Abstract
The aim of this paper is to formulate and analyze a cyclic iterative algorithm in real Hilbert spaces which converges strongly to a common solution of fixed point problem and multiple-sets split common fixed point problem involving demicontractive operators without prior knowledge of operator norm. Significance and range of applicability of our algorithm has been shown by solving the problem of multiple-sets split common null point, multiple-sets split feasibility, multiple-sets split variational inequality, multiple-sets split equilibrium and multiple-sets split monotone variational inclusion.
Highlights
In 1994, Censor et al [1] firstly suggested the split feasibility problem (SFP) for modelling inverse problems
In this paper, inspired and motivated by above work, we present a new cyclic iterative scheme without prior knowledge of operator norm and prove its strong convergence for approximating a common solution of fixed point problem and multiple-sets split common fixed point problem for demicontractive operators in real Hilbert spaces
Consider B : H1 → 2 H1 and F : H2 → 2 H2 two set valued operators defined on Hilbert spaces H1 and H2 respectively and A : H1 → H2 is a bounded linear operator, split common null point problem (SCNPP) is to identify z∗ ∈ H1 such that 0 ∈ B(z∗ ) and y∗ = Az∗ solves 0 ∈ F (y∗ )
Summary
Nishu Gupta 1,† , Mihai Postolache 2,3,4,5, *,† , Ashish Nandal 6,† and Renu Chugh 7,†. Iacob Institute of Mathematical Statistics and Applied Mathematics, Romanian Academy, 050711 Bucharest, Romania.
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