Vrsta uparenih preslikavanja tipa Chatterjee: novi rezultati fiksne tačke i svojstva kontinuiteta u metričkim prostorima
Sažetak
Uvod/cilj: U radu je razmatrano uvođenje uparenih preslikavanja tipa Chatterjee koja predstavljaju proširenje tradicionalnih kontraktivnih preslikavanja ovog tipa, a koja deluju na tri tačke umesto na dve, u okviru standardnih metričkih prostora.
Metode: Kontraktivna preslikavanja tipa Chatterjee koriste se u metričkom prostoru na tri tačke, umesto na dve primenom ideje uparenih kontraktivnih preslikavanja.
Rezultati: Razmotren je niz svojstava predmetnih preslikavanja. Ustanovljeno je da uparena preslikavanja tipa Chatterjee čine posebnu klasu u odnosu na tradicionalna preslikavanja ovog tipa koja poseduju najmanje jednu fiksnu tačku u odsustvu periodičnih tačaka prostog perioda 2 unutar kompletnih metričkih prostora. Takođe, pokazano je da dodatni kriterijumi za ova preslikavanja, kao što su neprekidnost i asimptotska regularnost, proširuju opseg rezultata fiksne tačke. Proširujući doprinose Chatterjeea, uspostavljena su dva dodatna rezultata fiksne tačke primenljiva na uparena preslikavanja tipa Chatterjee u metričkim prostorima, čak i u situacijama gde nije potrebna kompletnost.
Zaključak: Uparena preslikavanja tipa Chatterjee koja su najčešće diskontinualna, pokazuju neprekidnost u fiksnim tačkama slično preslikavanjima tipa Kannan i Chatterjee. U odsustvu periodične tačke prostog perioda 2, ova preslikavanja imaju fiksnu tačku unutar kompletnog metričkog prostora.
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