Assume that f : X → Y is a proper map of a connected n-manifold X into a Hausdorff, connected, locally path-connected, and semilocally simply connected space Y , and y0 ∈ Y has a neighborhood homeomorphic to Euclidean n-space. The proper Nielsen number of f at y0 and the absolute degree of f at y0 are defined in this setting. The proper Nielsen number is shown to a lower bound on the number of ...

Results are obtained about the existence and behavior of hereditarily weakly confluent maps of continua onto the unit circle S1. A simple and useful necessary and sufficient condition is given for a map of a continuum, X, onto S1 to be hereditarily weakly confluent (HWC). It is shown that when X is arcwise connected, an HWC map of X onto S1 is monotone with arcwise connected fibers. A number of...

We consider a nonlinear fractional programming problem with inequality constraints, where the functions involved are ρ-semilocally b-preinvex, ρ-semilocally explicitly b-preinvex, ρ-semilocally quasi b-preinvex, ρ-semilocally pseudo bpreinvex and ρ-semi-locally strongly pseudo b-preinvex functions. Necessary optimality conditions are obtained in terms of the right derivative of a function along...