This project lies at the interface between Nonlinear Functional Analysis, unconstrained Optimization and Critical point theory. It concerns mainly the Ambrosetti-Rabinowitz's Mountain Pass Theorem which is a min-max theorem ...

In this thesis, we treated a Standard Finite Difference Scheme for a singularly perturbed parabolic reaction-diffusion equation. We proved that the Standard Finite Difference Scheme is not a robust technique for solving ...

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 ...

The theory of analytic functions plays a central role in operator theory. It has been a source of methods, examples and problems, and has led to numerous important results. Weighted shifts (which we shall see in the sequel) ...

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The scope of Quadratic Form Theory is historically wide although it usually appears almost as an afterthought when needed to solve a variety of problems such as the classification of Hessian matrices in finite dimensional ...

This work concerns one of the most important tools to solve well-posed problems in the theory of evolution equations (e.g di usion equation, wave equations, ...) and in the theory of stochastic process, namely the semigroups ...

In this work, we propose a one-step algorithm for solving variational inequality problems in a 2-uniformly con vex Banach space. Weak convergence of the scheme to a solution of variational inequality is established under ...

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Compact operators are linear operators on Banach spaces that maps bounded set to relatively compact sets. In the case of Hilbert space H it is an extension of the concept of matrix acting on a finite dimensional vector ...

This Project primarily falls into the field of Linear Functional Analysis and its Applications to Eigenvalue problems. It concerns the study of Compact Linear Operators (i.e., bounded linear operators which map the closed ...

Let E be a real 2-uniformly convex Banach space with topological dual E∗. We established strong convergence for the class of variational inclusion for the sum of three monotone operators. More over, we give a variant of ...

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 ...

The study of variational inequalities frequently deals with a mapping F from a vector 0 space X or a convex subset of X into its dual X . Let H be a real Hilbert space and a(u, v) be a real bilinear form on H. Assume that ...

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 ...

We consider classical Finite Difference Scheme for a system of singularly perturbed convection-diffusion equations coupled in their reactive terms, we prove that the classical SFD scheme is not a robust technique for solving ...