Some fixed point theorems for expansion onto mappings on cone metric spaces

Fixed point theorems for generalized contraction mappings on b-rectangular metric spaces

“…Furthermore, we extend results from [20] of Patil, from rectangular metric spaces to b-rectangular ones (b-g.m.s). Also, examples similar to those in [1], [12] and [20] justifying our theorems are given. Now, let's consider generalized contractions f : X → X on a b-g.m.s.…”

“…In this section, our aim is to extend the results of Moosaei [15] for generalized contraction mappings from metric spaces to b-rectangular metric spaces. Also, we extend and develop the fixed point results of Aage [1] from cone metric spaces to b-g.m.s. Furthermore, we extend results from [20] of Patil, from rectangular metric spaces to b-rectangular ones (b-g.m.s).…”

“…In 2011, Aage [1] considered expansive mappings in cone metric spaces. The more general form of these mappings, with some underlying assumptions, are…”

“…Definition 1.2. Let X = ∅, s ≥ 1 be a given real number and d : X × X → [0, ∞), such that for each x, y ∈ X and u, v ∈ X (each distinct from x and y), we have that (1) d(x, y) = 0 ⇐⇒ x = y, As in metric spaces, we recall the basic notions regarding sequences in b-g.m.s: Definition 1.3. Let (X, d) be a b-g.m.s, x ∈ X and (x n ) ⊂ X be a given sequence.…”

Tripled random coincidence point and common fixed point results of generalized Lipschitz mappings in cone b-metric spaces over Banach algebras

“…They greatly expanded the famous Banach contraction principle in such setting. Since then, a lot of papers have appeared on cone metric spaces and b-metric spaces (see [1,5,11,15,21,28,33,35]). Hussain and Shah [20] introduced cone b-metric space and generalized both cone metric space and b-metric space.…”