We introduce a concept of weak Bregman relatively nonexpansive mapping which is distinct from Bregman relatively nonexpansive mapping. By using projection techniques, we construct several modification of Mann type iterative algorithms with errors and Halpern-type iterative algorithms with errors to find fixed points of weak Bregman relatively nonexpansive mappings and Bregman relatively nonexpa...

In real Hilbert spaces, let the CFPP indicate a common fixed-point problem of asymptotically nonexpansive operator and countably many operators, suppose that HVI VIP represent hierarchical variational inequality problem, respectively. We put forward Mann hybrid deepest-descent extragradient approach for solving with constraints. The proposed algorithms are on basis Mann’s iterative technique, v...

and Applied Analysis 3 It is clear that 1.7 is equivalent to 〈 Sx − Sy, x − y ≤ ∥x − y∥2, ∀x, y ∈ C. 1.8 The class of κ-strict pseudocontractions which was introduced by Browder and Petryshyn 17 in 1967 has been considered by many authors. It is easy to see that the class of strict pseudocontractions falls into the one between the class of nonexpansive mappings and the class of pseudocontractio...

In this paper, we first prove the weak convergence for the Moudafi’s iterative scheme of two quasi-nonexpansive mappings. Then we prove the weak convergence for the Moudafi’s iterative scheme of quasi-nonexpansive mapping and nonexpansive mapping. Finally, we prove the strong convergence for the Moudafi’s iterative scheme of two quasi-nonexpansive mappings. Our results generalize the recent res...

Very recently, Moudafi proposed the following new convex feasibility problem in [10,11]: find x ∈ C, y ∈ Q such that Ax = By, where the two closed convex sets C and Q are the fixed point sets of two firmly quasi-nonexpansive mappings respectively, H1, H2 and H3 are real Hilbert spaces, A : H1 → H3 and B : H2 → H3 are two bounded linear operators. However, they just obtained weak convergence for...

The authors have obtained the following results: 1 the definition of uniformly closed countable family of nonlinear mappings, 2 strong convergence theorem by the monotone hybrid algorithm for two countable families of hemirelatively nonexpansive mappings in a Banach space with new method of proof, 3 two examples of uniformly closed countable families of nonlinear mappings and applications, 4 an...

There are mutants of Salmonella enterica (with mutations in fliF and fliL) that shed flagella when they are swimming in a viscous medium or on the surface of soft agar. Filaments with hooks and the distal rod segment FlgG are recovered. We tried to extract flagellar filaments from such cells by pulling on them with an optical trap but failed, even when we used forces large enough to straighten ...

and Applied Analysis 3 It is easy to see that a quasi-nonexpansive mapping is an asymptotically quasi-nonexpansive mapping with the sequence {1}. T is said to be asymptotically nonexpansive in the intermediate sense if and only if it is continuous, and the following inequality holds: lim sup n→∞ sup x,y∈C (∥ ∥Tx − Tny∥∥ − ∥∥x − y∥∥) ≤ 0. 2.6 T is said to be asymptotically quasi-nonexpansive in ...

and Applied Analysis 3 or the modified Mann iterative sequence method xn 1 QG ( 1 − αn xn αnT ΠGT xn ) , n 1, 2, . . . , x1 ∈ G, 1.6 where QG : B → G is a sunny nonexpansive retraction. So, in some ways, our results extend and improve some results of other authors such as, see 1–5, 7, 9–13 , from self mappings to non-self-mappings, from Hilbert spaces to Banach spaces. 2. Preliminaries In the s...