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We study the space of all continuous and increasing self-mappings of a real interval [a, b], where a < b are real numbers, equipped with the topology of uniform convergence. We show, in particular, that most such functions have infinitely many different fixed points. [ABSTRACT FROM AUTHOR]

Given a nonexpansive mapping which maps a closed subset of a complete metric space into the space, we study the convergence of its inexact iterates to its fixed point set in the case where the errors are nonsummable. Previous results in this direction concerned nonexpansive self-mappings of the complete metric space and inexact iterates with summable errors. [ABSTRACT FROM AUTHOR]

For certain classes of contractive mappings in complete metric spaces, we establish the existence of a fixed point which attracts all inexact orbits. [ABSTRACT FROM AUTHOR]

In this paper, we study three fixed point problems. The first one is a fixed point problem with a set-valued mapping, while the second and third problems are convex feasibility problems with infinitely many constraints solved by the subgradient projection algorithm. We show that an approximate solution is reached after a finite number of iterations under the presence of computational errors. [ABSTRACT FROM AUTHOR]

We first study the asymptotic behavior of infinite products of nonexpansive selfmappings of a star-shaped complete metric space which is not necessarily bounded. Using the notion of contractivity and the Baire category approach, we show that a typical (generic) sequence of nonexpansive mappings is contractive and generates infinite products which have the same asymptotic behavior. This result is then applied to certain classes of nonexpansive set-valued self-mappings of a closed and star-shaped subset of a Banach space. It is shown that in these classes most (in the sense of Baire category) mappings are contractive. In particular, we show that this fact is true for a certain class of compact-valued mappings. It follows that a generic mapping in this class has a fixed point. [ABSTRACT FROM AUTHOR]

In the context of a model due to Robinson, Solow and Srinivasan (the RSS model), we report results on the existence and characterization of locally optimal programs, a concept taken from theoretical physics. In particular, we propose a (new) transversality condition under which all locally optimal programs are good. An extended introduction places our theorems in the context of previous work on the existence question, including that on agreeable programs. It appears that there is no completely rational way to attack [the] problem without considering development programmes over an infinite horizon (Gale in Rev Econ Stud 34:1–8, 1967). The analysis of simple models is essential if we are to understand the corresponding situation for more complex models of the economy (Mirrlees and Stern in J Econ Theory 4:268–288, 1972). The technical convenience, for clear and quantitative results, of using an infinite time horizon is rather great (Hammond and Mirrlees in Models of economic growth, Wiley, New York, pp 283–299, 1973). [ABSTRACT FROM AUTHOR]

In this paper we study a class of minimax problems $${\max\{f(x),g(x)\} \to \min, x \,{\in} \, R^n}$$ where $${f,g \in C^1(R^n)}$$. We show that the subclass of all problems for which there exists a point of minimum $${z \in R^1}$$ such that $${f(z)=g(z)}$$ and $${\nabla f(z)=\nabla g(z)}$$ is small. [ABSTRACT FROM AUTHOR]

The article discusses a study which examines the equilibrium problems of a complete metric space of functions. The study revealed that the class of equilibrium problems has possessed a unique solution and is well-posed. The study found that the countable intersection of a complete metric space of functions will dense subsets that are satisfying and inequality for a generic problem. The study also assessed that metric space is a paracompact where the finite partition of unity is subordinated to the continuous function.

We provide sufficient conditions for the iterates of an asymptotic contraction on a complete metric space X to converge to its unique fixed point, uniformly on each bounded subset of X. [ABSTRACT FROM AUTHOR]