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We study the space of all continuous and increasing self-mappings of the real interval [0, 1] equipped with the topology of uniform convergence. In particular, we show that most such functions have at least two different fixed points. [ABSTRACT FROM AUTHOR]

We introduce a new class of nonlinear contractive mappings in Banach spaces, study their iterates and establish a fixed point theorem for them. [ABSTRACT FROM AUTHOR]

Given a Lipschitz and convex objective function of an unconstrained optimization problem, defined on a Banach space, we revisit the class of regular vector fields which was introduced in our previous work on descent methods. We study, in particular, the asymptotic behavior of the sequence of values of the objective function for a certain inexact process generated by a regular vector field when the sequence of computational errors converges to zero and show that this sequence of values converges to the infimum of the given objective function of the unconstrained optimization problem. [ABSTRACT FROM AUTHOR]

We study monotone nonexpansive self-mappings of a closed and convex cone in an ordered Banach space with particular emphasis on the asymptotic behavior of their inexact iterates. [ABSTRACT FROM AUTHOR]