Equality Common Fixed-point Problem Research Articles

Convergence analysis of multiple-sets split equality common fixed point problem with applications

In this paper, we suggest a new inertial type parallel iterative algorithm and prove its strong convergence for finding a solution of multiple-sets split equality common fixed point problem for a finite family of demicontractive mappings in real Hilbert spaces. The suggested algorithm does not require prior knowledge of operator norm. We apply our result to study multiple-sets split equality common fixed point problem for a finite family of quasi-pseudocontractive mappings. Further, we also apply our result to solve various split type problems and intensity-modulated radiation therapy. Moreover, we give numerical experiments for supporting our main result and compare it with other existing methods.

Viscosity approximation method for solving the multiple-set split equality common fixed-point problems for quasi-pseudocontractive mappings in Hilbert spaces

We propose a parallel iterative scheme with viscosity approximation method which converges strongly to a solution of the multiple-set split equality common fixed point problem for quasi-pseudocontractive mappings in real Hilbert spaces. We also give an application of our result to approximation of minimization problem from intensity-modulated radiation therapy. Finally, we present numerical examples to demonstrate the behaviour of our algorithm. This result improves and generalizes many existing results in literature in this direction.

General alternative regularization method for solving split equality common fixed point problem for quasi-pseudocontractive mappings in Hilbert spaces

We propose a general alternative regularization algorithm for solving the split equality fixed point problem for the class of quasi-pseudocontractive mappings in Hilbert spaces. We also illustrate the performance of our algorithm with numerical example and compare the result with some other algorithms in the literature in this direction. We found out that our algorithm requires a lesser number of iterations and CPU time for its convergence than some of the existing algorithms. Our results extend and generalize some existing results in the literature in this direction.

An alternating iteration algorithm for solving the split equality fixed point problem with L-Lipschitz and quasi-pseudo-contractive mappings

In this paper, we are concerned with the split equality common fixed point problem. It is a significant generalization of the split feasibility problem, which can be used in various disciplines, such as medicine, military and biology, etc. We propose an alternating iteration algorithm for solving the split equality common fixed point problem with L-Lipschitz and quasi-pseudo-contractive mappings and prove that the sequence generated by the algorithm converges weakly to the solution of this problem. Finally, some numerical results are shown to confirm the feasibility and efficiency of the proposed algorithm.

Simultaneous iterative methods of asymptotically quasi‐nonexpansive semigroups for split equality common fixed point problem in Banach spaces

In this paper, we present iteration methods to find a solution of asymptotically quasi‐nonexpansive semigroups for a split equality common fixed point in Banach spaces. The results show weak and strong convergence theorem of iteration that improve and extend some recent results.

General viscosity approximation methods for quasi-nonexpansive mappings with applications

The purpose of this paper is to introduce and study the general viscosity approximation methods for quasi-nonexpansive mappings in the setting of infinite-dimensional Hilbert spaces. Under suitable conditions, we prove that the sequences generated by the proposed new algorithm converge strongly to a fixed point of quasi-nonexpansive mappings in Hilbert spaces, which is also the unique solution of some variational inequality. Then this result is used to study the split equality fixed point problems, the split equality common fixed point problems, the split equality null point problems, etc. Our results improve and generalize many results in the literature and they should have many applications in nonlinear science.

Solving split equality common fixed point problem for infinite families of demicontractive mappings

In this paper, we consider the split equality common fixed point problem of infinite families of demicontractive mappings in Hilbert spaces. We introduce a simultaneous iterative algorithm for solving the split equality common fixed point problem of infinite families of demicontractive mappings and prove a strong convergence of the proposed algorithm under some control conditions.

On the split equality common fixed point problem for quasi-nonexpansive multi-valued mappings in Banach spaces

On the split equality common fixed point problem for quasi-nonexpansive multi-valued mappings in Banach spaces

Viscosity approximation methods for the split equality common fixed point problem of quasi-nonexpansive operators

Let H1, H2, H3 be real Hilbert spaces, let A: H1 → H3, B: H2 → H3 be two bounded linear operators. The split equality common fixed point problem (SECFP) in the infinite-dimensional Hilbert spaces introduced by Moudafi (Alternating CQ-algorithm for convex feasibility and split fixed-point problems. Journal of Nonlinear and Convex Analysis) is (1)to find x∈F(U),y∈F(T) such that Ax=By,where U: H1 → H1 and T: H2 → H2 are two nonlinear operators with nonempty fixed point sets F(U) = {x ∈ H1: Ux = x} and F(T) = {x ∈ H2: Tx = x}. Note that, by taking B = I and H2 = H3 in (1), we recover the split fixed point problem originally introduced in Censor and Segal. Recently, Moudafi introduced alternating CQ-algorithms and simultaneous iterative algorithms with weak convergence for the SECFP (1) of firmly quasi-nonexpansive operators. In this paper, we introduce two viscosity iterative algorithms for the SECFP (1) governed by the general class of quasi-nonexpansive operators. We prove the strong convergence of algorithms. Our results improve and extend previously discussed related problems and algorithms.

On the split equality common fixed point problem for asymptotically nonexpansive semigroups in Banach spaces

On the split equality common fixed point problem for asymptotically nonexpansive semigroups in Banach spaces