On estimating convergence for Picard sequences in b-metric space
Keywords:
Cauchy sequence, b-metric spaces, fixed point, contractionAbstract
In this paper, we give an estimate of d(xn, x∗) for a sequence {xn} in a b-metric space that satisfies the contractive condition d(xn+1, xn) ≤ λd(xn, xn−1), for all n ∈ N, where λ ∈ (0, 1). In addition, we give another proof for the convergence of a sequence {xn}. Examples of estimation for Banach’s, Kannan’s, and Reich’s fixed point theorems are given. In the end, we give some open problems in which research can be continued.
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