Symmetry with Operator Theory and Equations

• Main Author: Argyros, Ioannis (auth)
• Format: Electronic Book Chapter
• Language: English
• Published: MDPI - Multidisciplinary Digital Publishing Institute 2019
• Subjects: Lipschitz condition; order of convergence; Scalar equations; local and semilocal convergence; multiple roots; Nondifferentiable operator; optimal iterative methods; Order of convergence; convergence order; fast algorithms; iterative method; computational convergence order; generalized mixed equilibrium problem; nonlinear equations; systems of nonlinear equations; Chebyshev's iterative method; local convergence; iterative methods; divided difference; Multiple roots; semi-local convergence; scalar equations; left Bregman asymptotically nonexpansive mapping; basin of attraction; maximal monotone operator; Newton-HSS method; general means; Steffensen's method; derivative-free method; simple roots; fixed point problem; split variational inclusion problem; weighted-Newton method; ball radius of convergence; Traub-Steffensen method; Newton's method; fractional derivative; Banach space; multiple-root solvers; uniformly convex and uniformly smooth Banach space; Fréchet-derivative; optimal convergence; Optimal iterative methods; basins of attraction; nonlinear equation
• Online Access: DOAB: download the publication; DOAB: description of the publication

A plethora of problems from diverse disciplines such as Mathematics, Mathematical: Biology, Chemistry, Economics, Physics, Scientific Computing and also Engineering can be formulated as an equation defined in abstract spaces using Mathematical Modelling. The solutions of these equations can be found in closed form only in special case. That is why researchers and practitioners utilize iterative procedures from which a sequence is being generated approximating the solution under some conditions on the initial data. This type of research is considered most interesting and challenging. This is our motivation for the introduction of this special issue on Iterative Procedures.