Abstract
This research paper proves some interesting results on common fixed point for two pairs of non-self hybrid (single valued and multivalued) contractive mappings in metric spaces of hyperbolic type. The results are established without employing the weakly commutativity and continuity assumptions. We adopted an existing method of proof to obtain our results. The results generalize and improve some results proved in related works in literature. An example is given to validate our claim.
Highlights
Definition 1.1: Let (X, d) be a metric space where X is a non-empty set and d is a mapping d: X × X → R such that for every x, y, z ε X (Frechet, 1906)d1 d(x, y) ≥ 0, d2 d(x, y) = 0 if and only if x = y, d3 d(x, y) = d(y, x), d4 d(x, z) ≤ d(x, y) + d(y, z).Definition 1.2: Suppose X is a metric space and R = [0,1] the closed unit interval
X is called a metric space of hyperbolic type if the following axioms are satisfied (Kirk, 1982); (a) each two points x, y ε X are endpoints of exactly one number seg [x, y] of L and, (b) if u, x, y ε X and z ε seg [ x, y] satisfies d(x, z) = λ d(x, y) for λ ε [0, 1] d(u, z) ≤ (1 − λ)d(u, x) + λ d(u, y)
Huang et al (2014) established a common fixed point theorem for two pairs of non-self mappings satisfying certain generalized contractive conditions of Ciric type in cone metric spaces
Summary
*Fixed point theorem for single valued selfmappings in metric space was first proved by Banach (1992). Later Nadler (1969) introduced fixed point results for multivalued mappings in metric spaces. Takahashi (1970) introduced the property of convexity in metric spaces and established some fixed point theorems that generalized some results in Banach spaces.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
