Opial presented in 1967 a theorem, which can be applied in order to prove the weak convergence of sequences (xk) in a Hilbert space, generated by iterative schemes of the form xk+1 = Uxk for a nonexpansive and asymptotically regular operator U with nonempty FixU . Several iterative schemes have, however, the form xk+1 = Ukxk, where (Uk) is a sequence of operators with a common fixed point. We s...

We have introduced a new sequence space l(r,s,t, p;Δ(m) ) combining by using generalized means and difference operator of order m . Some topological properties as well as geometric properties namely Banach-Saks property of type p and uniform Opial property have been studied. Furthermore, the α -, β -, γ duals of this space are computed and also obtained necessary and sufficient conditions for s...

We consider the problem of minimizing a smooth convex objective function subject to the set of minima of another differentiable convex function. In order to solve this problem, we propose an algorithm which combines the gradient method with a penalization technique. Moreover, we insert in our algorithm an inertial term, which is able to take advantage of the history of the iterates. We show wea...

Inequalities involving functions of n independent variables, their partial derivatives, integrals play a fundamental role in establishing the existence and uniqueness of initial and boundary value problems for ordinary and partial differential equations as well as difference equations 1–10 . Especially, in view of wider applications, inequalities due to Agarwal, Opial, Pachpatte, Wirtinger, Poi...