Multiple stable reference points in oyster populations: implications for reference point-based management

In the second of two companion articles, a 54-year time series for the oyster population in the New Jersey waters of Delaware Bay is analyzed to examine how the presence of multiple stable states affects reference-point–based management. Multiple stable states are described by four types of reference points. Type I is the carrying capacity for the stable state: each has associated with it a type-II reference point wherein surplus production reaches a local maximum. Type-II reference points are separated by an intermediate surplus production low (type III). Two stable states establish a type-IV reference point, a point-of-no-return that impedes recovery to the higher stable state. The type-II to type-III differential in surplus production is a measure of the difficulty of rebuilding the population and the sensitivity of the population to collapse at high abundance. Surplus production projections show that the abundances defining the four types of reference points are relatively stable over a wide range of uncertainties in recruitment and mortality rates. The surplus production values associated with type-II and type-III reference points are much more uncertain. Thus, biomass goals are more easily established than fishing mortality rates for oyster population

A New Type of Coincidence and Common Fixed Point Theorem with Applications

Coincidence and common fixed point theorems for a class of 'Ciric-Suzuki hybrid contractions involving a multivalued and two single-valued maps in a metric space are obtained. Some applications including the existence of a common solution for certain class of functional equations arising in a dynamic programming are also discussed..

An approach version of fuzzy metric spaces including an ad hoc fixed point theorem

In this paper, inspired by two very different, successful metric theories such us the real view-point of Lowen's approach spaces and the probabilistic field of Kramosil and Michalek's fuzzymetric spaces, we present a family of spaces, called fuzzy approach spaces, that are appropriate to handle, at the same time, both measure conceptions. To do that, we study the underlying metric interrelationships between the above mentioned theories, obtaining six postulates that allow us to consider such kind of spaces in a unique category. As a result, the natural way in which metric spaces can be embedded in both classes leads to a commutative categorical scheme. Each postulate is interpreted in the context of the study of the evolution of fuzzy systems. First properties of fuzzy approach spaces are introduced, including a topology. Finally, we describe a fixed point theorem in the setting of fuzzy approach spaces that can be particularized to the previous existing measure spaces.