Drugačiji pristup prema b(αn,βn)-hipermetričkim prostorima
Sažetak
Uvod/cilj: Cilj ovog rada jeste da se predstavi koncept b(αn,βn) -hipermetričkih prostora.
Metode: Primenjene su konvencionalne teoretske metode funkcionalne analize.
Rezultati: U radu su predstavljeni inicijalni rezultati koji se odnose na b(αn,βn) -hipermetričke prostore. U prvom delu generalizuje se n-dimenzionalno (n ≥ 2) hipermetričko rastojanje na proizvoljnom nepraznom skupu X. Funkcija b(αn,βn) -hiperrastojanja može se definisati na proizvoljan način dokle god su zadovoljene tri osobine: nenegativnost, pozitivna definitnost, simetrija i (αn, βn)-nejednakost trougla. U drugom delu rada razmatrani su koncept (αn, βn)-kompletnosti u odnosu na b(αn,βn) )-hipermetriku i teorema fiksne tačke, koja ima značajnu ulogu u primenjenoj matematici na više polja.
Zaključak: Odgovarajućim generalizacijama moguće je formulisati poznate rezultate klasičnih metričkih prostora na slučaj b(αn,βn) -hipermetričkih prostora.
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