A Cyclic Iterative Algorithm for Multiple-Sets Split Common Fixed Point Problem of Demicontractive Mappings without Prior Knowledge of Operator Norm

Gupta, Nishu; Postolache, Mihai; Nandal, Ashish; Chugh, Renu

doi:10.3390/math9040372

Open AccessArticle

A Cyclic Iterative Algorithm for Multiple-Sets Split Common Fixed Point Problem of Demicontractive Mappings without Prior Knowledge of Operator Norm

¹

Department of Mathematics, Pt NRS Government College, Rohtak 124001, India

²

Department of General Education, China Medical University, Taichung 40402, Taiwan

³

Department of Interior Design, Asia University, Taichung 41354, Taiwan

⁴

Gh. Mihoc-C. Iacob Institute of Mathematical Statistics and Applied Mathematics, Romanian Academy, 050711 Bucharest, Romania

⁵

Department of Mathematics and Informatics, University “Politehnica” of Bucharest, 060042 Bucharest, Romania

⁶

Government College, Bhainswal Kalan 131001, India

⁷

Department of Mathematics, Maharshi Dayanand University, Rohtak 124001, India

^*

Author to whom correspondence should be addressed.

^†

These authors contributed equally to this work.

Mathematics 2021, 9(4), 372; https://doi.org/10.3390/math9040372

Submission received: 7 January 2021 / Revised: 29 January 2021 / Accepted: 10 February 2021 / Published: 13 February 2021

(This article belongs to the Special Issue Fixed Point, Optimization, and Applications)

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Abstract

The aim of this paper is to formulate and analyze a cyclic iterative algorithm in real Hilbert spaces which converges strongly to a common solution of fixed point problem and multiple-sets split common fixed point problem involving demicontractive operators without prior knowledge of operator norm. Significance and range of applicability of our algorithm has been shown by solving the problem of multiple-sets split common null point, multiple-sets split feasibility, multiple-sets split variational inequality, multiple-sets split equilibrium and multiple-sets split monotone variational inclusion.

Keywords: demicontractive operators; iterative algorithm; multiple-sets split common fixed point problem; split equilibrium problem

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MDPI and ACS Style

Gupta, N.; Postolache, M.; Nandal, A.; Chugh, R. A Cyclic Iterative Algorithm for Multiple-Sets Split Common Fixed Point Problem of Demicontractive Mappings without Prior Knowledge of Operator Norm. Mathematics 2021, 9, 372. https://doi.org/10.3390/math9040372

AMA Style

Gupta N, Postolache M, Nandal A, Chugh R. A Cyclic Iterative Algorithm for Multiple-Sets Split Common Fixed Point Problem of Demicontractive Mappings without Prior Knowledge of Operator Norm. Mathematics. 2021; 9(4):372. https://doi.org/10.3390/math9040372

Chicago/Turabian Style

Gupta, Nishu, Mihai Postolache, Ashish Nandal, and Renu Chugh. 2021. "A Cyclic Iterative Algorithm for Multiple-Sets Split Common Fixed Point Problem of Demicontractive Mappings without Prior Knowledge of Operator Norm" Mathematics 9, no. 4: 372. https://doi.org/10.3390/math9040372

APA Style

Gupta, N., Postolache, M., Nandal, A., & Chugh, R. (2021). A Cyclic Iterative Algorithm for Multiple-Sets Split Common Fixed Point Problem of Demicontractive Mappings without Prior Knowledge of Operator Norm. Mathematics, 9(4), 372. https://doi.org/10.3390/math9040372

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A Cyclic Iterative Algorithm for Multiple-Sets Split Common Fixed Point Problem of Demicontractive Mappings without Prior Knowledge of Operator Norm

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