In this paper, the notion of extended cone \(b\)-metric space is introduced, established structure open ball and defined convergence a sequence. Finally, restructured Banach Kannan contraction theorems without normality condition in new setting.

In this paper, we provide a generalization of rectangular b-metric space by relaxing the inequality to include unequal weights. We examples and restrictions for Lipschitz constant enabling convergence some sequences in proof fixed point theorems.