We prove a strong convergence result for a sequence generated by Halpern's type iteration for approximating a common fixed point of a countable family of quasi-Lipschitzian mappings in a real Hilbert space. Consequently, we apply our results to the problem of finding a common fixed point of asymptotically nonexpansive mappings, an equilibrium problem, and a variational inequality problem for co...

The sequence spaces ?p(?q2)(0?p<?) and ??(?q2) are introduced by using the q-difference operator ?q2 of second order. Apart from studying some basic properties these spaces, we construct basis obtain ?-, ?- ?-duals spaces. Besides matrix classes involving ?p(?q2) characterized. final section is devoted to classifying spectrum over space ?1 absolutely summable sequences.