A novel iterative approach for split feasibility problem
Abstract views: 415
/ 
PDF downloads: 366
Keywords:
Generalized α-Reich-Suzuki nonexpansive mappings, Fixed point, Strong and weak convergence, Split feasibility problemAbstract
The objective of this article is to study a three step iteration process in the framework of Banach spaces and obtain convergence results for generalized α-Reich-Suzuki nonexpansive mappings. We also provide numerical examples that support our main results and illustrate the convergence behaviour of the proposed process. In the end, we discuss about the solution of split feasibility problem by utilizing
our results.
References
W. A. Kirk, A fixed point theorem for mappings which do not increase distances, Amer. Math. Monthly, 1965, 72,
–1006.
T. Suzuki, Fixed point theorems and convergence theorems for some generalized non-expansive mapping, J. Math. Anal.
Appl., 2008, 340, 1088–1095
J. Garcia Falset, E. Llorens-Fuster, T. Suzuki, Fixed point theory for a class of generalized nonexpansive mappings J.
Math. Anal. Appl., (2011), 375, 185–195.
K. Aoyama and F. Kohsaka, Fixed point theorem for α-nonexpansive mappings in Banach spaces, Nonlinear Anal.,
, 74, 4387–4391.
R. Pant and R. Shukla, Approximating Fixed Points of Generalized α-Nonexpansive Mappings in Banach Spaces,
Numerical Functional Analysis and Optimization, 2017, 38(2), 248–266.
R. Pandey, R. Pant, V. Rakocevic and R. Shukla, Approximating Fixed Point of a General Class of Nonexpansive
Mapping in Banach Spaces with Applications, Results in Mathematics, 2019, 74(1), 24pp.
W. R. Mann, Mean value methods in iteration, Proc. Am. Math. Soc., 1953, 4, 506–510.
S. Ishikawa, Fixed points by a new iteration method, Proc. Amer. Math. Soc., 1974, 44, 147–150.
R. Glowinski and P.L. Tallec, Augmented Lagrangian and Operator-Splitting Methods in Nonlinear Mechanic, SIAM,
Philadelphia, 1989.
P. Peeyada, R. Suparatulatorn and W. Cholamjiak, An inertial Mann forward-backward splitting algorithm of variational inclusion problems and its applications, Chaos Solitons Fractals 158 (2022), Article ID 112048, 7pp.
W. Cholamjiak, U. Witthayarat and R. Suparatulatorn, Inertial parallel relaxed CQ algorithms for common split feasibility problems and its application in signal recovery, J. Nonlinear Convex Anal. 23(7), 1453–1468, 2022.
W. Cholamjiak, H. Dutta and Yambangwai, Image restorations using an inertial parallel hybrid algorithm with Armijo
linesearch for nonmonotone equilibrium problems, Chaos Solitons Fractals, 153 (2021), Article ID 111462, 9pp.
A. Åžahin, Some results of the Picard-Krasnoselskii hybrid iterative process, Filomat, 2019, 33(2), 359–365.
A. Åžahin, Z. Kalkan, H. Arısoy, On the solution of a nonlinear Volterra integral equation with delay, Sakarya
University Journal of Science, 2017, 21(6), 1367–1376.
M. A. Noor, New approximation schemes for general variational inequalities, Journal of Mathematical Analysis and
Applications, 2000, 251(1), 217–229.
R. P. Agarwal, D. Ó Regan and D. R. Sahu, Iterative construction of fixed points of nearly asymptotically nonexpansive
mappings, Journal of Nonlinear and Convex Analysis, 2007, 8(1), 61–79.
M. Abbas and T. Nazir, A new faster iteration process applied to constrained minimization and feasibility problems,
Matematicki Vesnik, 2014, 66(2), 223–234.
D. Thakur, B. S. Thakur and M. Postolache, A new iterative scheme for numerical reckoning fixed points of Suzuki’s
generalized nonexpansive mappings, Applied Mathematics and Computation, 2016, 275, 147–155.
B. S. Thakur, D. Thakur and M. Postolache, A New iteration scheme for approximating fixed points of nonexpansive
mappings, Filomat, 2016, 30(10), 2711–2720.
K. Ullah and M. Arshad, New iteration process and numerical reckoning fixed points in Banach spaces, U. P. B. Sci.
Bull., Series A, 2017, 79(4), 113–122.
K. Ullah and M. Arshad, Numerical Reckoning Fixed Points for Suzuki’s Generalized Nonexpansive Mappings via New
Iteration Process, Filomat, 2018, 32(1), 187–196.
N. Hussain, K. Ullah and M. Arshad, Fixed point approximation for Suzuki generalized nonexpansive mappings via
new iteration process, Journal of Nonlinear and Convex Analysis, 2018, 19(8), 1383–1393.
K. Ullah and M. Arshad, New three step iteration process and fixed point approximation in Banach spaces, Journal of
Linear and Topological Algebra, 2018, 7(2), 87–100.
K. Ullah, J. Ahmad and F. Muhammad Khan, Numerical reckoning fixed points via new faster iteration process, Appl.
Gen. Topol. 2022, 23, (1), 213–223.
S. Temir and O. Korkut, Approximating fixed points of generalized α-nonexpansive mappings by the new iteration process, Journal of Mathematical Sciences and Modelling, 2022, 5(1), 35–39.
J. Schu, Weak and strong convergence to fixed points of asymptotically nonexpansive mappings, Bulletin of the
Australian Mathematical Society, 1991, 43, 153–159.
K. Tan and H. Xu, Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process, Journal of
Mathematical Analysis and Applications, 1993, 178, 301–308.
H. F. Senter and W. G. Dotson, Approximating fixed points of nonexpansive mappings, Proceedings of the American
Mathematical Society, 1974, 44(2), 375–380.
Y. Censor and T. Elfving, A multiprojection algorithm using Bregman projections in a product space, Numer. Algorithms,
, 8(24), 221–239.
C. Byrne, Iterative oblique projection onto convex sets and the split feasibility problem, Inverse Probl., 2002, 18(2),
–453.
M. Feng, L. Shi and R. Chen, A new three-step iterative algorithm for solving the split feasibility problem, U. P. B. Sci.
Bull., Series A, 2019, 81(1), 93–102.
H. Xu, A variable Krasnosel’skii-Mann algorithm and the multiple-set split feasibility problem, Inverse Probl., 2006,
(6), 2021–2034.
H. Xu, Iterative methods for the split feasibility problem in infinite-dimensional Hilbert spaces, Inverse Probl., 26,
(2010), 17pp.
