Solving GNOVI frameworks involving "Equation missing" No EquationSource Format="TEX", only image and EquationSource Format="MATHML" -weak-GRD set-valued mappings in positive Hilbert spaces

Abstract

Abstract First, a new concept, positive Hilbert spaces, is introduced and some fundamental inequalities which are applied to studying the properties of the resolvent operator associated for ( γ G , λ ) -weak-GRD set-valued mappings are introduced and discussed in positive Hilbert spaces. Next, by using the resolvent operator and fixed point theory, an existence theorem and an approximation algorithm to solve a new class of general nonlinear ordered inclusions are established and suggested. In this field, the results obtained seem to be general in nature. MSC:49J40, 47H06.