Convergence Theorems for Hierarchical Fixed Point Problems and Variational Inequalities

This paper deals with a modifed iterative projection method for approximating a solution of hierarchical fixed point problems for nearly nonexpansive mappings. Some strong convergence theorems for the proposed method are presented under certain approximate assumptions of mappings and parameters. As a special case, this projection method solves some quadratic minimization problem. It should be noted that the proposed method can be regarded as a generalized version of Wang et.al. [15], Ceng et. al. [14], Sahu [4] and many other authors.Comment: 12 pages. arXiv admin note: substantial text overlap with arXiv:1403.321

Partial b_{v}(s) and b_{v}({\theta}) metric spaces and related fixed point theorems

In this paper, we introduced two new generalized metric spaces called partial b_{v}(s) and b_{v}({\theta}) metric spaces which extend b_{v}(s) metric space, b-metric space, rectangular metric space, v-generalized metric space, partial metric space, partial b-metric space, partial rectangular b-metric space and so on. We proved some famous theorems such as Banach, Kannan and Reich fixed point theorems in these spaces. Also, we give definition of partial v-generalized metric space and show that these fixed point theorems are valid in this space. We also give numerical examples to support our definitions. Our results generalize several corresponding results in literature.Comment: 15 page

On the Persistence of Income Shocks over the Life Cycle: Evidence, Theory, and Implications,Second Version

How does the persistence of earnings change over the life cycle? Do workers at different ages face the same variance of idiosyncratic shocks? This paper proposes a novel specification for residual earnings that allows for an age profile in the persistence and variance of labor income shocks. We show that the statistical model is identified and estimate it using PSID data. We find that shocks to earnings are only moderately persistent (around 0:75) for young workers. Persistence rises with age up to unity until midway in life. The variance of persistent shocks exhibits a U-shaped profile over the life cycle (with a minimum of 0:01 and a maximum of 0:05). These results suggest that the standard specification in the literature (with constant persistence and variances) cannot capture the earnings dynamics of young workers. We also argue that a calibrated job turnover model can account for these non-at profiles. The key idea is that workers sort into better jobs and settle down as they age; in turn, magnitudes of wage growth rates decline, thereby decreasing variance of shocks. Furthermore the decline in job mobility results in higher persistence. Finally, we investigate the implications of age profiles for consumption-savings behavior. The welfare cost of idiosyncratic risk implied by the age-dependent income process is 34 percent lower compared with its age-invariant counterpart. This difference is mostly due to a higher degree of consumption insurance for young workers, for whom persistence is moderate. These results suggest that age profilles of persistence and variances should be taken into account when calibrating life-cycle models.Idiosyncratic income risk, Incomplete markets models, Earnings persistence, onsumption insurance