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Stability and convergence analysis of hybrid algorithms for Berinde contraction mappings and its applications

Year 2021, , 159 - 168, 30.09.2021
https://doi.org/10.53006/rna.950067

Abstract

In this paper, we construct a new hybrid iteration, called SR-iteration, and prove its stability and convergence analysis for weak contraction mappings in a Banach space. We compare rate of convergence between the SR-iteration and other iterations. Moreover, we provide numerical comparisons for supporting our main theorem and apply our main result to prove existence problem of mixed type Volterra-Fredholm functional nonlinear integral equation.

References

  • [1] W. Chaolamjiak, D. Yambangwai, H.A. Hammad, Modified hybrid projection methods with SP iterations for quasi- nonexpansive multivalued mappings in Hilbert spaces, Bull. Iran. Math. Soc. (2020). https://doi.org/10.1007/s41980-020- 00448-9.
  • [2] W. Cholamjiak, D. Yambangwai, H. Dutta, H.A. Hammad, Modi?ed CQ-algorithms for G-nonexpansive mappings in Hilbert spaces involving graphs, New Math. Nat. Comput. 16(1) (2019) 89-103.
  • [3] W. Cholamjiak, S. Suantai, R. Suparatulatorn, S. Kesornprom, P. Cholamjiak, Viscosity approximation methods for fixed point problems in Hilbert spaces endowed with graphs, J. Appl. Numer. Optim. 1 (2019) 25-38.
  • [4] E. Picard, Mémoire sur la théorie des équations aux dérivées partielles et la méthode des approximations successives, J. Math. Pures Appl. 6(4) (1890) 145-210.
  • [5] W.R. Mann, Mean value methods in iteration, Proc. Amer. Math. Soc. 4 (1953) 506-510.
  • [6] S. Ishikawa, Fixed point by a new iteration method, Proc. Amer. Math. Soc. 44 (1974) 147-150.
  • [7] M.A. Noor, New approximation schemes for general variational inequalities, J. Math. Anal. Appl. 251(1) (2000) 217-229.
  • [8] W. Phuengrattana, S. Suantai, On the rate of convergence of Mann, Ishikawa, Noor and SP-iterations for continuous functions on an arbitrary interval, J. Comput. Appl. Math. 235(9) (2011) 3006-3014.
  • [9] W. Phuengrattana, S. Suantai, Comparison of the rate of convergence of various iterative methods for the class of weak contractions in Banach spaces, Thai J. Math. 11(1) (2013) 217-226.
  • [10] M.O. Osilike, Stability results for Ishikawa fixed point iteration procedure, Indian J. Pure Appl. Math. 26(10) (1995) 937-941.
  • [11] B.E. Rhoades, Fixed point theorems and stability results for fixed point iteration procedures, Indian J. Pure Appl. Math. 21 (1990) 1-9.
  • [12] R.L. Burden, J.D. Faires, Numerical Analysis, 9th edn. Brooks/Cole Cengage Learning, Boston (2010).
  • [13] V. Berinde, Iterative Approximation of Fixed Points. Editura Efemeride, Baia Mare (2002).
  • [14] F. Gürsoy, A Picard-S iterative method for approximating fixed point of weak-contraction mappings, Filomat, 30(10) (2016) 2829-2845.
  • [15] F. Gürsoy, V. Karakaya, A Picard-S hybrid type iteration method for solving a differential equation with retarded argument, arXiv:1403.2546v2 (2014).
  • [16] C. Craciun, M.A. Serban, A nonlinear integral equation via Picard operators, Fixed Point Theory. 12(1) (2011) 57-70.
  • [17] H.A. Hammad, M. De la Sen, Solution of nonlinear integral equation via fixed point of cyclic α ψ L -rational contraction mappings in metric-like spaces, Bull. Braz. Math. Soc. New Ser. 51 (2020) 81-105.
  • [18] H.A. Hammad, M. De la Sen, Generalized contractive mappings and related results in b-metric like spaces with an application, Symmetry, 11(5) (2019) 667.
  • [19] H.A. Hammad, M. De la Sen, A solution of Fredholm integral equation by using the cyclic η q s -rational contractive mappings technique in b-metric-like spaces, Symmetry, 11(9) (2019) 1184.
Year 2021, , 159 - 168, 30.09.2021
https://doi.org/10.53006/rna.950067

