# Two inertial CQ-algorithms for generalized split inverse problem of infinite family of demimetric mappings

Volume 16, Issue 1, pp 1--17
Publication Date: March 10, 2023 Submission Date: October 10, 2022 Revision Date: February 14, 2023 Accteptance Date: February 22, 2023
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### Authors

C. Suanoom - Program of Mathematics, Science and Applied Science center, Faculty of Science and Technology, Kamphaeng Phet Rajabhat, Kamphaeng Phet 62000, Thailand. S. E. Yimer - Department of Mathematics, College of Computational and Natural Science, Debre Berhan University, Debre Berhan, Ethiopia. A. G. Gebrie - Department of Mathematics, College of Computational and Natural Science, Debre Berhan University, Debre Berhan, Ethiopia.

### Abstract

In this paper, two new inertial CQ-algorithms with strong convergence results are constructed to approximate the solution of the generalized split common fixed point problem: given as a task of finding a point that belongs to the intersection of an infinite family of fixed point sets of demimetric mappings such that its image under an infinite number of linear transformations belongs to the intersection of another infinite family of fixed point sets of demimetric mappings in the image space. The algorithms are established based on the CQ-projection method with inertial effect and step-size selection technique so that the implementation of the proposed algorithms does not need any prior information about the operator norms. The proposed methods improve, complement, and generalize many of the important results in the literature.

### Share and Cite

##### ISRP Style

C. Suanoom, S. E. Yimer, A. G. Gebrie, Two inertial CQ-algorithms for generalized split inverse problem of infinite family of demimetric mappings, Journal of Nonlinear Sciences and Applications, 16 (2023), no. 1, 1--17

##### AMA Style

Suanoom C., Yimer S. E., Gebrie A. G., Two inertial CQ-algorithms for generalized split inverse problem of infinite family of demimetric mappings. J. Nonlinear Sci. Appl. (2023); 16(1):1--17

##### Chicago/Turabian Style

Suanoom, C., Yimer, S. E., Gebrie, A. G.. "Two inertial CQ-algorithms for generalized split inverse problem of infinite family of demimetric mappings." Journal of Nonlinear Sciences and Applications, 16, no. 1 (2023): 1--17

### Keywords

• Split common fixed-point problem
• $\kappa$-demimetric mapping
• inertial term
• CQ-algorithm
• Hilbert space
• strong convergence

•  90C25
•  47N10
•  65J15
•  47J25