TY  - JOUR
T1  - A Hybrid Third-Order Iterative Process To Solve Nonlinear Equations
TT  - A Hybrid Third-Order Iterative Process To Solve Nonlinear Equations
AU  - Doğan, Kadri
PY  - 2020
DA  - March
Y2  - 2019
DO  - 10.21597/jist.583528
JF  - Journal of the Institute of Science and Technology
JO  - J. Inst. Sci. and Tech.
PB  - Igdir University
WT  - DergiPark
SN  - 2536-4618
SP  - 563
EP  - 575
VL  - 10
IS  - 1
LA  - en
AB  - In this study, by using the iterative method discussed in (Kang et al., 2013) and adopting a technique given in details (Biazar and Amirteimoori, 2006) introduced a new hybrid third-order iterative method to solve nonlinear equations derived from the Picard-Mann fixed-point iterative method. Some problems have been solved in order to demonstrate the performance of the established iterative method for the solution of the nonlinear equations.
KW  - Fixed Point Method
KW  - Picard-Mann Iterative Method
KW  - Newton Iterative Method
KW  - Nonlinear Equations
KW  - Convergence Analysis
N2  - In this study, by using the iterative method discussed in (Kang et al., 2013) and adopting a technique given in details (Biazar and Amirteimoori, 2006) introduced a new hybrid third-order iterative method to solve nonlinear equations derived from the Picard-Mann fixed-point iterative method. Some problems have been solved in order to demonstrate the performance of the established iterative method for the solution of the nonlinear equations.
CR  - Abbas M, Nazir T, 2014. A new faster iteration process applied to constrained minimization and feasibility problems, Matematicki Vesnik 66(2): 223-234.
CR  - Ashiq A, Qaisar M, Tanveer M, Aslam A, NazeerW, 2015. Modified new third-order iterative method for non-linear equations, Sci.Int.(Lahore), 27(3), 1741-1744, 2015.
CR  - Babolian E, Biazar J, 2002.  Solution of nonlinear equations by modified Adomian decomposition method, Appl. Math. Comput. 132 (1): 167–172.
CR  - Berinde V, 2014.  Picard iteration converges faster than Mann iteration for a class of quasi-contractive operators, Fixed Point Theory Appl. 2014 (2004):1.
CR  - Biazar J, Amirteimoori A, 2006. An improvement to the fixed point iterative method, Appl. Math. Comput. 182 (1): 567–571.
CR  - Chugh R, Malik P, Kumar V, 2015. On a new faster implicit xed point iterative scheme in convex metric spaces, J. Function Spaces (2015), Article ID 905834.
CR  - Dogan K, Karakaya V, 2018. A study in the fixed point theory for a new iterative scheme and a class of generalized mapings, Creat. Math. Inform. 27(2018), No. 2, 151-160.
CR  - Fukhar-ud-din H, Berinde V, 2016. Iterative methods for the class of quasi-contractive type operators and comparsion of their rate of convergence in convex metric spaces, Filomat 30 (2016) 223-230.
CR  - Isaacson E, Keller HB, 1966.  Analysis of Numerical Methods, John Wiley & Sons, Inc., No:1, 106-108 New York, USA.
CR  - Khan SH, 2013. A Picard-Mann hybrid iterative process. Fixed Point Theory Appl. (2013). doi:10.1186/1687-1812-2013-69.
CR  - Kang SM, Rafiq A, and Kwun Y C, 2013. A New Second-Order Iteration Method for Solving Nonlinear Equations, Abstract and Applied Analysis. Volume 2013, Article ID 487062, 4 pages.
CR  - Karakaya V, Dogan K, Gursoy F, Erturk M, 2013. Fixed point of a new three-step iteration algorithm under contractive-like operators over normed spaces, Abstract and Applied Analysis, 2013(2013), 9 pages.
CR  - Karakaya V, Dogan K, 2014. On the convergence and stability results for a new general iterative process, The Scientific World Journal, 2014(2014), 8 pages.
CR  - Karakaya V, Atalan Y, Dogan K, Bouzara N. El Houda, 2017. Some fixed point results for a new three steps iteration process in Banach spaces, Fixed Point Theory, 18(2017), No. 2, 625-640.
CR  - Picard E, 1890. Memoire sur la theorie des equations aux derivees partielles et la methode des approximations successives, J. Math. Pures Appl., 6(1890), 145-210.
CR  - Phuengrattana W, Suantai S, 2013. Comparison of the rate of convergence of various iterative methods for the class of weak contractions in Banach Spaces, Thai J. Math. 11 (2013) 217-226.
UR  - https://doi.org/10.21597/jist.583528
L1  - https://dergipark.org.tr/en/download/article-file/970187
ER  -