Some discussion on the existence of common fixed points for a pair of maps
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Author list: Patel D.K., Kumam P., Gopal D.
Publisher: SpringerOpen
Publication year: 2013
Journal: Fixed Point Theory and Applications (1687-1820)
Volume number: 2013
ISSN: 1687-1820
eISSN: 1687-1812
Languages: English-Great Britain (EN-GB)
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Abstract
In this paper, the concepts of conditionally sequential absorbing and pseudo-reciprocal continuous maps are introduced in connection to giving a brief discussion on the role of various types of commutativity (e.g., weakly compatible, occasionally weakly compatible, subcompatible, pseudo-compatible, etc.) and continuity-type conditions (e.g., reciprocal, weak reciprocal, g-reciprocal, conditionally reciprocal, subsequential and sequential continuity of type (Ag) and (Af)) in the context of existence of common fixed points of a pair of maps. Here, the utility of newly introduced maps (i.e., conditionally sequential absorbing and pseudo-reciprocal continuous) in view of common fixed points for a pair of maps satisfying contractive as well as nonexpansive Lipschitz-type conditions is shown. ฉ 2013 Patel et al.; licensee Springer.
Keywords
Conditionally sequential absorbing, Pseudo-reciprocal continuity
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