Deferred Epigraphical Convergence for Sequences of Lower Semicontinuous Functions

Şükrü Tortop; Esra Gülle

doi:10.36753/mathenot.1979600

Deferred Epigraphical Convergence for Sequences of Lower Semicontinuous Functions

Abstract

In this paper, we introduce deferred epi-convergence for sequences of lower semicontinuous functions defined on metric spaces. The notion is formulated by using deferred Kuratowski convergence of epigraphs. In this framework, ordinary Ces\`aro averages are replaced by averages taken over the intervals $(p_n,q_n]$. We first define deferred lower and upper Kuratowski limits for sequences of closed sets. These set limits are then used to define the lower and upper deferred epi-limits of a sequence of functions. We prove that ordinary epi-convergence implies deferred epi-convergence and give an example showing that the converse need not hold. Finally, we obtain distance representations of the deferred epi-limit functions in terms of averaged distances to epigraphs.

Keywords

Deferred Cesàro convergence, epi-convergence, Kuratowski convergence, lower semicontinuous functions.

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Details

Primary Language

English

Subjects

Mathematical Methods and Special Functions, Applied Mathematics (Other)

Journal Section

Research Article

Authors

Şükrü Tortop ^*
0000-0001-5342-7612
Türkiye

Esra Gülle
0000-0001-5575-2937
Türkiye

Early Pub Date

August 17, 2026

Publication Date

-

Submission Date

June 26, 2026

Acceptance Date

August 5, 2026

Published in Issue

Year 2026 Number: Advanced Online Publication

DOI

https://doi.org/10.36753/mathenot.1979600

IZ

https://izlik.org/JA85GR34ST

APA

Tortop, Ş., & Gülle, E. (2026). Deferred Epigraphical Convergence for Sequences of Lower Semicontinuous Functions. Mathematical Sciences and Applications E-Notes, Advanced Online Publication, 191-205. https://doi.org/10.36753/mathenot.1979600

AMA

1.Tortop Ş, Gülle E. Deferred Epigraphical Convergence for Sequences of Lower Semicontinuous Functions. Math. Sci. Appl. E-Notes. 2026;(Advanced Online Publication):191-205. doi:10.36753/mathenot.1979600

Chicago

Tortop, Şükrü, and Esra Gülle. 2026. “Deferred Epigraphical Convergence for Sequences of Lower Semicontinuous Functions”. Mathematical Sciences and Applications E-Notes, no. Advanced Online Publication: 191-205. https://doi.org/10.36753/mathenot.1979600.

EndNote

Tortop Ş, Gülle E (August 1, 2026) Deferred Epigraphical Convergence for Sequences of Lower Semicontinuous Functions. Mathematical Sciences and Applications E-Notes Advanced Online Publication 191–205.

IEEE

[1]Ş. Tortop and E. Gülle, “Deferred Epigraphical Convergence for Sequences of Lower Semicontinuous Functions”, Math. Sci. Appl. E-Notes, no. Advanced Online Publication, pp. 191–205, Aug. 2026, doi: 10.36753/mathenot.1979600.

ISNAD

Tortop, Şükrü - Gülle, Esra. “Deferred Epigraphical Convergence for Sequences of Lower Semicontinuous Functions”. Mathematical Sciences and Applications E-Notes. Advanced Online Publication (August 1, 2026): 191-205. https://doi.org/10.36753/mathenot.1979600.

JAMA

1.Tortop Ş, Gülle E. Deferred Epigraphical Convergence for Sequences of Lower Semicontinuous Functions. Math. Sci. Appl. E-Notes. 2026;:191–205.

MLA

Tortop, Şükrü, and Esra Gülle. “Deferred Epigraphical Convergence for Sequences of Lower Semicontinuous Functions”. Mathematical Sciences and Applications E-Notes, no. Advanced Online Publication, Aug. 2026, pp. 191-05, doi:10.36753/mathenot.1979600.

Vancouver

1.Şükrü Tortop, Esra Gülle. Deferred Epigraphical Convergence for Sequences of Lower Semicontinuous Functions. Math. Sci. Appl. E-Notes. 2026 Aug. 1;(Advanced Online Publication):191-205. doi:10.36753/mathenot.1979600