Best proximity problems for Ćirić type multivalued operators satisfying a cyclic condition

Abstract

Abstract. The aim of this paper is to present some best proximity results for multivalued cyclic operators satisfying aĆirić type condition. Our results extend to the multivalued case some recent results in the literature.Mathematics Subject Classification (2010): 47H04, 47H09, 54H25.

Coupled fixed points and coupled best proximity points for cyclic Ćirić type operators

“…( [25] ). Let false(X,dfalse) be a complete metric space, A∈Pcl(X),B∈P(X) such that false(A,Bfalse) satisfies the property UC.…”

“…( [ 21 ] ) . Let T:Y→Pprox(Y) be as in Theorem 4.2 , ε>0 and x∈Y be such that D(x,Tfalse(xfalse))≤ε .…”

“…The following theorem (which is a particular case of Theorem 2.7 in [21]) will be used to prove the first result in this section.…”

“…Theorem 4.1. ( [21] ). Let false(X,dfalse) be a complete metric space, A,B∈Pcl(X) and T:A ∪ B→Pprox(A ∪ B) a multivalued cyclic ϕ -contraction of Ćirić type, that is: (i) T(A)⊆B and T(B) ⊆ A ; (ii) there exists a strong comparison function ϕ : ℝ+→ℝ+ such that for any x∈A and y∈B .…”