[PDF] Top 20 Viscosity iterative algorithm for the zero point of monotone mappings in Banach spaces

... Although the above results have better theoretical properties, such as, but not only, weak and strong convergence to a solution of the equation 0 ∈ Au, there are still some difficulties to overcome. For instance, the ... See full document

... in Banach spaces which converges strongly to a zero of monotone operators? Let C be a nonempty, closed, and convex subset of a uniformly smooth strictly convex real Banach space ... See full document

... maximal monotone operators on C into H , and let g : H → H be a k-contraction with 0 < k < ...strongly monotone mapping, V : H → H is a γ ¯ -strongly monotone and L-Lipschitzian mapping with γ ... See full document

... Throughout this paper, we assume that E and E ∗ is a real Banach space and the dual space of E, respectively. Let T be a mapping from C into itself, where C is a subset of E. We denoted by F(T) the set of fixed ... See full document

... modified viscosity implicit-type proximal point algorithm for ap- proximating a common solution of monotone inclusion problem and fixed point problem for an asymptotically nonexpansive ... See full document

... a zero point of a monotone ...a monotone operator satisfying a range condition; see Theorem ...maximal monotone operator; see Theorem ... See full document

... Shahzad, “Strong convergence theorems for a common zero for a finite family of m - accretive mappings,” Nonlinear Analysis: Theory, Methods & Applications, vol. Kang, “Zeros and mapp[r] ... See full document

... Halpern-type iterative method for finding a common element of the fixed point set of a relatively nonexpansive mapping and the zero set of a maximal monotone ...This iterative method is ... See full document

... fixed point construction iteration processes for generalized nonexpansive mappings have been successfully used to develop efficient and powerful nu- merical methods for solving various nonlinear equations and ... See full document

... new iterative algorithms with errors for approximating common zero point of an infinite family of m-accretive mappings in a real Banach space are ...m-accretive mappings and ... See full document

... Hilbert spaces, (m-)accretive mappings, (m-)d-accretive mappings and (maximal) monotone operators are the ...Hilbertian Banach spaces, they belong to different classes of ... See full document

... the sets of zero points of A + B and F, respectively. A strong convergence theorem is established under appropriate conditions imposed on the parameters. Further, we consider the problem for finding a common ... See full document

... the iterative scheme 3.1 for finding a common element of the set of zero of a maximal monotone operator and the solution set of the variational inequality problem for an ... See full document

... or Banach spaces, there exist several iterative algorithms to nonexpansive mappings ...(e.g., Viscosity iteration algorithm [7], Hybrid projection algorithm [8], Hybrid ... See full document

... a monotone nonexpansive mapping T in a Banach space E with the partial order ‘≤’, where a such mapping may be ...dimensional spaces, such a mapping T has a fixed point in E if and only if the ... See full document

... real Banach space E with E ∗ as its dual. A is said to be maximal monotone if its graph is not properly contained in the graph of any other monotone ...strongly monotone if there exists a ... See full document

... Proximal point algorithm, which was proposed by Martinet [, ] and generalized by Rockafellar [, ], is a classical method for investigating zeros of monotone ...proximal point ... See full document

... common zero (fixed) points of nonlinear operators, for instance, image recovery, inverse problems, transportation problems and optimization ...common zero (fixed) points of nonlin- ear ...parallel ... See full document

... fuzzy mappings T, V , Z, mappings A, g , N, and space E, we can obtain a number of known and new classes of (fuzzy) variational inequalities, (fuzzy) variational inclusions, and the corresponding (fuzzy) ... See full document

... We introduce a new nonlinear mapping similar to the nonspreading mapping which is defined by Kohsaka and Takahashi (Arch. Math. 91:166-177, 2008). We prove fixed point theorems for such a mapping without the ... See full document