Towards Viscosity Approximations of Hierarchical Fixed-point Problems

Convergence Comparison of Several Iteration Algorithms for the Common Fixed Point Problems

We discuss the following viscosity approximations with the weak contraction A for a nonexpansive mapping sequence {Tn}, yn αnAyn 1 − αn Tnyn, xn 1 αnAxn 1 − αn Tnxn. We prove that Browder’s and Halpern’s type convergence theorems imply Moudafi’s viscosity approximations with the weak contraction, and give the estimate of convergence rate between Halpern’s type iteration and Mouda’s viscosity ap...

Iterative algorithms for families of variational inequalities fixed points and equilibrium problems

Common Fixed Points and Invariant Approximations for Cq-commuting Generalized nonexpansive mappings

Some common fixed point theorems for Cq-commuting generalized nonexpansive mappings have been proved in metric spaces. As applications, invariant approximation results are also obtained. The results proved in the paper extend and generalize several known results including those of M. Abbas and J.K. Kim [Bull. Korean Math. Soc. 44(2007) 537-545], I. Beg, N. Shahzad and M. Iqbal [Approx. Theory A...

Retracts , fixed point index and differential equations ∗ Rafael Ortega

Many problems in the theory of differential equations were initially treated with analytic techniques and later evolved towards more topological approaches. Perhaps the most paradigmatic case is found in the study of nonlinear boundary value problems. The classical proofs based on successive approximations or in the implicit function theorem were soon replaced by the use of fixed points and deg...

Viscosity Method for Hierarchical Fixed Point Problems with an Infinite Family of Nonexpansive Nonself-Mappings

for all x ∈ X, whereX denotes the dual space ofX and ⟨⋅, ⋅⟩ the generalized duality pairing between X and X. If X = H is a Hilbert space, then J becomes the identitymapping onH. A point x ∈ C is a fixed point of T : C ⊂ X → X provided Tx = x. Denote by F(T) the set of fixed points of T; that is, F(T) = {x ∈ C : Tx = x}. Let X be a normed linear space with dim X ≥ 2. The modulus of smoothness of...