Abstract
AbstractWe present generalized versions of Caristi's fixed point theorem for multivalued maps. Our results either improve or generalize the corresponding generalized Caristi's fixed point theorems due to Bae (2003), Suzuki (2005), Khamsi (2008), and others.
Highlights
A number of extensions of the Banach contraction principle have appeared in literature
Kada et al 9 and Suzuki 10 introduced the concepts of w-distance and τ-distance on metric spaces, respectively
In this paper, using the concepts of w-distance and τ-distance, we present some generalizations of the Caristi’s fixed point theorem for multivalued maps
Summary
A number of extensions of the Banach contraction principle have appeared in literature. A function ω : X × X → 0, ∞ is a w-distance on X if it satisfies the following conditions for any x, y, z ∈ X: w1 ω x, z ≤ ω x, y ω y, z ; w2 the map ω x, · : X → 0, ∞ is lower semicontinuous; w3 for any > 0, there exists δ > 0 such that ω z, x ≤ δ and ω z, y d x, y ≤ .
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