id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-6086	Massit, Hafida ; Rossafi, Mohamed ; Mitrovic, Zoran D.; Aloqaily, Ahmad ; Mlaiki, Nabil	Some Fixed Point Theorems for \(\Theta-\phi\)-Multivalued Contraction Mappings in Rectangular \(b\)-Metric Spaces	2025	19	.pdf	application/pdf	5238	363	85	If {xn} is not a Cauchy sequence then there exist ε > 0 and two sequences {mk} and {nk} of positive integers such that ε ≤ lim k→+∞ inf d(xmk , xnk ) ≤ lim k→+∞ sup d(xmk , xnk ) ≤ bε, ε ≤ lim k→+∞ inf d(xmk , xmk+1 ) ≤ lim k→+∞ sup d(xnk , xmk+1 ) ≤ bε, ε ≤ lim k→+∞ inf d(xmk , xnk+1 ) ≤ lim k→+∞ sup d(xmk , xnk+1 ) ≤ bε, ε b ≤ lim k→+∞ inf d(xmk+1 , xnk+1 ) ≤ lim k→+∞ sup d(xmk+1 , xnk+1 ) ≤ b2ε. Letting n→ +∞ we obtain lim n→+∞ supM(xn, z) = lim n→+∞ supmax{d(xn, z), d(xn, Txn), d(z, Tz), d(z, Txn)} ≤ lim n→+∞ supmax{d(xn, z), d(xn, xn+1), d(z, Tz), d(z, xn+1)} ≤ d(z, Tz) and lim n→+∞ supW (xn, z) = lim n→+∞ supmin{d(xn, Txn), d(z, Tz), d(Txn, z), d(xn, T z)} ≤ lim n→+∞ supmin{d(xn, xn+1), d(z, Tz), d(xn+1, z), d(xn, T z)} = 0.	cache/ejpam-6086.pdf	txt/ejpam-6086.txt