CONSTRUCTIVE PROOF OF FIXED-POINT THEOREM FOR COMPLETE T-LATTICE

2017 ◽  
Vol 12 (1) ◽  
pp. 37-46
Author(s):  
Bouzkoura Khadija ◽  
Benkaddour Said
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Constructive Proof

Efficient self-interpretation in lambda calculus

1992 ◽  
Vol 2 (3) ◽  
pp. 345-364 ◽  
Author(s):  
Torben Æ. Mogensen
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Lambda Calculus ◽  
The Self ◽  
Constructive Proof ◽  
Compact Representation ◽  
Direct Execution

AbstractWe start by giving a compact representation schema for λ-terms, and show how this leads to an exceedingly small and elegant self-interpreter. We then define the notion of aself-reducer, and show how this too can be written as a small λ-term. Both the self-interpreter and the self-reducer are proved correct. We finally give a constructive proof for the second fixed point theorem for the representation schema. All the constructions have been implemented on a computer, and experiments verify their correctness. Timings show that the self-interpreter and self-reducer are quite efficient, being about 35 and 50 times slower than direct execution using a call-by-need reductions strategy

scholarly journals Solving Fixed-Point Problems with Inequality and Equality Constraints via a Non-Interior Point Homotopy Path-Following Method

2017 ◽  
Vol 2017 ◽  
pp. 1-9
Author(s):  
Menglong Su ◽  
Yufeng Shang
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Interior Point ◽  
Fixed Point Theorems ◽  
Path Following ◽  
Fixed Point Problems ◽  
Constructive Proof ◽  
Nonconvex Sets ◽  
Smooth Path

In recent years, fixed-point theorems have attracted increasing attention and have been widely investigated by many authors. Moreover, determining a fixed point has become an interesting topic. In this paper, we provide a constructive proof of the general Brouwer fixed-point theorem and then obtain the existence of a smooth path which connects a given point to the fixed point. We also present a non-interior point homotopy algorithm for solving fixed-point problems on a class of nonconvex sets by numerically tricking this homotopy path.

Solution of Volterra integral inclusion in b-metric spaces via new fixed point theorem

2016 ◽  
Vol 2017 (1) ◽  
pp. 17-30 ◽  
Author(s):  
Muhammad Usman Ali ◽  
◽  
Tayyab Kamran ◽  
Mihai Postolache ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Integral Inclusion
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