article · Symmetry
We introduce (Ω,Π)-contractions in complete S-metric spaces, where Ω,Π:(0,∞)→R satisfy Π(t)<Ω(t). Under natural comparison conditions, we prove asymptotic regularity and S-Cauchy Picard iterates. With either a closed-graph condition or lim supt→0+Π(t)<lim inft→ε+Ω(t) for every ε>0, we establish unique fixed points and strong convergence from any initial point. Our results generalize the Banach contraction principle to S-metric spaces and subsume recent theorems on asymptotically regular mappings and implicit contractions. An application solves a nonlinear boundary value problem for diffusion between parallel walls.
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DOI: 10.3390/sym18071066
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