A fixed point problem under a finite number of equality constraints involving a Ćirić operator


Vladimir Rakočević, Bessem Samet




Let (E, ·) be a Banach space with a cone P. Let T, ϕ i : E → E (i = 1, 2, · · · , r) be a finite number of mappings. We obtain sufficient conditions for the existence of solutions to the problem Tx = x, ϕ i (x) = 0 E , i = 1, 2, · · · , r, where 0 E is the zero vector of E, and T is a mapping satisfying a ´ Ćirić-contraction. Some interesting consequences are deduced from our main results.