Figure 1.
Manuscript statistics from 2020 to 2022.
The local convergence analysis of the parameter based sixth-order iterative method is the primary focus of this article. This investigation was conducted based on the Fréchet derivative of the first order that satisfies the Lipschitz continuity condition. In addition, we developed a conceptual radius of convergence for these methods. Also, we discussed the solution behavior of complex polynomials with the basin of attraction. Finally, some numerical examples are provided to illustrate how the conclusions we got can be employed to determine the iterative approach's radius of convergence ball in the context of solving nonlinear equations. We compare the numerical results with our method and the existing sixth order methods proposed by Argyros et al. We observe that using our method yields significantly larger balls than those that already exist.
Citation: Kasmita Devi, Prashanth Maroju. Complete study of local convergence and basin of attraction of sixth-order iterative method[J]. AIMS Mathematics, 2023, 8(9): 21191-21207. doi: 10.3934/math.20231080
| [1] | Kelly Pagidas . 2024 Annual Report. AIMS Medical Science, 2025, 12(1): 63-68. doi: 10.3934/medsci.2025005 |
| [2] | Ragini C Bhake, Stafford L Lightman . A Simple Complex Case: Restoration of Circadian Cortisol Activity. AIMS Medical Science, 2015, 2(3): 182-185. doi: 10.3934/medsci.2015.3.182 |
| [3] | Mpumelelo Nyathi, Autherlia Dimpho Rinkie Mosiame . Evaluating radiation exposure risks from patient urine in a PET-CT center: should concerns arise?. AIMS Medical Science, 2025, 12(2): 238-246. doi: 10.3934/medsci.2025016 |
| [4] | Piero Pavone, Ottavia Avola, Claudia Oliva, Alessandra Di Nora, Tiziana Timpanaro, Chiara Nannola, Filippo Greco, Raffaele Falsaperla, Agata Polizzi . Genetic epilepsy and role of mutation variants in 27 epileptic children: results from a “single tertiary centre” and literature review. AIMS Medical Science, 2024, 11(3): 330-347. doi: 10.3934/medsci.2024023 |
| [5] | Muhammad Bilal . Leukemoid reaction in paraplegic male with pressure injuries: A case report. AIMS Medical Science, 2024, 11(2): 72-76. doi: 10.3934/medsci.2024006 |
| [6] | Niccolò Stomeo, Giacomo Simeone, Leonardo Ciavarella, Giulia Lionetti, Arosh S. Perera Molligoda Arachchige, Francesco Cama . Fluid overload during operative hysteroscopy for metroplasty: A case report. AIMS Medical Science, 2023, 10(4): 310-317. doi: 10.3934/medsci.2023024 |
| [7] | Ryan T. Borne, Arash Aghel, Amit C. Patel, Robert K. Rogers . Innominate Steal Syndrome: A Two Patient Case Report and Review. AIMS Medical Science, 2015, 2(4): 360-370. doi: 10.3934/medsci.2015.4.360 |
| [8] | Rosario Megna . Evolution of the COVID-19 pandemic in Italy at the national and regional levels from February 2020 to March 2022. AIMS Medical Science, 2023, 10(3): 237-258. doi: 10.3934/medsci.2023019 |
| [9] | Juliet A Harvey, Sebastien FM Chastin, Dawn A Skelton . What happened to my legs when I broke my arm?. AIMS Medical Science, 2018, 5(3): 252-258. doi: 10.3934/medsci.2018.3.252 |
| [10] | Jamie L. Flexon, Lisa Stolzenberg, Stewart J. D'Alessio . The effect of cannabis legislation on opioid and benzodiazepine use among aging Americans. AIMS Medical Science, 2024, 11(4): 361-377. doi: 10.3934/medsci.2024025 |
The local convergence analysis of the parameter based sixth-order iterative method is the primary focus of this article. This investigation was conducted based on the Fréchet derivative of the first order that satisfies the Lipschitz continuity condition. In addition, we developed a conceptual radius of convergence for these methods. Also, we discussed the solution behavior of complex polynomials with the basin of attraction. Finally, some numerical examples are provided to illustrate how the conclusions we got can be employed to determine the iterative approach's radius of convergence ball in the context of solving nonlinear equations. We compare the numerical results with our method and the existing sixth order methods proposed by Argyros et al. We observe that using our method yields significantly larger balls than those that already exist.
It is with admiration that we share with you our publication data for the 2022 calendar year for the AIMS Medical Science Journal. It was another successful year with the highest number of publication submissions to date over the past three years. Our depth and breadth of publications spanned multiple basic and clinical science disciplines that originated from talented authors across the globe. We look forward to an exciting year ahead and welcome the opportunity to review original manuscripts for consideration for publication in the journal. Our goals are to provide a forum of high-quality manuscripts that can positively impact the expansion of scientific knowledge and advance the health of our population.