Abstract

References

  • [1] W. Chaolamjiak, D. Yambangwai, H.A. Hammad, Modified hybrid projection methods with SP iterations for quasi- nonexpansive multivalued mappings in Hilbert spaces, Bull. Iran. Math. Soc. (2020). https://doi.org/10.1007/s41980-020- 00448-9.
  • [2] W. Cholamjiak, D. Yambangwai, H. Dutta, H.A. Hammad, Modi?ed CQ-algorithms for G-nonexpansive mappings in Hilbert spaces involving graphs, New Math. Nat. Comput. 16(1) (2019) 89-103.
  • [3] W. Cholamjiak, S. Suantai, R. Suparatulatorn, S. Kesornprom, P. Cholamjiak, Viscosity approximation methods for fixed point problems in Hilbert spaces endowed with graphs, J. Appl. Numer. Optim. 1 (2019) 25-38.
  • [4] E. Picard, Mémoire sur la théorie des équations aux dérivées partielles et la méthode des approximations successives, J. Math. Pures Appl. 6(4) (1890) 145-210.
  • [5] W.R. Mann, Mean value methods in iteration, Proc. Amer. Math. Soc. 4 (1953) 506-510.
  • [6] S. Ishikawa, Fixed point by a new iteration method, Proc. Amer. Math. Soc. 44 (1974) 147-150.
  • [7] M.A. Noor, New approximation schemes for general variational inequalities, J. Math. Anal. Appl. 251(1) (2000) 217-229.
  • [8] W. Phuengrattana, S. Suantai, On the rate of convergence of Mann, Ishikawa, Noor and SP-iterations for continuous functions on an arbitrary interval, J. Comput. Appl. Math. 235(9) (2011) 3006-3014.
  • [9] W. Phuengrattana, S. Suantai, Comparison of the rate of convergence of various iterative methods for the class of weak contractions in Banach spaces, Thai J. Math. 11(1) (2013) 217-226.
  • [10] M.O. Osilike, Stability results for Ishikawa fixed point iteration procedure, Indian J. Pure Appl. Math. 26(10) (1995) 937-941.
  • [11] B.E. Rhoades, Fixed point theorems and stability results for fixed point iteration procedures, Indian J. Pure Appl. Math. 21 (1990) 1-9.
  • [12] R.L. Burden, J.D. Faires, Numerical Analysis, 9th edn. Brooks/Cole Cengage Learning, Boston (2010).
  • [13] V. Berinde, Iterative Approximation of Fixed Points. Editura Efemeride, Baia Mare (2002).
  • [14] F. Gürsoy, A Picard-S iterative method for approximating fixed point of weak-contraction mappings, Filomat, 30(10) (2016) 2829-2845.
  • [15] F. Gürsoy, V. Karakaya, A Picard-S hybrid type iteration method for solving a differential equation with retarded argument, arXiv:1403.2546v2 (2014).
  • [16] C. Craciun, M.A. Serban, A nonlinear integral equation via Picard operators, Fixed Point Theory. 12(1) (2011) 57-70.
  • [17] H.A. Hammad, M. De la Sen, Solution of nonlinear integral equation via fixed point of cyclic α ψ L -rational contraction mappings in metric-like spaces, Bull. Braz. Math. Soc. New Ser. 51 (2020) 81-105.
  • [18] H.A. Hammad, M. De la Sen, Generalized contractive mappings and related results in b-metric like spaces with an application, Symmetry, 11(5) (2019) 667.
  • [19] H.A. Hammad, M. De la Sen, A solution of Fredholm integral equation by using the cyclic η q s -rational contractive mappings technique in b-metric-like spaces, Symmetry, 11(9) (2019) 1184.
There are 19 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Raweerote Suparatulatorn 0000-0003-0790-3811

Suthep Suantai

Publication Date September 30, 2021
Published in Issue Year 2021

Cite

APA Suparatulatorn, R., & Suantai, S. (2021). Stability and convergence analysis of hybrid algorithms for Berinde contraction mappings and its applications. Results in Nonlinear Analysis, 4(3), 159-168. https://doi.org/10.53006/rna.950067
AMA Suparatulatorn R, Suantai S. Stability and convergence analysis of hybrid algorithms for Berinde contraction mappings and its applications. RNA. September 2021;4(3):159-168. doi:10.53006/rna.950067
Chicago Suparatulatorn, Raweerote, and Suthep Suantai. “Stability and Convergence Analysis of Hybrid Algorithms for Berinde Contraction Mappings and Its Applications”. Results in Nonlinear Analysis 4, no. 3 (September 2021): 159-68. https://doi.org/10.53006/rna.950067.
EndNote Suparatulatorn R, Suantai S (September 1, 2021) Stability and convergence analysis of hybrid algorithms for Berinde contraction mappings and its applications. Results in Nonlinear Analysis 4 3 159–168.
IEEE R. Suparatulatorn and S. Suantai, “Stability and convergence analysis of hybrid algorithms for Berinde contraction mappings and its applications”, RNA, vol. 4, no. 3, pp. 159–168, 2021, doi: 10.53006/rna.950067.
ISNAD Suparatulatorn, Raweerote - Suantai, Suthep. “Stability and Convergence Analysis of Hybrid Algorithms for Berinde Contraction Mappings and Its Applications”. Results in Nonlinear Analysis 4/3 (September 2021), 159-168. https://doi.org/10.53006/rna.950067.
JAMA Suparatulatorn R, Suantai S. Stability and convergence analysis of hybrid algorithms for Berinde contraction mappings and its applications. RNA. 2021;4:159–168.
MLA Suparatulatorn, Raweerote and Suthep Suantai. “Stability and Convergence Analysis of Hybrid Algorithms for Berinde Contraction Mappings and Its Applications”. Results in Nonlinear Analysis, vol. 4, no. 3, 2021, pp. 159-68, doi:10.53006/rna.950067.
Vancouver Suparatulatorn R, Suantai S. Stability and convergence analysis of hybrid algorithms for Berinde contraction mappings and its applications. RNA. 2021;4(3):159-68.