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Topology and Approximate Fixed Points

Part of the Developments in Mathematics Book Series (volume 71)

DOI: 10.1007/978-3-030-92204-7

ISBN: 978-3-030-92203-0

Publisher: Springer International Publishing - Springer Journals

Dec 8, 2021

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Chapter 1Basic Concepts

Ben Amar, Afif; O’Regan, Donal

Pages: 1 –97

[This chapter collects well known concepts and results that will play a major role in constructing approximate fixed point theory in the remaining chapters. We note that we will reference the appropriate source papers after Sect. 1.2.8 (before this subsection well known results are presented so...
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Chapter 2Almost Fixed Points

Ben Amar, Afif; O’Regan, Donal

Pages: 99 –144

[This chapter presents various almost fixed points results from the literature. In proofs of many fixed point theorems, almost fixed points have usually appeared in an auxiliary role. In certain cases, almost fixed points, unlike fixed points, can be obtained numerically, and in some other cases,...
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Chapter 3Approximate Fixed Points in Ultrametric Spaces

Ben Amar, Afif; O’Regan, Donal

Pages: 145 –153

[A strictly contracting mapping of a spherically complete ultrametric space has a unique fixed point. In this chapter, we indicate how to reach or approximate this fixed point. In general, the fixed point can be approached by a pseudo-convergent family.]
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Chapter 4Synthetic Approaches to Problems of Fixed Points

Ben Amar, Afif; O’Regan, Donal

Pages: 155 –185

[In this chapter, we introduce synthetic approaches to fixed point problems involving regular-global-inf functions. Such functions satisfy a condition weaker than continuity. Additionally, under appropriate assumptions, it assures that approximate fixed point sequences always approach the fixed...
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Chapter 5Approximate Fixed Points in Topological Vector Spaces

Ben Amar, Afif; O’Regan, Donal

Pages: 187 –237

[In this chapter, we study problems concerning approximate fixed point property on an ambient space with different topologies.]

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