Discussion on some coupled fixed point theorems

Abstract

In this paper, we show that, unexpectedly, most of the coupled fixed point theorems (on ordered metric spaces) are in fact immediate consequences of well-known fixed point theorems in the literature. MSC: 47H10; 54H25

Shorter proofs of some recent even-tupled coincidence theorems for weak contractions in ordered metric spaces

“…This technique of proof is different, slightly simpler, shorter and more effective than classical technique. In this paper, we prove the main results of Imdad et al [14] following the techniques of Samet et al [34].…”

“…Very recently, Samet et al [34] have shown that the coupled (analogously n-tupled) fixed results can be more easily obtained using well-known fixed point theorems on ordered metric spaces (see also [10,28,29]). This technique of proof is different, slightly simpler, shorter and more effective than classical technique.…”

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]). …”

Common Coupled Fixed Point Theorem Under Generalized Mizoguchi-Takahashi Contraction for Hybrid Pair of Mappings Generalized Mizoguchi-Takahashi Contraction

“…Samet et al [28] claimed that most of the coupled fixed point theorems for single valued mappings on ordered metric spaces are consequences of well-known fixed point theorems.…”