Drugačiji pristup prema b(αn,βn)-hipermetričkim prostorima

Ključne reči: b(αn,βn)-hipermetrički prostori, G-metrika, fiksne tačke

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.

Reference

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Objavljeno
2022/01/05
Rubrika
Originalni naučni radovi