Absorbing pairs facilitating common fixed point theorems for Lipschitzian type mappings in symmetric spaces. (English) Zbl 1246.54038

Gopal, Dhananjay; Hasan, Mohammad; Imdad, Mohammad

Commun. Korean Math. Soc. 27, No. 2, 385-397 (2012).

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.

Reviewer: Hemant Kumar Nashine (Raipur)

MSC:

54H25	Fixed-point and coincidence theorems (topological aspects)
47H10	Fixed-point theorems

Keywords:

tangential mappings; Lipschitzian mappings; absorbing pairs