Research in Mathematics at Cameron University

Ioannis K. Argyros was born in 1956 in Athens, Greece. He received a B.Sc. from the University of Athens, Greece; and a M.Sc. And Ph.D. from the University of Georgia, Athens, Georgia, USA, under the supervision of Dr. Douglas N. Clark. Dr. Argyros is currently a full Professor of Mathematics at Cameron University, Lawton, OK, USA. His research interests include: Applied mathematics, Operator theory, Computational mathematics and iterative methods especially on Banach spaces. He has published more than a thousand peer reviewed papers, thirty two books and seventeen chapters in books in his area of research, computational mathematics. He is an active reviewer of a plethora of papers and books, and has received several national and international awards. He has supervised two PhD students, several MSc. and undergraduate students, and has been the external evaluator for many PhD theses, tenure and promotion applicants.

Preface; Author Contact Information; The History of Newtons Method and Extended Classical Results; Extended Global Convergence of Iterative Methods; Extended Gauss-Newton-Approximate Projection Methods of Constrained Nonlinear Least Squares Problems; Convergence Analysis of Inexact Gauss-Newton Like for Solving Systems; Local Convergence of the Gauss-Newton Scheme on Hilbert Spaces Under a Restricted Convergence Domain; Ball Convergence for Inexact Newton-type Conditional Gradient Solver for Constrained Systems; Newton-like Methods with Recursive Approximate Inverses; Updated Mesh Independence Principle; Ball Convergence for Ten Solvers Under the Same Set of Conditions; Extended Newtons Solver for Generalized Equations Using a Restricted Convergence Domain; Extended Newtons Method for Solving Generalized Equations: Kantorovichs Approach; Extended Robust Convergence Analysis of Newtons Method for Cone Inclusion Problems in Banach Spaces; Extended and Robust Kantorovichs Theorem on the Inexact Newtons Method with Relative Residual Error Tolerance; Extended Local Convergence for Iterative Schemes Using the Gauge Function Theory; Improved Local Convergence of Inexact Newton Methods under Average Lipschitz-type Conditions; Semi-Local Convergence of Newtons Method Using the Gauge Function Theory: An Extension; Extending the Semi-Local Convergence of Newtons Method Using the Gauge Theory; Global Convergence for Chebyshevs Method; Extended Convergence of Efficient King-Werner-Type Methods of Order 1+√2; Extended Convergence for Two Chebyshev-Like Methods; Extended Convergence Theory for Newton-Like Methods of Bounded Deterioration; Extending the Kantorovich Theorem for Solving Equations Using Telescopic Series; Extended ω-Convergence Conditions for the Newton-Kantorovich Method; Extended Semilocal Convergence Analysis for Directional Newton Method; Extended Convergence of Damped Newtons Method; Extended Convergence Analysis of a One-Step Intermediate Newton Iterative Scheme for Nonlinear Equations; Enlarging the Convergence Domain of Secant-Type Methods; Two-Step Newton-Type Method for Solving Equations; Two-Step Secant-Type Method for Solving Equations; Unified Convergence for General Iterative Schemes; Extending the Applicability of Gauss-Newton Method for Convex Composite Optimization; Local Convergence Comparison Between Newtons and the Secant Method: Part-I; Convergence Comparison Between Newtons and Secant Method: Part-II; Extended Convergence Domains for a Certain Class of Fredholm Hammerstein Equations; Extended Convergence of the Gauss-Newton-Kurchatov Method; Extended Semi-Local Convergence of Newtons Method under Conditions on the Second Derivative; Extended Convergence for the Secant Method Under Mysovskii-like Conditions; Glossary of Symbols.