Starting with a positive linear operator we apply the Kantorovich modification and related modification. The resulting operators are investigated. We interested in eigenstructure, Voronovskaya formula, induced generalized convexity, invariant measures iterates. Some known results from literature extended.

In the area of sparse recovery, numerous researches hint that non-convex penalties might induce better sparsity than convex ones, but up until now the non-convex algorithms lack convergence guarantee from the initial solution to the global optimum. This paper aims to provide theoretical guarantee for sparse recovery via non-convex optimization. The concept of weak convexity is incorporated into...