In this paper we introduce STRONG IK-CONVERGENCE of functions which is common generalization of STRONG I,-CONVERGENCE of functions in probabilistic metric spaces. We also de, ne and study STRONG IK-limit points of functions in same space.

We introduce an implicit method for finding a common element of the set of solutions of systems of equilibrium problems and the set of common fixed points of a sequence of nonexpansive mappings and a representation of nonexpansive mappings. Then we prove the STRONG CONVERGENCE of the proposed implicit schemes to the unique solution of a variational inequality, which is the optimality condition for a minimization problem and is also a common fixed point for a sequence of nonexpansive mappings and a representation of nonexpansive mappings.

We prove a STRONG CONVERGENCE theorem for the modified Noor iterations in the framework of CAT (0) spaces. Our results extend and improve the corresponding results of X. Qin, Y. Su and M. Shang, T.H. Kim and H.K. Xu and S. Saejung and some others.

X. Qin and Y. Su proved a STRONG CONVERGENCE theorems of modified Ishikawa iteration by CQ method for relatively nonexpansive mappings in a Banach space [Xiao long Qin, Yongfu Su, Nonlinear Anal. 67 (2007), no. 6, 1958–1965]. The result of this paper extends and improves the result of X. Qin and Y. Su in the two respects: (1). By using the monotone CQ method to modify the CQ method, so that the new method of proof is used. (2). Relax the restriction on T from uniformly continuous to continuous. The result of this paper also extends and improves the recent ones announced by Nakajo, Takahashi, Kim, Martinez-Yanes, Xu and some others.

We discuss in this paper the STRONG CONVERGENCE for weighted sums of negatively orthant dependent (NOD) random variables by generalized Gaussian techniques. As a corollary, a Cesaro law of large numbers of i.i.d. random variables is extended in NOD setting by generalized Gaussian techniques.  

The purpose of this paper is to propose a composite iterative scheme for approximating a common solution for a finite family of m-accretive operators in a strictly convex Banach space having a uniformly Gateaux dierentiable norm. As a consequence, the STRONG CONVERGENCE of the scheme for a common fixed point of a finite family of pseudocontractive mappings is also obtained.