Search

We consider mixed parallel and cyclic iterative algorithms in this paper to solve the multiple-set split equality common fixed-point problem which is a generalization of the split equality problem and the split feasibility problem for the demicontractive mappings without prior knowledge of operator norms in real Hilbert spaces. Some weak and strong convergence results are established. The results obtained in this paper generalize and improve the recent ones announced by many others. [ABSTRACT FROM AUTHOR]

In this paper, we propose an extension of quasi-equilibriumproblems fromthe convex case to the nonconvex case and fromHilbert spaces to Banach spaces. The proposed problem is called quasi-variational problem. We study the convergence of some algorithms to solutions of the proposed nonconvex problems in Banach spaces. [ABSTRACT FROM AUTHOR]

The aim of this paper is to construct a novel implicit iterative algorithm for the split common fixed point problem for the demicontractive operators U, T, and  xn=αnfxn+1-αnUλxn-ρnA*I-TAxn, n≥0, where Uλ=(1-λ)I+λU, and we obtain the sequence which strongly converges to a solution x^ of this problem, and the solution x^ satisfies the variational inequality. 〈x^-f(x^),x^-z〉≤0, ∀z∈S, where S denotes the set of all solutions of the split common fixed point problem. [ABSTRACT FROM AUTHOR]

This paper deals with the second-order nonlinear neutral delay difference equation Δ(anh(xn-τ1n,xn-τ2n,…,xn-τmn)Δ(xn-qnxn-τ0))+f(n,xn-σ1n,xn-σ2n,…,xn-σkn)=bn, n≥n0. Using the Banach fixed point theorem, Mann iterative method with errors, and some new techniques, we prove the existence of uncountably many positive solutions and the convergence of the sequences generated by the Mann iterative method with errors relative to these solutions for the above equation. Six examples are included. Our results extend and improve essentially the known results in this field. [ABSTRACT FROM AUTHOR]