Abstract
In this paper, we present a new self-adaptive inertial projection method for solving split common null point problems in p-uniformly convex and uniformly smooth Banach spaces. The algorithm is designed such that its convergence does not require prior estimate of the norm of the bounded operator and a strong convergence result is proved for the sequence generated by our algorithm under mild conditions. Moreover, we give some applications of our result to split convex minimization and split equilibrium problems in real Banach spaces. This result improves and extends several other results in this direction in the literature.
Highlights
Let H1 and H2 be real Hilbert spaces and C and Q be nonempty, closed and convex subsets ofH1 and H2, respectively
Can we provide a new iterative method for solving Split Common Null Point Problem (SCNPP) in real Banach spaces such that the step size does not require prior estimate of the norm of the bounded linear operator?
We introduce a new inertial shrinking projection method for solving the split common null point problem in uniformly convex and uniformly smooth real Banach spaces
Summary
Let H1 and H2 be real Hilbert spaces and C and Q be nonempty, closed and convex subsets ofH1 and H2 , respectively. The SCNPP contains several important optimization problems such as split feasibility problem, split equilibrium problem, split variational inequalities, split convex minimization problem, split common fixed point problems, etc., as special cases (see, e.g., [1,2,3,4,5]). Due to their importance, several researchers have studied and proposed various iterative methods for finding its solutions (see, e.g., [1,4,5,6,7,8,9]). Byrne et al [1] introduced the following iterative scheme for solving SCNPP in real Hilbert spaces:
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