372 research outputs found
Algorithm for solutions of nonlinear equations of strongly monotone type and applications to convex minimization and variational inequality problems
Real-life problems are governed by equations which are nonlinear in nature.
Nonlinear equations occur in modeling problems, such as minimizing costs in
industries and minimizing risks in businesses. A technique which does not
involve the assumption of existence of a real constant whose calculation is
unclear is used to obtain a strong convergence result for nonlinear equations
of (p, {\eta})-strongly monotone type, where {\eta} > 0, p > 1. An example is
presented for the nonlinear equations of (p, {\eta})-strongly monotone type. As
a consequence of the main result, the solutions of convex minimization and
variational inequality problems are obtained. This solution has applications in
other fields such as engineering, physics, biology, chemistry, economics, and
game theory.Comment: 11 page
Alternative iterative methods for nonexpansive mappings, rates of convergence and application
Alternative iterative methods for a nonexpansive mapping in a Banach space
are proposed and proved to be convergent to a common solution to a fixed point
problem and a variational inequality. We give rates of asymptotic regularity
for such iterations using proof-theoretic techniques. Some applications of the
convergence results are presented
Iterative algorithms for solutions of nonlinear equations in Banach spaces.
Doctoral Degree. University of KwaZulu-Natal, Durban.Abstract available in PDF
Alternative iterative methods for nonexpansive mappings, rates of convergence and applications
Alternative iterative methods for a nonexpansive mapping in a Banach space are
proposed and proved to be convergent to a common solution to a fixed point problem and
a variational inequality. We give rates of asymptotic regularity for such iterations using
proof-theoretic techniques. Some applications of the convergence results are presented
Holomorphic functions on Banach spaces
This is a survey about some problems from the theory of holomorphic functions on Banach spaces which have attracted the attention of many researchers during the last thirty years
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