Approximation of Fixed Points of Nonexpansive Mappings and Solutions of Variational Inequalities

Abstract Let be a real -uniformly smooth Banach space with constant , . Let and be a nonexpansive map and an -strongly accretive map which is also -Lipschitzian, respectively. Let be a real sequence in that satisfies the following condition: and . For and , define a sequence iteratively in by , , . Then, converges strongly to the unique solution of the variational inequality problem (search for such that for all , where . A convergence theorem related to finite family of nonexpansive maps is also proved

A New Iteration Process for Approximation of Common Fixed Points for Finite Families of Total Asymptotically Nonexpansive Mappings

LetEbe a real Banach space, andKa closed convex nonempty subset ofE. LetT1,T2,…,Tm:K→Kbemtotal asymptotically nonexpansive mappings. A simple iterative sequence{xn}n≥1is constructed inEand necessary and sufficient conditions for this sequence to converge to a common fixed point of{Ti}i=1mare given. Furthermore, in the case thatEis a uniformly convex real Banach space, strong convergence of the sequence{xn}n=1∞to a common fixed point of the family{Ti}i=1mis proved. Our recursion formula is much simpler and much more applicable than those recently announced by several authors for the same problem

Convergece Theorems for Finite Families of Asymptotically Quasi-Nonexpansive Mappings

Let be a real Banach space, a closed convex nonempty subset of , and asymptotically quasi-nonexpansive mappings with sequences (resp.) satisfying as , and . Let be a sequence in . Define a sequence by , , , , , . Let . Necessary and sufficient conditions for a strong convergence of the sequence to a common fixed point of the family are proved. Under some appropriate conditions, strong and weak convergence theorems are also proved

Strong and Δ

Let K be a nonempty closed and convex subset of a complete CAT(0) space. Let Ti:K→CBK,i=1,2,…,m, be a family of multivalued demicontractive mappings such that F:=⋂i=1mF(Ti)≠∅. A Krasnoselskii-type iterative sequence is shown to Δ-converge to a common fixed point of the family Ti,i=1,2,…,m. Strong convergence theorems are also proved under some additional conditions. Our theorems complement and extend several recent important results on approximation of fixed points of certain nonlinear mappings in CAT(0) spaces. Furthermore, our method of the proof is of special interest

Convergence Theorems for Fixed Points of Multivalued Strictly Pseudocontractive Mappings in Hilbert Spaces

Let K be a nonempty, closed, and convex subset of a real Hilbert space H. Suppose that T:K→2K is a multivalued strictly pseudocontractive mapping such that F(T)≠∅. A Krasnoselskii-type iteration sequence {xn} is constructed and shown to be an approximate fixed point sequence of T; that is, limn→∞d(xn,Txn)=0 holds. Convergence theorems are also proved under appropriate additional conditions

United Nations Educational Scientific and Cultural Organization and International Atomic Energy Agency THE ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS SOLVING THE GENERAL TRUNCATED MOMENT PROBLEM BY r-GENERALIZED FIBONACCI SEQUENCES METHOD

Abstract We give in this paper a new method for solving the generalized truncated power moment problem. To this aim we use r-generalized Fibonacci sequences and their associated minimal polynomials. We provide an algorithm of construction of solutions in a short method. This method allows us to avoid any appeal to Hankel matrices or any positive difiniteness conditions as in Flessas-Burton-Whitehead (FBW) approach. Examples and general cases are discussed