Wijsman Statistical, Strong Cesàro, and Ideal Convergence of Closed Sets in Idempotent Bicomplex Metric Spaces
Journal of Function Spaces, cilt.2026, sa.1, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 2026 Sayı: 1
- Basım Tarihi: 2026
- Doi Numarası: 10.1155/jofs/7648703
- Dergi Adı: Journal of Function Spaces
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, MathSciNet, zbMATH, Directory of Open Access Journals, Academic Search Ultimate (EBSCO), Middle East & Africa Database (ProQuest), Natural Science Collection (ProQuest), Materials Science & Engineering Collection (ProQuest), Technology Collection (ProQuest)
- Anahtar Kelimeler: IK-convergence, ideal convergence, idempotent bicomplex metric space, point-to-set distance, statistical convergence, strong Cesàro convergence, Wijsman convergence
- Süleyman Demirel Üniversitesi Adresli: Evet
Özet
This paper studies generalized Wijsman convergence for sequences of nonempty closed subsets of an idempotent bicomplex metric space. Let ρ = d1e1 + d2e2, where d1 and d2 are metrics on the same underlying set X. For a nonempty subset A of X, we define the bicomplex point-to-set distance by ρ(x, A) = d1(x, A)e1 + d2(x, A)e2. This definition retains the idempotent decomposition of the metric and allows the convergence of closed sets to be studied through the two component distance functions. For an exponent sequence p = (pk) satisfying 0 < infkpk ≤ supkpk < ∞, we introduce Wijsman statistical convergence, Wijsman strong Cesàro convergence of power type p, Wijsman (Formula presented.) -convergence, and Wijsman (Formula presented.) -convergence. We prove that each of these notions is equivalent to the simultaneous validity of the corresponding Wijsman convergence conditions with respect to the component metrics d1 and d2. As consequences, ordinary Wijsman convergence implies Wijsman statistical convergence, while Wijsman strong Cesàro convergence implies Wijsman statistical convergence. The converse implication holds when the component distance deviations are pointwise bounded. For admissible ideals (Formula presented.) and (Formula presented.), we show that (Formula presented.) -convergence implies (Formula presented.) -convergence for every sequence if and only if (Formula presented.). We also compare the componentwise bicomplex point-to-set distance with the point-to-set distance determined by the associated real metric. Examples show that these two constructions need not agree and that the principal implications obtained in the paper cannot, in general, be reversed.