Several Fixed Point Theorems concerning Τ-distance
نویسنده
چکیده
for all x, y ∈ X . Then there exists a unique fixed point x0 ∈ X of T . This theorem, called the Banach contraction principle, is a forceful tool in nonlinear analysis. This principle has many applications and is extended by several authors: Caristi [2], Edelstein [5], Ekeland [6, 7], Meir and Keeler [14], Nadler [15], and others. These theorems are also extended; see [4, 9, 10, 13, 23, 25, 26, 27] and others. In [20], the author introduced the notion of τ-distance and extended the Banach contraction principle, Caristi’s fixed point theorem, and Ekeland’s ε-variational principle. In 1969, Kannan proved the following fixed point theorem [12]. Let (X ,d) be a complete metric space. Let T be a Kannan mapping on X , that is, there exists α∈ [0,1/2) such that d(Tx,Ty) ≤ α(d(Tx,x) +d(Ty, y)) (1.2)
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