Equivalents of Some Ordered Fixed Point Theorems
Journal of Advances in Mathematics and Computer Science · pp. 52–67 · Published 21 Jan 2023
10.9734/jamcs/2023/v38i11741Abstract
Some ordered fixed point theorems on metric spaces are equivalent to completeness and existences of maximal (or minimal) elements, common fixed points, common stationary points, etc. Some known or new theorems related to the Caristi fixed point theorem can be equivalently formulated. Consequently, dual versions of the Ekeland principle, the Caristi theorem, theorems of Bae-Park, Takahashi, Chen-Cho-Yang, Jachymski, Cobzas, and others are substantially improved and strengthened.
References (25)
- 1 On the variational principle [DOI]
- 2 Journal of Mathematical Analysis and Applications [DOI]
- 3 Fixed point theorems for multivalued mappings on complete metric spaces [DOI]
- 4 A general principle on ordered sets in nonlinear functional analysis [DOI]
- 5 Fixed Point Theorems for Mappings Satisfying Inwardness Conditions [DOI]
- 6 Caristi's fixed point theorem and metric convexity [DOI]
- 7 Fixed Points and Completeness in Metric and Generalized Metric Spaces [DOI]
- 8 Inductive properties of fixed point sets of mappings on posets and on partially ordered topological spaces [DOI]
- 9 NOTE ON THE RESULTS WITH LOWER SEMI-CONTINUITY [DOI]
- 10 Systems of equilibrium problems with applications to new variants of Ekeland’s variational principle, fixed point theorems and parametric optimization problems [DOI]
- 11 Converses to fixed point theorems of Zermelo and Caristi [DOI]
- 12 Characterizations of metric completeness [DOI]
- 13 FIXED POINT THEORY AND INWARDNESS CONDITIONS [DOI]
- 14 Ekeland, Takahashi and Caristi principles in preordered quasi-metric spaces [DOI]
- 15 Maximality, fixed points and variational principles for mappings on quasi-uniform spaces [DOI]
- 16 Equivalents of various maximum principles [DOI]
- 17 Equivalents of Ordered Fixed Point Theorems of Kirk, Caristi, Nadler, Banach, and others [DOI]
- 18 Remarks on the Metatheorem in Ordered Fixed Point Theory [DOI]
- 19 Equivalents of maximum principles for several spaces [DOI]
- 20 A relational improvement of a true particular case of Fierro’s maximality theorem [DOI]
- 21 A New Proof of Caristi's Fixed Point Theorem [DOI]
- 22 Variants of the New Caristi Theorem [DOI]
- 23 On Fixed Points in Partially Ordered Sets and Kirk-Caristi Theorem [DOI]
- 24 Weakly Picard mappings
- 25 Equivalence of some geometric and related results of nonlinear functional analysis
Cited by 5
Sehie Park · Journal of Advances in Mathematics and Computer Science · 2023
Sehie PARK · Advances in the Theory of Nonlinear Analysis and its Application · 2023
Showing 2 of 5 known citations — external sources report more than can currently be individually listed.
Related research
- The Kannan’s Fixed Point Theorem in a Cone Hexagonal Metric Spaces — shares topic coverage
- On Some Generalized Fixed Point Theorems in 2 – Metric Space — shares topic coverage
- Common Fixed Point Theorems for Commuting Self Maps in Banach Spaces via a Measure of Non-compactness — shares topic coverage
- Results of Existence Fixed Point for Integral Type Contractive Condition with ω-distance — shares topic coverage
- Some Fixed Point Theorems for Berinde-Type Contraction Mappings on Gp-Metric Spaces — shares topic coverage
Article metrics
Real usage data collected on this platform.
36
Page views
0
PDF downloads
6
Outbound clicks
5
Citations
Views over time
Views by country
Approximate, from request IP at view time — not citizenship or institution. Countries with fewer than 5 views are grouped as "Other".
Traffic sources
Referring site, by host.
Views and downloads exclude known bots/crawlers. Citations combines this platform's own DOI-resolved index with each external source's own reported total — see Cited by above for individually listed citing works. Last refreshed 0 seconds ago.