Generalized Yosida Approximations Based on Relatively A -Maximal m -Relaxed Monotonicity Frameworks

Abstract

We introduce and study a new notion of relatively A-maximal m-relaxed monotonicity framework and discuss some properties of a new class of generalized relatively resolvent operator associated with the relatively A-maximal m-relaxed monotone operator and the new generalized Yosida approximations based on relatively A-maximal m-relaxed monotonicity framework. Furthermore, we give some remarks to show that the theory of the new generalized relatively resolvent operator and Yosida approximations associated with relatively A-maximal m-relaxed monotone operators generalizes most of the existing notions on (relatively) maximal monotone mappings in Hilbert as well as Banach space and can be applied to study variational inclusion problems and first-order evolution equations as well as evolution inclusions.