A New System of Nonlinear Fuzzy Variational Inclusions Involving (A,η)-Accretive Mappings in Uniformly Smooth Banach Spaces

A new system of nonlinear fuzzy variational inclusions involving (A,η)-accretive mappings in uniformly smooth Banach spaces is introduced and studied many fuzzy variational and variational inequality (inclusion) problems as special cases of this system. By using the resolvent operator technique associated with (A,η)-accretive operator due to Lan et al. and Nadler's fixed points theorem for set-valued mappings, an existence theorem of solutions for this system of fuzzy variational inclusions is proved. We also construct some new iterative algorithms for the solutions of this system of nonlinear fuzzy variational inclusions in uniformly smooth Banach spaces and discuss the convergence of the sequences generated by the algorithms in uniformly smooth Banach spaces. Our results extend, improve, and unify many known results in the recent literatures

A New System of Nonlinear Fuzzy Variational Inclusions Involving <inline-formula> <graphic file="1029-242X-2009-806727-i1.gif"/></inline-formula>-Accretive Mappings in Uniformly Smooth Banach Spaces

<p>Abstract</p> <p>A new system of nonlinear fuzzy variational inclusions involving <inline-formula> <graphic file="1029-242X-2009-806727-i2.gif"/></inline-formula>-accretive mappings in uniformly smooth Banach spaces is introduced and studied many fuzzy variational and variational inequality (inclusion) problems as special cases of this system. By using the resolvent operator technique associated with <inline-formula> <graphic file="1029-242X-2009-806727-i3.gif"/></inline-formula>-accretive operator due to Lan et al. and Nadler's fixed points theorem for set-valued mappings, an existence theorem of solutions for this system of fuzzy variational inclusions is proved. We also construct some new iterative algorithms for the solutions of this system of nonlinear fuzzy variational inclusions in uniformly smooth Banach spaces and discuss the convergence of the sequences generated by the algorithms in uniformly smooth Banach spaces. Our results extend, improve, and unify many known results in the recent literatures.</p

Conditions of regularity in cone metric spaces

In this paper we prove some fixed points results on cone metric spaces for maps satisfying general contractive type conditions. Among other things, we extend some results of Nguyen [11] from metric spaces to cone metric spaces. The example is included