Common fixed point of mappings satisfying implicit contractive conditions in TVS-valued ordered cone metric spaces

Abstract

Using the setting of TVS-valued ordered cone metric spaces ( order is induced by a non normal cone), common fixed point results for four mappings satisfying implicit contractive conditions are obtained. These results extend, unify and generalize several well known comparable results in the literature.

Common fixed points for generalized (v,o)-weak contractions in ordered cone metric spaces

“…All hypotheses of Theorem 3.2 are verified and x = 0 is a common fixed point of S, T, I and J. The following example (which is inspired by [18]) demonstrates the validity of Theorem 3.2.…”

“…(ii) ψ is said to be continuous at x 0 ∈ K if for any sequence {x n } in K, we have 18]). Let X = [0, 1] be endowed with usual ordering and f : X → X be defined by f x = x n for all n ≥ 1.…”

On mixed g-monotone and w-compatible mappings in ordered cone b-metric spaces

“…X. In subsequent papers several authors proved various coupled and common coupled fixed point theorems (e.g., [5][6][7][8][9][10][11][12][13][14]). …”

The existence of fixed and periodic point theorems in cone metric type spaces

“…Afterward, several fixed point theorems were considered by other people [4,7,12,14,26]. The cone metric space was initiated in 2007 by Huang and Zhang [8] and several fixed and common fixed point results in cone metric spaces were introduced in [1,9,13,17,18,19,20,21,22,23,25,27,28].…”