Abstract
In this paper, we propose a generalized explicit algorithm for approximating the common solution of generalized split feasibility problem and the fixed point of demigeneralized mapping in uniformly smooth and 2-uniformly convex real Banach spaces. The generalized split feasibility problem is a general mathematical problem in the sense that it unifies several mathematical models arising in (symmetry and non-symmetry) optimization theory and also finds many applications in applied science. We designed the algorithm in such a way that the convergence analysis does not need a prior estimate of the operator norm. More so, we establish the strong convergence of our algorithm and present some computational examples to illustrate the performance of the proposed method. In addition, we give an application of our result for solving the image restoration problem and compare with other algorithms in the literature. This result improves and generalizes many important related results in the contemporary literature.
Highlights
Let C and Q be nonempty, closed, and convex subsets of two real Hilbert spaces H1 and H2, respectively, and B : H1 → H2 be a bounded linear operator
In the methods mentioned above, the stepsize γn depends on prior estimates of the norm of the bounded linear operator, i.e., k Bk, which, in general, it is very difficult to estimate, the following question arises naturally: Question A: Can we provide an iterative scheme which does not depend on a prior estimate of the norm of the bounded linear operator for solving the generalized split feasibility problem in real Banach spaces?
Motivated by the above results, in this paper, we provide an affirmative answer to Question A using the technique above in real Banach spaces
Summary
Generalized Split Feasibility Problem and Fixed Point Problem in Real Banach Spaces. Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, P.O.
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