FIXED POINT THEOREMS FOR MULTIVALUED MAPPINGS IN MODULAR B-METRIC SPACES

Hartono Hartono (Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Negeri Yogyakarta, Indonesia)
Lusi Harini (Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Negeri Yogyakarta, Indonesia)
Afifah Hayati (Department of Mathematics, Faculty of Science and Technology, Universitas Nahdlatul Ulama Purwokerto, Indonesia)
Syamsudin Mas'ud (Department of Mathematics, Faculty of Mathematics and Natural Science, Universitas Negeri Makassar, Indonesia)
Thesa Adi Saputra Yusri (Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Negeri Yogyakarta, Indonesia)
Karyati Karyati (Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Negeri Yogyakarta, Indonesia)
Fitriana Yuli Saptaningtyas (Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Negeri Yogyakarta, Indonesia)

BAREKENG: Jurnal Ilmu Matematika dan Terapan
Vol 20 No 2 (2026): BAREKENG: Journal of Mathematics and Its Application

This paper explores multivalued mappings in modular b-metric spaces, with particular emphasis on contraction-type mappings. It introduces the concept of a Hausdorff distance adapted to this setting and investigates fixed point theorems associated with these mappings. The existence of fixed points is established under the assumptions that the space is complete, the considered subset is closed, and the modular -metric satisfies the -condition. These results not only extend classical fixed point theory but also provide a theorem that guarantees the existence of solutions to integral equations, with potential applications in mathematical modeling.