New types of common fixed point theorems in 2-metric spaces

Strict Common Fixed Point Theorems for Hybrid Pairs of Mappings via Altering Distances and an Application

“…Definition 2.4 [17]. A sequence {A n } of subsets of a 2-metric space (X, d) is said to be convergent to a subset A of X if:…”

“…Definition 2.5 [17]. The mappings f : X → X and F : X → B(X) are said to be weakly commuting if f F x ∈ B(X) and…”

“…Remark 2.3 [17]. Any δ-compatible pair (f, F ) is weakly compatible but the converse is not true in general.…”

Fixed points and lines in 2-metric spaces

“…This notion has been considered by several authors (see [9]), who have notably generalized Banach's principle to obtain fixed point theorems, for example White [31], Iseki [14], Rhoades [28], Khan [16], Singh, Tiwari and Gupta [30], Naidu and Prasad [25], Naidu [26] and Zhang [18], Abd El-Monsef, Abu-Donia, Abd-Rabou [2], Ahmed [3] and others. The contractivity conditions used in these works are usually of the form d(F (x), F (y), a) ≤ .…”

Hybrid pairs of mappings with some weaker conditions in consideration of common fixed point on 2-metric spaces

“…Monsef et al [2] generalized some concepts in 2-metric spaces for set valued mappings. They also proved some common fixed point theorems in 2-metric spaces.…”