Generalizations of Accretivity for Nonlinear Mappings of Banach Spaces by Felix
نویسندگان
چکیده
Let X and Y be real Banach spaces, ƒ a mapping of X into 2, y0 an element of Y It is our object in the present discussion to present a new existence theory for solutions of the equation y0£f(x) which extends, sharpens, and simplifies the corresponding theory for X — Y and ƒ hypermaximal accretive. This new existence theory is founded in a very basic way upon the fixed point theory of self-mappings of the Banach space Y (for example, of mappings of nonexpansive or of condensive type) and yields in its turn an interesting extension of these fixed point theories. In its most general form, the class of mappings which we wish to treat is given in the following form : DEFINITION 1. Let X and Y be Banach spaces, K a mapping of X into Y, F a class of mappings of Y into 2. The mapping f of X into 2 is said to (F, K)-generative if the mapping g = K( ƒ + K)~ x lies in the class F.If X = Y and K is the identity mapping, we say that ƒ is F-generative. If, in addition, F is the class of nonexpansive mappings of Y into Y, we say that ƒ is generative. We recall that a mapping ƒ of Y into 2 is said to be hypermaximal accretive (m-accretive) if for each Ç > 0, (ƒ + if)' is a nonexpansive mapping of Y [ l]-[5]. In terms of Definition 1, ƒ is hypermaximal accretive if if is generative for each £ > 0. If Y is a Hilbert space and the range of (ƒ + ƒ) is all of Y, then ƒ is hypermaximal accretive whenever
منابع مشابه
A new approximation method for common fixed points of a finite family of nonexpansive non-self mappings in Banach spaces
In this paper, we introduce a new iterative scheme to approximate a common fixed point for a finite family of nonexpansive non-self mappings. Strong convergence theorems of the proposed iteration in Banach spaces.
متن کاملOn intermediate value theorem in ordered Banach spaces for noncompact and discontinuous mappings
In this paper, a vector version of the intermediate value theorem is established. The main theorem of this article can be considered as an improvement of the main results have been appeared in [textit{On fixed point theorems for monotone increasing vector valued mappings via scalarizing}, Positivity, 19 (2) (2015) 333-340] with containing the uniqueness, convergent of each iteration to the fixe...
متن کاملExtensions of Saeidi's Propositions for Finding a Unique Solution of a Variational Inequality for $(u,v)$-cocoercive Mappings in Banach Spaces
Let $C$ be a nonempty closed convex subset of a real Banach space $E$, let $B: C rightarrow E $ be a nonlinear map, and let $u, v$ be positive numbers. In this paper, we show that the generalized variational inequality $V I (C, B)$ is singleton for $(u, v)$-cocoercive mappings under appropriate assumptions on Banach spaces. The main results are extensions of the Saeidi's Propositions for fi...
متن کاملNew hybrid method for equilibrium problems and relatively nonexpansive mappings in Banach spaces
In this paper, applying hybrid projection method, a new modified Ishikawa iteration scheme is presented for finding a common element of the solution set of an equilibrium problem and the set of fixed points of relatively nonexpansive mappings in Banach spaces. A numerical example is given and the numerical behaviour of the sequences generated by this algorithm is compared with several existence...
متن کامل