Research Article

$E$-Compactness and Frum-Ketkov Operators in $E$-Metric Spaces

Number: 56 September 30, 2026

$E$-Compactness and Frum-Ketkov Operators in $E$-Metric Spaces

Abstract

This paper studies Frum-Ketkov operators in $E$-metric spaces, that is, operators whose contractive condition involves the distance from a point to a prescribed compact subset rather than the distance between two points. Two properties that hold in the real-valued case fail in this setting. An $E$-compact set need not be $E$-bounded when $E$ has no order unit, and the infimum defining the distance from a point to a set, being taken in the lattice order, need not be attained. The notion of $E$-compactness is introduced and its relations to $E$-closedness and $E$-boundedness are established. It is then shown that an $E$-compact subset need not be proximinal, and sufficient conditions for proximinality are obtained. Under the proximinality assumption, the fixed-point set and the $\omega$-limit sets of a Frum-Ketkov operator are located in the prescribed compact set, the invariance of this set is proved, and contractive Frum-Ketkov operators are shown to be Picard operators. For $E=\mathbb{R}$, these results reduce to the corresponding results in metric spaces.

Keywords

References

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Details

Primary Language

English

Subjects

Operator Algebras and Functional Analysis, Topology

Journal Section

Research Article

Publication Date

September 30, 2026

Submission Date

August 6, 2026

Acceptance Date

September 16, 2026

Published in Issue

Year 2026 Number: 56

APA
Özeken, Ç. C., & Şola Erduran, F. (2026). $E$-Compactness and Frum-Ketkov Operators in $E$-Metric Spaces. Journal of New Theory, 56, 80-93. https://doi.org/10.53570/jnt.2012331
AMA
1.Özeken ÇC, Şola Erduran F. $E$-Compactness and Frum-Ketkov Operators in $E$-Metric Spaces. JNT. 2026;(56):80-93. doi:10.53570/jnt.2012331
Chicago
Özeken, Çetin Cemal, and Ferhan Şola Erduran. 2026. “$E$-Compactness and Frum-Ketkov Operators in $E$-Metric Spaces”. Journal of New Theory, nos. 56: 80-93. https://doi.org/10.53570/jnt.2012331.
EndNote
Özeken ÇC, Şola Erduran F (September 1, 2026) $E$-Compactness and Frum-Ketkov Operators in $E$-Metric Spaces. Journal of New Theory 56 80–93.
IEEE
[1]Ç. C. Özeken and F. Şola Erduran, “$E$-Compactness and Frum-Ketkov Operators in $E$-Metric Spaces”, JNT, no. 56, pp. 80–93, Sept. 2026, doi: 10.53570/jnt.2012331.
ISNAD
Özeken, Çetin Cemal - Şola Erduran, Ferhan. “$E$-Compactness and Frum-Ketkov Operators in $E$-Metric Spaces”. Journal of New Theory. 56 (September 1, 2026): 80-93. https://doi.org/10.53570/jnt.2012331.
JAMA
1.Özeken ÇC, Şola Erduran F. $E$-Compactness and Frum-Ketkov Operators in $E$-Metric Spaces. JNT. 2026;:80–93.
MLA
Özeken, Çetin Cemal, and Ferhan Şola Erduran. “$E$-Compactness and Frum-Ketkov Operators in $E$-Metric Spaces”. Journal of New Theory, no. 56, Sept. 2026, pp. 80-93, doi:10.53570/jnt.2012331.
Vancouver
1.Çetin Cemal Özeken, Ferhan Şola Erduran. $E$-Compactness and Frum-Ketkov Operators in $E$-Metric Spaces. JNT. 2026 Sep. 1;(56):80-93. doi:10.53570/jnt.2012331

 

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