming is a subset of Mathematical Programming that is concerned with efficient allocation of limited resources to known activities with the objective of meeting a desired goal of maximization or minimization of a function. Linear Programming determines the way to achieve the best outcome (such as maximum profit or lowest cost) in a given mathematical model, given some list of requirements as linear equations. Linear Progra...
ABSTRACT Finite deformation of Elastic rotating solid spheres of blatz-ko material are studied in this research work. The analysis resulted into non-linear boundary value problem governed by non-linear partial differential equations for the displacements. An asymptotic method of solution is employed for the solution of equations. The method assumes a trial solution for the displacements in a particular space. Here, the Sobolev space of order two is used. The resulting error is minimized in...