# 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

## 664 Citations

### Generalized Lefschetz fixed point theorems in extension type spaces

- Mathematics
- 2015

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

- Mathematics
- 2018

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

- Mathematics
- 2007

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

- MathematicsArabian Journal of Mathematics
- 2022

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

- MathematicsJ. Optim. Theory Appl.
- 2019

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

- Mathematics
- 2012

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

- Mathematics
- 2016

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

- Mathematics
- 2012

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

- Mathematics
- 2014

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

- Mathematics
- 2004

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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### Degree for Equivariant Maps in R n 551

- Degree for Equivariant Maps in R n 551

### Categories and Functors 616 Bibliography 620

- Categories and Functors 616 Bibliography 620

### Miscellaneous Results and Examples 570 5. Notes and Comments 573 Appendix: Preliminaries 588

- Miscellaneous Results and Examples 570 5. Notes and Comments 573 Appendix: Preliminaries 588

### C. Linear Topological Spaces

- C. Linear Topological Spaces

### D. Algebraic Preliminaries

- D. Algebraic Preliminaries

### The Infinite-Dimensional E^-Cohomology 558

- The Infinite-Dimensional E^-Cohomology 558

### I. General Reference Texts

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### II. Monographs, Lecture Notes, and Surveys 621 III. Articles 625 IV. Additional References

- II. Monographs, Lecture Notes, and Surveys 621 III. Articles 625 IV. Additional References