... Xissaidtobe a set- valued ψ-contraction, ifH(Tx, Ty)≤ ψ(d(x, y), D(x, Tx), D(y, Ty), D(x, Ty)), D(y, Tx)) for all x, y Î X.We now st ate the main fixed point theorem for a set- valued ... hold:(1) (0) = 0, 0 <(t)<t for all t >0;(2) is a strictly increasing function;(3) for each t Î ℝ+,{n(t)}nÎNis decreasing;(4) for eachtn∈ R+{0}, if limn®∞tn= ... limn®∞(tn)<g;(5) for each tnÎ ℝ+, if limn®∞tn=0,then limn®∞(tn)=0.Definition 7 Let (X, d) be a metric space. The set- valued map T : X ® Xissaidtobe a set- valued weaker Meir-Keeler...