Abstract
We concern this manuscript with Geraghty type contraction mappings via simulation functions and pull down some sufficient conditions for the existence and uniqueness of point of coincidence for several classes of mappings involving Geraghty functions in the setting of metric spaces. These findings touch up many of the existing results in the literature. Additionally, we elicit one of our main result by a non-trivial example and pose an interesting open problem for the enthusiastic readers.
Highlights
If w = T x = Sx for some x ∈ X, x is called a coincidence point of T and S and w is called a point of coincidence of T and S
If T and S have a unique point of coincidence w = T x = Sx, w is the unique common fixed point of T and S
All the assumptions of Theorem 2.11 are satisfied and by the conclusion of it, T and S have a unique point of coincidence x = 2 and it is their unique common fixed point
Summary
[12] A mapping ζ : [0, ∞)2 → R is called a simulation function if it satisfies the following conditions: (ζ1) ζ(0, 0) = 0; (ζ2) ζ(t, s) < s − t for all t, s > 0; (ζ3) if {tn}, {sn} are sequences in (0, ∞) such that nl→im∞tn = nl→im∞sn > 0, lim ζ n→∞ [11] Two self-mappings f and g of a metric space (X, d) are compatible if lim d(gf (xn), f g(xn)) = 0 n→∞ We investigate for some existence and uniqueness conditions for the point of coincidence for a few kinds of Geraghty type contraction mappings using simulation functions in the framework of metric spaces.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
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 callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
