Fixed point theorems of
-monotone mappings in Hilbert spaces
Department of Mathematics, National Changhua University of Education, Changhua, 50058, Taiwan
Fixed Point Theory and Applications 2012, 2012:131 doi:10.1186/1687-1812-2012-131Published: 7 August 2012
We propose a new class of nonlinear mappings, called -monotone mappings, and show that this class of nonlinear mappings contains nonspreading mappings, hybrid mappings, firmly nonexpansive mappings, and -generalized hybrid mappings with . We also give an example to show that a -monotone mapping is not necessary to be a quasi-nonexpansive mapping. We establish an existence theorem of fixed points and the demiclosed principle for the class of -monotone mappings. As a special case of our result, we give an existence theorem of fixed points for -generalized hybrid mappings with . We also consider Mann’s type weak convergence theorem and CQ type strong convergence theorem for -monotone mappings. We give an example of -monotone mappings which assures the Mann’s type weak convergence.