Fixed Point Theory

@inproceedings{Granas2003FixedPT,
  title={Fixed Point Theory},
  author={Andrzej Granas and James Dugundji},
  year={2003}
}
Elementary Fixed Point Theorems * Theorem of Borsuk and Topological Transversality * Homology and Fixed Points * Leray-Schauder Degree and Fixed Point Index * The Lefschetz-Hopf Theory * Selected Topics * Index 

Generalized Lefschetz fixed point theorems in extension type spaces

Several Lefschetz fixed point theorems for compact type self maps in new classes of spaces are presented in this paper.

GENERAL LEFSCHETZ FIXED POINT THEORY FOR MULTIVALUED MAPS

Some generalizations of the Lefschetz fixed point theorem are presented for admissible maps on Hausdorff topological spaces. AMS Subject Classification: 47H10, 54C60, 54H25, 55M20

Some Fixed Point Theorems for Non Self Maps

We prove some fixed point theorems for condensing, compact and non-expansive non-self maps.

An elementary proof of the Brouwer’s fixed point theorem

We provide an elementary proof of the Brouwer’s fixed point theorem based solely on introductory topological concepts such as compactness and connectedness both covered in a first undergraduate

Fixed Point Theorems for Classes of Nonlinear Mappings of Contractive Type

TLDR
For certain classes of contractive mappings in complete metric spaces, the existence of a fixed point which attracts all inexact orbits is established.

A Fixed Point Theorem for Kannan-type Maps in Metric Spaces

We prove a generalization of Kannan's fixed point theorem, based on a recent result of Vittorino Pata.

Some stability results related to some fixed point theorems

In this paper, we introduce two types of stability and we investigate some fixed point theorems, as Schauder Theorem, Borsuk Theorem and Knaster Lemma, from this viewpoint. Mathematics subject

A generalization of Krasnosel’skii fixed point theorem for sums of compact and contractible maps with application

The existence of a fixed point for the sum of a generalized contraction and a compact map on a closed convex bounded set is proved. The result is applied to a kind of nonlinear integral equations.

Lefschetz type theorems for a class of noncompact mappings

In this paper we present new xed point results for general compact absorbing type contractions in new extension spaces. c 2014 All rights reserved.

Local fixed point theory involving three operators in Banach algebras

The present paper studies the local versions of a fixed point theorem of Dhage (1987) in Banach algebras. An application of the newly developed fixed point theorem is also discussed for proving the
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