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ITERATION SCHEME FOR APPROXIMATING FIXED POINTS OF G-NONEXPANSIVE MAPS ON BANACH SPACES VIA A DIGRAPH

Year 2023, Issue: 053, 28 - 40, 30.06.2023
https://doi.org/10.59313/jsr-a.1244484

Abstract

In this writing, an influential modified multistep iterative process for finding a common fixed point of G-nonexpansive maps is presented. Some convergence theorems are constructed by Property P for the recommended schema on Banach spaces by which digraph. Two numerical examples are given to illustrate the convergence behavior and the validity of the process. The achieved conclusions enlarge, generalise and complement some well-known fixed point results from the literature.

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References

  • [1] Khan, A. R., Domlo, AA., and Fukhar-ud-din, H. (2008). Common fixed point noor iteration for a finite family of asymptotically quasi-nonexpansive mappings in banach spaces. The Journal of Mathematical Analysis and Applications, 341(1), 1-11.
  • [2] Yıldırım, İ., and Özdemir, M. (2009). A new iterative process for common fixed points of finite families of non-self-asymptotically non-expansive mappings. Nonlinear Analysis: Theory, Methods & Applications, 71 (3-4), 991-999.
  • [3] Kettapun, A., Kananthai, A., and Suantai, S. (2010). A new approximation method for common fixed points of a finite family of asymptotically quasi-nonexpansive mappings in Banach spaces. Computers and Mathematics with Applications, 60, 1430-1439.
  • [4] Jachymski, J. (2008). The contraction principle for mappings on a metric space with a graph. Proceedings of the American Mathematical Society, 136, 1359-1373.
  • [5] Aleomraninejad, S. M. A., Rezapour, S., and Shahzad, N. (2012). Some fixed point result on a metric space with a graph. Topology and its Applications, 159, 659-663.
  • [6] Alfuraidan, M. R., and Khamsi, M. A. (2015). Fixed points of monotone nonexpansive mappings on a hyperbolic metric space with a graph. Fixed Point Theory Applications, 44.
  • [7] Tripak, O. (2016). Common fixed points of G-nonexpansive mappings on Banach spaces with a graph. Fixed Point Theory Applications, 87.
  • [8] Suparatulatorn, R., Cholamjiak, W., and Suantai, S. (2018). A modified S-iteration process for G- nonexpansive mappings in Banach spaces with a graph. Numerical Algorithms, 77, 479-490.
  • [9] Hunde, T. W., Sangago, M. G., and Zegeye, H. (2017). Approximation of a common fixed point of a family of G-nonexpansive mappings in Banach spaces with a graph. International journal of Advances in Mathematics, 6, 137-152.
  • [10] Phuengrattana, W., and Suantai, S. (2011). On the rate of convergence of Mann, Ishikawa, Noor and SP-iterations for continuous functions on an arbitrary interval. Journal of Computational and Applied Mathematics, 235 (9), 3006-3014.
  • [11] Thianwan, S. (2009). Common fixed points of new iterations for two asymptotically nonexpansive nonself-mappings in a Banach space. Journal of Computational and Applied Mathematics, 224 (2), 688-695.
  • [12] Sridarat, P., Suparatulatorn, R., Suantai, S., and Cho, Y. J. (2018). Convergence analysis of SP-iteration for G-nonexpansive mappings with directed graphs. Bulletin of the Malaysian Mathematical Sciences Society, 42, 2361–2380.
  • [13] Alfuraidan, M. (2015). Fixed points of monotone nonexpansive mappings with a graph. Fixed Point Theory and Applications, 49.
  • [14] Sahu, J. (1991). Weak and strong convergence to fixed points of asymptotically nonexpansive mappings. Bulletin of the Australian Mathematical Society, 43, 153-159.
