Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
843998 | Nonlinear Analysis: Theory, Methods & Applications | 2008 | 13 Pages |
Abstract
The concepts of “weak/strong topological contraction” and a generalization of Banach contraction mappings called “pp-contraction” are introduced and used to prove fixed point theorems for self-mappings from a topological/metric space into itself satisfying topological contraction/metric pp-contraction, respectively. Certain non-linear integral equations defined on C[a,b]C[a,b] satisfying generalized Lipschitzian conditions can easily be solved by applying these theorems. In the sequel, we shall study the possibility of optimally controlling the solution of the ordinary differential equation via dynamic programming.
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Authors
Hemant Kumar Pathak, Naseer Shahzad,