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Remarks on Fixed Point Assertions in Digital Topology, 8

Laurence Boxer

Abstract

This paper continues a series in which we study deficiencies in previously published works concerning fixed point assertions for digital images.

Remarks on Fixed Point Assertions in Digital Topology, 8

Abstract

This paper continues a series in which we study deficiencies in previously published works concerning fixed point assertions for digital images.
Paper Structure (31 sections, 14 theorems, 46 equations)

This paper contains 31 sections, 14 theorems, 46 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Adjacencies, continuity, fixed point
  4. Digital metric spaces
  5. Iterations of BotmartEtal
  6. Contractive type mappings of GuptaEtal
  7. Improper citations
  8. GuptaEtal's Theorem 3.1
  9. GuptaEtal's Corollary 3.1
  10. GuptaEtal's Theorem 3.2
  11. Jain18's expansive maps
  12. Jain18's Theorem 3.2
  13. Jain18's Theorem 3.3
  14. JyotiRani17's $\beta$--$\psi$ contractive maps
  15. Fundamentals of $\beta$--$\psi$ contractive maps
  16. ...and 16 more sections

Key Result

Theorem 2.5

Bx99 A function $f: X \to Y$ between digital images $(X,\kappa)$ and $(Y,\lambda)$ is $(\kappa,\lambda)$-continuous if and only if for every $x,y \in X$, if $x \leftrightarrow_{\kappa} y$ then $f(x) \leftrightarroweq_{\lambda} f(y)$.

Theorems & Definitions (36)

  • Definition 2.1
  • Definition 2.2
  • Definition 2.3
  • Definition 2.4
  • Theorem 2.5
  • Remark 2.6
  • Remark 2.7
  • Proposition 2.8
  • Definition 4.1
  • Definition 4.2
  • ...and 26 more