  • [15] Tan, K. K., and Xu, H. K. (1993). Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process. Journal of Mathematical Analysis and Applications, 178, 301-308.
  • [16] Kangtunyakarn, A. (2018). Modified Halpern's iteration for fixed point theory of a finite family of G-nonexpansive mappings endowed with graph. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 112, 437-448.
  • [17] Shahzad, N., and Al-Dubiban, P. (2006). Approximating common fixed points of nonexpansive mappings in Banach spaces. Georgian Mathematical Journal, 13 (3), 529-537.
  • [18] Gürsoy, F., Karakaya, V., and Rhoades, B. E. (2013). Data dependence results of new multi-step and S- iterative schemes for contractive-like operators. Fixed Point Theory and Applications, 76.
  • [19] Beg, I., Butt, A. R., and Radojevic, S. (2010). The contraction principle for set valued mappings on a metric space with a graph. Computers & Mathematics with Applications, 60, 1214-1219.
  • [20]Alfuraidan, M. (2015). Remark on monotone multivalued mappings on a metric space with a graph. Journal of Inequalities and Applications, 202.
  • [21] Kır, M., Yolacan, E., and Kızıltunc H. (2017). Coupled fixed point theorems in complete metric spaces endowed with a directed graph and application. Open Mathematics, 15, 734-744.
  • [22]Yolacan, E. (2017). A Brief note concerning non-self contractions in Banach Space endowed with a Graph. General Letters in Mathematics, 3 (1), 25-30.
  • [23]Yolacan, E., Kızıltunc, H., and Kır, M. (2016). Coincidence point theorems for φ-ψ- contraction mappings in metric spaces involving a graph. Carpathian Mathematical Publications, 8 (2), 251-262.
  • [24]Yolacan, E., Debnath, P., and Aktürk, M. A. (2018). Common coupled fixed point theorems for generalized nonlinear contractions on metric spaces involving a graph. Sigma Journal of Engineering and Natural Sciences, 36 (2), 419-432.
  • [25]Suparatulatorn, R., Suantai, S., and Cholamjiak, W. (2017). Hybrid methods for a finite family of G- nonexpansive mappings in Hilbert spaces endowed with graphs. AKCE International Journal of Graphs and Combinatorics, 14 (2), 101-111.
  • [26]Hansen, P. C., Nagy, J. G., and O'Learg, D. P. (2006). Deblurring Images Matrices, Spectra, and Filtering. (1st Edition). Philadelphia: Society for Industrial and Applied Mathematics, 16-22. [27]Wilmshurst, T. H. (1990). Signal recovery from noise in electronic instrumentation. (2nd Edition). Florida: CRC Press, 7-10.
  • [28]Chairatsiripong, C., Yambangwai, D., and Thianwan, T. (2023). New iterative methods for nonlinear operators as concerns convex programming applicable in differential problems, image deblurring, and signal recovering problems. Mathematical Methods in the Applied Sciences, 46(2), 3332–3355.
  • [29]Janngam, K., and Wattanataweekul, R. (2022). An accelerated fixed-point algorithm with an inertial technique for a countable family of G-nonexpansive mappings applied to image recovery. Symmetry, 14(4), 662.
  • [30]Yambangwai, D., and Thianwan, T. (2021). Convergence point of G-nonexpansive mappings in Banach spaces endowed with graphs applicable in image deblurring and signal recovering problems. Ricerche di Matematica.
  • [31] Ahmad, J., Ullah, K., Arshad, M., De la Sen, M., and Ma, Z. (2021). Convergence results on Picard-Krasnoselskii hybrid iterative process in CAT(0) spaces. Open Mathematics, 19, 1713–1720.
  • [32]El Kouch, Y., and Mouline, J. (2022). Convergence of mann and ishikawa iterative processes for some contractions in convex generalized metric space. Abstract and Applied Analysis, volume 2022, Article ID 3168414, 11 pages.
Year 2023, Issue: 053, 28 - 40, 30.06.2023
https://doi.org/10.59313/jsr-a.1244484

