We introduce a new class of mappings, called p-cyclic \phi-contractions, which contains the p-cyclic contraction mappings as a subclass. Then, convergence and existence results of best proximity points for p-cyclic \phi-contraction mappings are obtained. Moreover, we prove results of the existence of best proximity points in a reflexive Banach space. These results are generalizations of the results of Al-Thagafi and Shahzad (2009) [8].
Vetro, C. (2010). Best proximity points: Convergence and existence theorems for p-cyclic mappings. NONLINEAR ANALYSIS, 73(7), 2283-2291 [doi:10.1016/j.na.2010.06.008].
Best proximity points: Convergence and existence theorems for p-cyclic mappings
VETRO, Calogero
2010-01-01
Abstract
We introduce a new class of mappings, called p-cyclic \phi-contractions, which contains the p-cyclic contraction mappings as a subclass. Then, convergence and existence results of best proximity points for p-cyclic \phi-contraction mappings are obtained. Moreover, we prove results of the existence of best proximity points in a reflexive Banach space. These results are generalizations of the results of Al-Thagafi and Shahzad (2009) [8].
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