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Absorbing pairs facilitating common fixed point theorems for Lipschitzian type mappings in symmetric spaces. (English) Zbl 1246.54038
In this paper, the authors prove unified theorems in symmetric (semi-metric) spaces using the notion of absorbing pairs, which generalize various existing results in the literature. A proposition is given to show that the pointwise S-absorbing as well as the pointwise T-absorbing property is equivalent to the pointwise absorbing property. Some related results are also proved on continuity. Some illustrative examples are also furnished to highlight the realized improvements.
MSC:
54H25Fixed-point and coincidence theorems in topological spaces
47H10Fixed point theorems for nonlinear operators on topological linear spaces