Below is a graphic depiction of the manuscript submission and publication data for the journal for the past three years (Figure 1). There are slightly more submissions that were received in 2022 than in 2021, and the number of accepted and published manuscripts remain stable for the past three years. Our hope is increasing the footprint of quality manuscripts submitted to the journal that will translate into an increased number of high-quality publications for the upcoming year.
2022 manuscripts status:
Publications: 28
Reject rate: 71%
Publication time (from submission to online): 109 days
The geographic distribution of the corresponding authors of the published manuscripts are depicted below (Figure 2). We are honored to attract authors from around the world who chose to submit their research to the journal for publication (USA, Canada, Nigeria, Japan, etc.). Of note the majority of publications originate from authors based in the United States representing 39% of the publications followed by Canada and Nigeria standing at 11% each.
Table 1 depicts the type of manuscripts published. A total of 28 articles were published in 2022, of which, the majority were research based, 12 (43%) followed by reviews, 10 (36%).
| Article type | Number | Percent |
| Research article | 12 | 43% |
| Review | 10 | 36% |
| Others | 6 | 21% |
| Total | 28 |
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Table 2 depicts the top 10 articles with the highest views, published in 2022. A focus of these top 10 articles was: Fall Risks, Monoclonal Antibody development and COVID-19.
| Title | Corresponding author | Views | |
| 1 | Knowledge, attitudes on falls and awareness of hospitalized patient's fall risk factors among the nurses working in Tertiary Care Hospitals | Surapaneni Krishna Mohan | 1861 |
| 2 | Clinical pharmacology to support monoclonal antibody drug development | Sharon Lu | 1861 |
| 3 | Telehealth during COVID-19 pandemic era: a systematic review | Jonathan Kissi | 1787 |
| 4 | Understanding the psychological impact of the COVID-19 pandemic on university students | Belgüzar Kara | 1786 |
| 5 | Soluble Fas ligand, soluble Fas receptor, and decoy receptor 3 as disease biomarkers for clinical applications: A review | Michiro Muraki | 1697 |
| 6 | Non-small cell lung cancer: epidemiology, screening, diagnosis, and treatment | Anuj A. Shukla | 1613 |
| 7 | Recurrence after treatment of arteriovenous malformations of the head and neck | Nguyen Minh Duc | 1583 |
| 8 | Staphylococcus aureus antimicrobial efflux pumps and their inhibitors: recent developments | Manuel Varela | 1467 |
| 9 | The mental health of the health care professionals in India during the COVID-19 pandemic: a cross-sectional study | B Shivananda Nayak | 1268 |
| 10 | Recognition, treatment, and prevention of perioperative anaphylaxis: a narrative review | Julena Foglia | 1210 |
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AIMS Medical Science Journal has 94 members, representing 26 countries. Thirty three percent of the members are from the United States, and other members represent Italy, France, and several other countries (Figure 3). We want to particularly acknowledge our editors: Kelly Pagidas (Editor-in-Chief), Belgüzar Kara, Gulshan Sunavala-Dossabhoy, Gwendolyn Quinn, Panayota Mitrou, Kimberly Udlis (retired), Mai Alzamel, Yi-Jang Lee, Sreekumar Othumpangat, Ji Hyun Kim, Athanasios Alexiou, Robert Striker, Andrei Kelarev, Casey Peiris, Patrick Legembre, Ramin Ataee, Louis Ragolia, Bogdan Borz, Robert Kratzke, Maria Fiorillo, Lars Malmström, Giuliana Banche, Jean-Marie Exbrayat and Elias El-Habr. Importantly, a special thank you to all the Editorial Board members, reviewers and in-house editors, and staff for their dedication, commitment, and unrelenting hard work throughout the year. We hope to attract additional scholars that will be able to join our team for the upcoming year.
