On Modular $b-$Suprametric Spaces and Fixed Point Results

Abdurrahman Büyükkaya

doi:10.32323/ujma.1936538

On Modular $b-$Suprametric Spaces and Fixed Point Results

Abstract

In this paper, we introduce modular $b$-suprametric spaces, which extend the classical modular framework by combining a scaling parameter with a nonlinear interaction term. This structure unifies and generalizes modular metric, modular $b$-metric, and modular suprametric spaces. Within this setting, we establish a Banach-type fixed point theorem under natural conditions, including the $\Delta_2$ property and the non-increasing behavior with respect to the modular parameter. As an application, we consider a nonlinear Volterra integral model arising in drug absorption with memory effects and prove the existence and uniqueness of a stable solution. These results show that the proposed framework is suitable for analysing nonlinear problems involving memory and interaction phenomena.

Keywords

Modular $b$-suprametric space, Fixed point theory, Nonlinear contraction, Volterra integral equation, Drug absorption model

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Details

Primary Language

English

Subjects

Topology

Journal Section

Research Article

Authors

Abdurrahman Büyükkaya ^*
0000-0001-6197-8975
Türkiye

Early Pub Date

July 29, 2026

Publication Date

-

Submission Date

April 23, 2026

Acceptance Date

July 28, 2026

Published in Issue

Year 2026 Number: Advanced Online Publication

DOI

https://doi.org/10.32323/ujma.1936538

IZ

https://izlik.org/JA38TF24PM

APA

Büyükkaya, A. (2026). On Modular $b-$Suprametric Spaces and Fixed Point Results. Universal Journal of Mathematics and Applications, Advanced Online Publication. https://doi.org/10.32323/ujma.1936538

AMA

1.Büyükkaya A. On Modular $b-$Suprametric Spaces and Fixed Point Results. Univ. J. Math. Appl. 2026;(Advanced Online Publication). doi:10.32323/ujma.1936538

Chicago

Büyükkaya, Abdurrahman. 2026. “On Modular $b-$Suprametric Spaces and Fixed Point Results”. Universal Journal of Mathematics and Applications, no. Advanced Online Publication. https://doi.org/10.32323/ujma.1936538.

EndNote

Büyükkaya A (July 1, 2026) On Modular $b-$Suprametric Spaces and Fixed Point Results. Universal Journal of Mathematics and Applications Advanced Online Publication

IEEE

[1]A. Büyükkaya, “On Modular $b-$Suprametric Spaces and Fixed Point Results”, Univ. J. Math. Appl., no. Advanced Online Publication, July 2026, doi: 10.32323/ujma.1936538.

ISNAD

Büyükkaya, Abdurrahman. “On Modular $b-$Suprametric Spaces and Fixed Point Results”. Universal Journal of Mathematics and Applications. Advanced Online Publication (July 1, 2026). https://doi.org/10.32323/ujma.1936538.

JAMA

1.Büyükkaya A. On Modular $b-$Suprametric Spaces and Fixed Point Results. Univ. J. Math. Appl. 2026. doi:10.32323/ujma.1936538.

MLA

Büyükkaya, Abdurrahman. “On Modular $b-$Suprametric Spaces and Fixed Point Results”. Universal Journal of Mathematics and Applications, no. Advanced Online Publication, July 2026, doi:10.32323/ujma.1936538.

Vancouver

1.Abdurrahman Büyükkaya. On Modular $b-$Suprametric Spaces and Fixed Point Results. Univ. J. Math. Appl. 2026 Jul. 1;(Advanced Online Publication). doi:10.32323/ujma.1936538