id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
cana-2862	Jitender Kumar	Common Fixed Point Theorem In Complex Valued Extended B-Metric Space	2024	9	.pdf	application/pdf	3307	142	78	Subsequently, many authors have studied the existence and uniqueness of common fixed point of self- mappings in view of contractive conditions. Since |1 + 𝑑(𝑥, 𝑦)| > |𝑑(𝑥, 𝑦)| i.e. |𝑑(𝑥, 𝑦)| |1 + 𝑑(𝑥, 𝑦)| < 1, so we get |𝑑(𝑥, 𝑦)| = |𝑑(𝑓𝑥, 𝑔𝑦)| < 𝐴. |𝑑(𝑥, 𝑦)| + 𝐵. 0 + 𝐶. |𝑑(𝑥, 𝑦)| + 𝐷. 0 + 𝐸. 0 i.e. |𝑑(𝑥, 𝑦)| = |𝑑(𝑓𝑥, 𝑔𝑦)| < 𝐴 ⋅ |𝑑(𝑥, 𝑦)| + 𝐶. |𝑑(𝑥, 𝑦)| i.e. (1 − 𝐴 − 𝐶)|𝑑(𝑥, 𝑦)| < 0, a contradiction since 𝐴 + 𝐵 + 𝐶 + 2𝐷 + 2𝐸 < 1 ⇒ 𝐴 + 𝐶 < 1 So, 𝑥 = 𝑦, which proves the uniqueness of common fixed point of 𝑓 and 𝑔 in 𝑋. Corollary 3.1.	cache/cana-2862.pdf	txt/cana-2862.txt