| [1] |
C. Chun, B. Neta, Developing high order methods for the solution of systems of nonlinear equations, Appl. Math. Comput., 342 (2019), 178–190. https://doi.org/10.1016/j.amc.2018.09.032 doi: 10.1016/j.amc.2018.09.032
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H. Montazeri, F. Soleymani, S. Shateyi, S. S. Motsa, On a new method for computing the numerical solution of systems of nonlinear equations, J. Appl. Math., 2012 (2012), 751975. https://doi.org/10.1155/2012/751975 doi: 10.1155/2012/751975
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S. Abbasbandy, P. Bakhtiari, A. Cordero, J. R. Torregrosa, T. Lotfi, New efficient methods for solving nonlinear systems of equations with arbitrary even order, Appl. Math. Comput., 287–288 (2016), 94–103. https://doi.org/10.1016/j.amc.2016.04.038 doi: 10.1016/j.amc.2016.04.038
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I. K. Argyros, Á. A. Magreñán, A study on the local convergence and the dynamics of Chebyshev-Halley-Type methods free from second derivative, Numer. Algor., 71 (2016), 1–23. http://doi.org/10.1007/s11075-015-9981-x doi: 10.1007/s11075-015-9981-x
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| [5] | L. V. Kantorovich, G. P. Akilov, Functional analysis, Oxford: Pergamon Press, 1982. https://doi.org/10.1016/C2013-0-03044-7 |
| [6] | L. B. Rall, Computational solution of nonlinear operator equations, New York: Robert E. Krieger, 1979. |
| [7] |
A. S. Alshomrani, R. Behl, P. Maroju, Local convergence of parameter based method with six and eighth order of convergence, J. Math. Chem., 58 (2020), 841–853. https://doi.org/10.1007/s10910-020-01113-6 doi: 10.1007/s10910-020-01113-6
|
| [8] |
I. K. Argyros, S. George, Local convergence for an almost sixth order method for solving equations under weak conditions, SeMA, 75 (2018), 163–171. https://doi.org/10.1007/s40324-017-0127-z doi: 10.1007/s40324-017-0127-z
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| [9] |
I. K. Argyros, S. K. Khattri, S. George, Local convergence of an at least sixth-order method in Banach spaces, J. Fixed Point Theory Appl., 21 (2019), 23. https://doi.org/10.1007/s11784-019-0662-6 doi: 10.1007/s11784-019-0662-6
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P. Maroju, Á. A. Magreñán, Í. Sarría, A. Kumar, Local convergence of fourth and fifth order parametric family of iterative methods in Banach spaces, J. Math. Chem., 58 (2020), 686–705. https://doi.org/10.1007/s10910-019-01097-y doi: 10.1007/s10910-019-01097-y
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| [11] |
S. Singh, E. Martínez, P. Maroju, R. Behl, A study of the local convergence of a fifth order iterative method, Indian J. Pure Appl. Math., 51 (2020), 439–455. https://doi.org/10.1007/s13226-020-0409-5 doi: 10.1007/s13226-020-0409-5
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| [12] |
I. K. Argyros, S. George, Local convergence of deformed Halley method in Banach space under Holder continuity conditions, J. Nonlinear Sci. Appl., 8 (2015), 246–254. http://doi.org/10.22436/jnsa.008.03.09 doi: 10.22436/jnsa.008.03.09
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| [13] |
A. A. Magrenãn, I. K. Argyros, On the local convergence and the dynamics of Chebyshev-Halley methods with six and eight order of convergence, J. Comput. Appl. Math., 298 (2016), 236–251. https://doi.org/10.1016/j.cam.2015.11.036 doi: 10.1016/j.cam.2015.11.036
|
| [14] |
A. S. Alshomrani, R. Behl, P. Maroju, Local convergence of parameter based method with six and eighth order of convergence, J. Math. Chem., 58 (2020), 841–853. https://doi.org/10.1007/s10910-020-01113-6 doi: 10.1007/s10910-020-01113-6
|
| [15] |
J. R. Sharma, R. K. Guha, R. Sharma, An efficient fourth order weighted-Newton method for systems of nonlinear equations, Numer. Algor., 62 (2013), 307–323. https://doi.org/10.1007/s11075-012-9585-7 doi: 10.1007/s11075-012-9585-7
|
| [16] |
F. Soleymani, Regarding the accuracy of optimal eighth-order methods, Math. Comput. Model., 53 (2011), 1351–1357. https://doi.org/10.1016/j.mcm.2010.12.032 doi: 10.1016/j.mcm.2010.12.032
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| [17] |
M. Scott, B. Neta, C. Chun, Basins attractors for various methods, Appl. Math. Comput., 218 (2011), 2584–2599. https://doi.org/10.1016/j.amc.2011.07.076 doi: 10.1016/j.amc.2011.07.076
|
| [18] |
