The Equivalence of Convergence Results of Modified Mann and Ishikawa Iterations with Errors without Bounded Range Assumption

Let E be an arbitrary uniformly smooth real Banach space, let D be a nonempty closed convex subset of E, and let T:D→D be a uniformly generalized Lipschitz generalized asymptotically Φ-strongly pseudocontractive mapping with q∈F(T)≠∅. Let {an},{bn},{cn},{dn} be four real sequences in [0,1] and satisfy the conditions: (i) an+cn≤1, bn+dn≤1; (ii) an,bn,dn→0 as n→∞ and cn=o(an); (iii) Σn=0∞an=∞. For some x0,z0∈D, let {un},{vn},{wn} be any bounded sequences in D, and let {xn},{zn} be the modified Ishikawa and Mann iterative sequences with errors, respectively. Then the convergence of {xn} is equivalent to that of {zn}

Convergence Analysis for the SMC-MeMBer and SMC-CBMeMBer Filters

The convergence for the sequential Monte Carlo (SMC) implementations of the multitarget multi-Bernoulli (MeMBer) filter and cardinality-balanced MeMBer (CBMeMBer) filters is studied here. This paper proves that the SMC-MeMBer and SMC-CBMeMBer filters, respectively, converge to the true MeMBer and CBMeMBer filters in the mean-square sense and the corresponding bounds for the mean-square errors are given. The significance of this paper is in theory to present the convergence results of the SMC-MeMBer and SMC-CBMeMBer filters and the conditions under which the two filters satisfy mean-square convergence