CONVERGENCE ANALYSIS OF MULTIPLE-SETS SPLIT EQUALITY COMMON FIXED POINT PROBLEM WITH APPLICATIONS

Nishu Gupta; Lateef Olakunle Jolaoso; Ashish Nandal; Renu Chugh

doi:10.3934/naco.2023012

CONVERGENCE ANALYSIS OF MULTIPLE-SETS SPLIT EQUALITY COMMON FIXED POINT PROBLEM WITH APPLICATIONS

Nishu Gupta
, Lateef Olakunle Jolaoso
, Ashish Nandal^*
, Renu Chugh

^*Corresponding author for this work

Mathematics and Applied Mathematics

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	273-299
Number of pages	27
Journal	Numerical Algebra, Control and Optimization
Volume	15
Issue number	2
DOIs	https://doi.org/10.3934/naco.2023012
Publication status	Published - 1 Jun 2025

Keywords

Split feasibility problem
demicontractive mappings
quasi-pseudocontractive mappings
split equality common fixed point problem
variational inequality problem

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10.3934/naco.2023012

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abstract = "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.",

keywords = "Split feasibility problem, demicontractive mappings, quasi-pseudocontractive mappings, split equality common fixed point problem, variational inequality problem",

author = "Nishu Gupta and Jolaoso, \{Lateef Olakunle\} and Ashish Nandal and Renu Chugh",

year = "2025",

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AU - Gupta, Nishu

AU - Jolaoso, Lateef Olakunle

AU - Nandal, Ashish

AU - Chugh, Renu

PY - 2025/6/1

Y1 - 2025/6/1

N2 - 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.

AB - 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.

KW - Split feasibility problem

KW - demicontractive mappings

KW - quasi-pseudocontractive mappings

KW - split equality common fixed point problem

KW - variational inequality problem

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VL - 15

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EP - 299

JO - Numerical Algebra, Control and Optimization

JF - Numerical Algebra, Control and Optimization

IS - 2

ER -

CONVERGENCE ANALYSIS OF MULTIPLE-SETS SPLIT EQUALITY COMMON FIXED POINT PROBLEM WITH APPLICATIONS

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Keywords

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