R. Behl, P. Maroju, S. S. Motsa, A family of second derivative free fourth order continuation method for solving nonlinear equations, J. Comput. Appl. Math., 318 (2017), 38–46. https://doi.org/10.1016/j.cam.2016.12.008 doi: 10.1016/j.cam.2016.12.008
|
| [19] |
R. Behl, S. S. Motsa, Geometric construction of eighth-order optimal families of Ostrowski's method, Sci. World J., 2015 (2015), 614612. https://doi.org/10.1155/2015/614612 doi: 10.1155/2015/614612
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| [20] |
S. M. Kang, S. M. Ramay, M. Tanveer, W. Nazeer, Polynomiography via an iterative method corresponding to Simpsons 1/3 rule, J. Nonlinear Sci. Appl., 9 (2016), 967–976. http://doi.org/10.22436/jnsa.009.03.25 doi: 10.22436/jnsa.009.03.25
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| [21] |
I. K. Argyros, S. George, Local convergence of deformed Halley method in Banach space under Holder continuity conditions, J. Nonlinear Sci. Appl., 8 (2015), 246–254. http://doi.org/10.22436/jnsa.008.03.09 doi: 10.22436/jnsa.008.03.09
|
| [22] |
A. S. Alshomrani, I. K. Argyros, R. Behl, An optimal reconstruction of Chebyshev-Halley-Type methods with local convergence analysis, Int. J. Comp. Meth., 17 (2020), 1940017. https://doi.org/10.1142/S0219876219400176 doi: 10.1142/S0219876219400176
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Figures(14) / Tables(5)
Kasmita Devi, Prashanth Maroju. Complete study of local convergence and basin of attraction of sixth-order iterative method[J]. AIMS Mathematics, 2023, 8(9): 21191-21207. doi: 10.3934/math.20231080
| Article type | Number | Percent |
| Research article | 12 | 43% |
| Review | 10 | 36% |
| Others | 6 | 21% |
| Total | 28 |
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| Title | Corresponding author | Views | |
| 1 | Knowledge, attitudes on falls and awareness of hospitalized patient's fall risk factors among the nurses working in Tertiary Care Hospitals | Surapaneni Krishna Mohan | 1861 |
| 2 | Clinical pharmacology to support monoclonal antibody drug development | Sharon Lu | 1861 |
| 3 | Telehealth during COVID-19 pandemic era: a systematic review | Jonathan Kissi | 1787 |
| 4 | Understanding the psychological impact of the COVID-19 pandemic on university students | Belgüzar Kara | 1786 |
| 5 | Soluble Fas ligand, soluble Fas receptor, and decoy receptor 3 as disease biomarkers for clinical applications: A review | Michiro Muraki | 1697 |
| 6 | Non-small cell lung cancer: epidemiology, screening, diagnosis, and treatment | Anuj A. Shukla | 1613 |
| 7 | Recurrence after treatment of arteriovenous malformations of the head and neck | Nguyen Minh Duc | 1583 |
| 8 | Staphylococcus aureus antimicrobial efflux pumps and their inhibitors: recent developments | Manuel Varela | 1467 |
| 9 | The mental health of the health care professionals in India during the COVID-19 pandemic: a cross-sectional study | B Shivananda Nayak | 1268 |
| 10 | Recognition, treatment, and prevention of perioperative anaphylaxis: a narrative review | Julena Foglia | 1210 |
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CSV
| Article type | Number | Percent |
| Research article | 12 | 43% |
| Review | 10 | 36% |
| Others | 6 | 21% |
| Total | 28 |
| Title | Corresponding author | Views | |
| 1 | Knowledge, attitudes on falls and awareness of hospitalized patient's fall risk factors among the nurses working in Tertiary Care Hospitals | Surapaneni Krishna Mohan | 1861 |
| 2 | Clinical pharmacology to support monoclonal antibody drug development | Sharon Lu | 1861 |
| 3 | Telehealth during COVID-19 pandemic era: a systematic review | Jonathan Kissi | 1787 |
| 4 | Understanding the psychological impact of the COVID-19 pandemic on university students | Belgüzar Kara | 1786 |
| 5 | Soluble Fas ligand, soluble Fas receptor, and decoy receptor 3 as disease biomarkers for clinical applications: A review | Michiro Muraki | 1697 |
| 6 | Non-small cell lung cancer: epidemiology, screening, diagnosis, and treatment | Anuj A. Shukla | 1613 |
| 7 | Recurrence after treatment of arteriovenous malformations of the head and neck | Nguyen Minh Duc | 1583 |
| 8 | Staphylococcus aureus antimicrobial efflux pumps and their inhibitors: recent developments | Manuel Varela | 1467 |
| 9 | The mental health of the health care professionals in India during the COVID-19 pandemic: a cross-sectional study | B Shivananda Nayak | 1268 |
| 10 | Recognition, treatment, and prevention of perioperative anaphylaxis: a narrative review | Julena Foglia | 1210 |
