In this paper, two new iterative schemes are introduced in Hilbert space. They can be used to find a common element of the set of solutions of an equilibrium problem and the set of fixed point of the nonexpansive mapping. Under suitable conditions, some weak and strong convergence theorems are obtained.

An iterative algorithm is introduced to solve the split common fixed point problems for asymptotically quasi-nonexpansive mappings in Hilbert spaces. The strong and weak convergence of the presented algorithm to some split common fixed point are obtained. The results presented in this paper improve and extend some recent results of Moudafi [Nonlinear Anal. 74 (2011), 4083-4087], Xu [Inverse Pro...

In this paper, we first prove a weak convergence theorem by Mann’s iteration for a commutative family of positively homogeneous nonexpansive mappings in a Banach space. Next, using the shrinking projection method defined by Takahashi, Takeuchi and Kubota, we prove a strong convergence theorem for such a family of the mappings. These results are new even if the mappings are linear and contractive.

In this paper, we introduce an iterative sequence by using a hybrid generalized f−projection algorithm for finding a common element of the set of fixed points of a relatively weak nonexpansive mapping and the set of solutions of a generalized variational inequality in a Banach space. Our results extend and improve the recent ones announced by Y. Liu [Strong convergence theorems for variational ...

Different convergence and comparison theorems for proper regular splittings and proper weak regular splittings are discussed. The notion of double splitting is also extended to rectangular matrices. Finally, convergence and comparison theorems using this notion are presented.

Strong laws of large numbers are given for L-statistics (linear com­ binations of order statistics) and for U -statistics (averages of kernels of ran­ dom samples) for ergodic stationary processes, extending classical theorems of Hoeffding and of Helmers for iid sequences. Examples are given to show that strong and even weak convergence may fail if the given sufficient conditions are not satisf...