Fixed point theorems of contraction mappings with variations in cone metric space domains

Abstract

Fixed point iterations of some contraction mappings with variations in cone metric space (CMS) domains have been discussed in this paper. More specifically, an increasing sequence of subsets of an order complete CMSs has been considered such that one member of the sequence is mapped into the next member of the sequence by a map for which a contraction condition is satisfied. The usual iteration method has been considered to establish generalized fixed point results in CMSs. Furthermore, some examples are provided to illustrate our main results.

Fixed points of multiplicative closed graph operators on b-multiplicative metric spaces

“…C. G. Moorthy and P. X. Raj considered an increasing sequence of subsets Ξ 1 ⊆ Ξ 2 ⊆ ... of a metric space (Ξ, d), and a map G : Ξ → Ξ satisfying a contraction condition such that G(Ξ i ) ⊆ Ξ i+1 , ∀i, and Ξ = ∞ j=1 Ξ j in [11]. Also, the fixed point results of [11] are generalized in some articles [14][15][16].…”