We prove several new weak and strong ergodic theorems, as well as weak and strong convergence theorems for solutions to the following second order difference equation: { un+1 − 2un + un−1 ∈ cnAun; n ≥ 1 u0 ∈ H, supn≥0 |un| < +∞, where A is a maximal monotone operator in a real Hilbert space H, and {cn} is a positive sequence of real numbers. We do not assume that A−1(0) ̸= ∅, and we prove among ...

In this note first we define the notions of fuzzy positive implicativehyper BCK-ideals of types 1,2,3 and 4. Then we prove some theorems whichcharacterize the above notions according to the level subsets. Also we obtainthe relationships among these notions, fuzzy (strong, weak, reflexive) hyperBCK-ideals and fuzzy positive implicative hyper BCK-ideals of types 5,6,7and 8. Then, we define the no...

We introduce three-step iterative schemes with errors for two and three nonexpansive maps and establish weak and strong convergence theorems for these schemes. Mann-type and Ishikawa-type convergence results are included in the analysis of these new iteration schemes. The results presented in this paper substantially improve and extend the results due to Khan and Fukhar-ud-din (2005), Shahzad (...