Abstract
Multidimensional common fixed point theorems for multivalued mappings in dislocated metric spaces
Highlights
Introduction and preliminariesThe fundamental theorem in metric fixed point theory is the well-known Banach contraction principle [8], introduced by the Polish mathematician S
In 2012 Wardowski [27] introduced a new type of contraction mapping known as F -contraction, and using it he proved a fixed point theorem that generalizes the Banach contraction principle
Secelean [24] replaced the second condition of F -contraction by an equivalent but simpler condition and proved a couple of fixed point theorems
Summary
We introduce three types of multidimensional Ciric-type rational F -contractions where F is sub-additive and prove multidimensional fixed point theorems in dislocated metric spaces. The pair (S, T ) is said to be (i) a multidimensional Ciric-type rational F -contraction of type I if there exists τ > 0 such that τ. (ii) a multidimensional Ciric-type rational F -contraction of type II if there exists τ > 0 such that τ dl(yi, Tyi ) 1 + dl(xi, Sxi ). Construct the sequences {xni }Ni=1 by taking x1i ∈ Sx0i such that dl(x0i , Sx0i ) = dl(x0i , x1i ) for all i = 1, 2, . Let (X, dl) be a complete dislocated metric space and let (S, T ) be a pair of multidimensional Ciric-type rational F -contractions of type I.
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