 About 1,380 results  books.google.com Now we shall generalize Schauder's theorem to condensing maps (see
Definition 1.2.20(c)). The result is often called as the "DarboSadovski Fixed Point
Theorem". Theorem 1.7.27 IfX is a Banach space, C C X is nonempty, bounded,
closed, ... 

 books.google.com It is an easy exercise to show that F is ^contracting, if it is the sum F = C + K of a
contraction C and a compact operator K. So the above mentioned fixed point
theorem of KrasnoselskiT is indeed a special case of Darbo's fixed point theorem. 

 books.google.com We pass now to an important result for αcontractive operators which is known as
Darbo's fixed point theorem and which we will use later several times. Theorem
2.1. Let X be a Banach space, M ⊂ X nonempty, bounded, closed, and convex, ... 

 books.google.com It is essentially a restatement of Darbo's definition in terms of the graph of the
map. Jerrard defined the homology theory in this category, showed that it verifies
all the axioms of a homology theory and proved the Lefschetz fixed point theorem
... 

 books.google.com 7Yien T has at least one fixed point in U . We point out that each extension of
Theorem 1.2 is based on a fixed point theorem for selfmaps of a subset of X.
Thus, Theorem 1.2 for setcontractions is derived from the Darbo fixed point
principle, ... 

 books.google.com He was the first to use the index a in the theory of fixed points [3]. Darbo's fixed
point theorem is a generalization of the wellknown Schauder fixedpoint theorem
(cf. also Schauder theorem) . It states that if S is a nonempty bounded closed ... 

 books.google.com If X is a Banach space and the metric d on X is taken to be the norm on X, G.
Darbo [16] proved that for all bounded sets A and B in X and all ... As Darbo
observed, these properties of a make it a powerful tool for proving fixed point
theorems. 

 books.google.com Theorem 1.3.2, Theorem 1.3.3 and Theorem 1.3.4 are called, respectively, as
Daher's fixed point theorem (see Daher [1]), Sadovskii's fixed point theorem (see
Sadvskii [7]), Darbo's fixed point theorem (see Darbo [1]). The results on the fixed
... 

 books.google.com Topological fixed point theorems and Hyperconvexity Another important branch
of fixed point theory comprises those ... Surprisingly, as it was noted in 40], a
hyperconvex version of the DarboSadovekii theorem does not require the use of
this ... 

 books.google.com 117 Banach, S., 109 Borsuk theorem on antipodes, 23 Brouwer, L.E.J., 5
Brouwer's fixed point theorem, 7 Cantor's intersection ... 168 Condensing
operator (</>condensing operator), 38 0contractive operator, 38 Darbo's fixed
point theorem, ... 

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