Abstract
We obtain a certain property of F-contractions, which enables us to generalize and extend Wardowski’s (Fixed Point Theory and Applications 2012:94, 2012) result and other fixed point theorems to the class of nonexpansive operators in real Banach spaces. We give illustrative examples to demonstrate nontrivial applicability of the property and use it to prove that F-contractions are closely related to -weak contractions introduced by Berinde (Carpath. J. Math. 19(1):7-22, 2003; Nonlinear Anal. Forum 9(1):43-53, 2004). MSC:47H09, 47H10, 54H25.
Highlights
Introduction and preliminariesThis work is concerned with contractive maps defined on real Banach spaces
T is called a contraction if L ∈ [, ) and for L =, T is called a nonexpansive operator
A point p ∈ X is called a fixed point of an operator T if p = Tp and the collection of all fixed points of an operator T is denoted by Fix(T)
Summary
Introduction and preliminariesThis work is concerned with contractive maps defined on real Banach spaces. Examples of contractive conditions making use of the displacements d(x, Tx) and d(y, Tx) is the class of (δ, k)-weak contractions introduced and used by Berinde [ ] to obtain fixed point and uniqueness theorems for a large class of weakly Picard operators.
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