A Self-Adaptive Shrinking Projection Method with an Inertial Technique for Split Common Null Point Problems in Banach Spaces

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...

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Bibliographic Details
Published in:Axioms 2020-12, Vol.9 (4), p.140
Main Authors: Okeke, Chibueze Christian, Jolaoso, Lateef Olakunle, Nwokoye, Regina
Format: Article
Language:English
Subjects:
Algorithms
Banach spaces
Codes
Convergence
Iterative methods
Methods
metric resolvent
resolvent
split common null point
split equilibrium problem
split minimization problem
strong convergence
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Summary: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.
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms9040140