Abstract

Project Number

-

References

  • [1] Khan, A. R., Domlo, AA., and Fukhar-ud-din, H. (2008). Common fixed point noor iteration for a finite family of asymptotically quasi-nonexpansive mappings in banach spaces. The Journal of Mathematical Analysis and Applications, 341(1), 1-11.
  • [2] Yıldırım, İ., and Özdemir, M. (2009). A new iterative process for common fixed points of finite families of non-self-asymptotically non-expansive mappings. Nonlinear Analysis: Theory, Methods & Applications, 71 (3-4), 991-999.
  • [3] Kettapun, A., Kananthai, A., and Suantai, S. (2010). A new approximation method for common fixed points of a finite family of asymptotically quasi-nonexpansive mappings in Banach spaces. Computers and Mathematics with Applications, 60, 1430-1439.
  • [4] Jachymski, J. (2008). The contraction principle for mappings on a metric space with a graph. Proceedings of the American Mathematical Society, 136, 1359-1373.
  • [5] Aleomraninejad, S. M. A., Rezapour, S., and Shahzad, N. (2012). Some fixed point result on a metric space with a graph. Topology and its Applications, 159, 659-663.
  • [6] Alfuraidan, M. R., and Khamsi, M. A. (2015). Fixed points of monotone nonexpansive mappings on a hyperbolic metric space with a graph. Fixed Point Theory Applications, 44.
  • [7] Tripak, O. (2016). Common fixed points of G-nonexpansive mappings on Banach spaces with a graph. Fixed Point Theory Applications, 87.
  • [8] Suparatulatorn, R., Cholamjiak, W., and Suantai, S. (2018). A modified S-iteration process for G- nonexpansive mappings in Banach spaces with a graph. Numerical Algorithms, 77, 479-490.
  • [9] Hunde, T. W., Sangago, M. G., and Zegeye, H. (2017). Approximation of a common fixed point of a family of G-nonexpansive mappings in Banach spaces with a graph. International journal of Advances in Mathematics, 6, 137-152.
  • [10] Phuengrattana, W., and Suantai, S. (2011). On the rate of convergence of Mann, Ishikawa, Noor and SP-iterations for continuous functions on an arbitrary interval. Journal of Computational and Applied Mathematics, 235 (9), 3006-3014.
  • [11] Thianwan, S. (2009). Common fixed points of new iterations for two asymptotically nonexpansive nonself-mappings in a Banach space. Journal of Computational and Applied Mathematics, 224 (2), 688-695.
  • [12] Sridarat, P., Suparatulatorn, R., Suantai, S., and Cho, Y. J. (2018). Convergence analysis of SP-iteration for G-nonexpansive mappings with directed graphs. Bulletin of the Malaysian Mathematical Sciences Society, 42, 2361–2380.
  • [13] Alfuraidan, M. (2015). Fixed points of monotone nonexpansive mappings with a graph. Fixed Point Theory and Applications, 49.
  • [14] Sahu, J. (1991). Weak and strong convergence to fixed points of asymptotically nonexpansive mappings. Bulletin of the Australian Mathematical Society, 43, 153-159.
  • [15] Tan, K. K., and Xu, H. K. (1993). Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process. Journal of Mathematical Analysis and Applications, 178, 301-308.
  • [16] Kangtunyakarn, A. (2018). Modified Halpern's iteration for fixed point theory of a finite family of G-nonexpansive mappings endowed with graph. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 112, 437-448.
  • [17] Shahzad, N., and Al-Dubiban, P. (2006). Approximating common fixed points of nonexpansive mappings in Banach spaces. Georgian Mathematical Journal, 13 (3), 529-537.
  • [18] Gürsoy, F., Karakaya, V., and Rhoades, B. E. (2013). Data dependence results of new multi-step and S- iterative schemes for contractive-like operators. Fixed Point Theory and Applications, 76.
  • [19] Beg, I., Butt, A. R., and Radojevic, S. (2010). The contraction principle for set valued mappings on a metric space with a graph. Computers & Mathematics with Applications, 60, 1214-1219.
  • [20]Alfuraidan, M. (2015). Remark on monotone multivalued mappings on a metric space with a graph. Journal of Inequalities and Applications, 202.
  • [21] Kır, M., Yolacan, E., and Kızıltunc H. (2017). Coupled fixed point theorems in complete metric spaces endowed with a directed graph and application. Open Mathematics, 15, 734-744.
  • [22]Yolacan, E. (2017). A Brief note concerning non-self contractions in Banach Space endowed with a Graph. General Letters in Mathematics, 3 (1), 25-30.
  • [23]Yolacan, E., Kızıltunc, H., and Kır, M. (2016). Coincidence point theorems for φ-ψ- contraction mappings in metric spaces involving a graph. Carpathian Mathematical Publications, 8 (2), 251-262.
  • [24]Yolacan, E., Debnath, P., and Aktürk, M. A. (2018). Common coupled fixed point theorems for generalized nonlinear contractions on metric spaces involving a graph. Sigma Journal of Engineering and Natural Sciences, 36 (2), 419-432.
  • [25]Suparatulatorn, R., Suantai, S., and Cholamjiak, W. (2017). Hybrid methods for a finite family of G- nonexpansive mappings in Hilbert spaces endowed with graphs. AKCE International Journal of Graphs and Combinatorics, 14 (2), 101-111.
  • [26]Hansen, P. C., Nagy, J. G., and O'Learg, D. P. (2006). Deblurring Images Matrices, Spectra, and Filtering. (1st Edition). Philadelphia: Society for Industrial and Applied Mathematics, 16-22. [27]Wilmshurst, T. H. (1990). Signal recovery from noise in electronic instrumentation. (2nd Edition). Florida: CRC Press, 7-10.
  • [28]Chairatsiripong, C., Yambangwai, D., and Thianwan, T. (2023). New iterative methods for nonlinear operators as concerns convex programming applicable in differential problems, image deblurring, and signal recovering problems. Mathematical Methods in the Applied Sciences, 46(2), 3332–3355.
  • [29]Janngam, K., and Wattanataweekul, R. (2022). An accelerated fixed-point algorithm with an inertial technique for a countable family of G-nonexpansive mappings applied to image recovery. Symmetry, 14(4), 662.
  • [30]Yambangwai, D., and Thianwan, T. (2021). Convergence point of G-nonexpansive mappings in Banach spaces endowed with graphs applicable in image deblurring and signal recovering problems. Ricerche di Matematica.
  • [31] Ahmad, J., Ullah, K., Arshad, M., De la Sen, M., and Ma, Z. (2021). Convergence results on Picard-Krasnoselskii hybrid iterative process in CAT(0) spaces. Open Mathematics, 19, 1713–1720.
  • [32]El Kouch, Y., and Mouline, J. (2022). Convergence of mann and ishikawa iterative processes for some contractions in convex generalized metric space. Abstract and Applied Analysis, volume 2022, Article ID 3168414, 11 pages.
There are 31 citations in total.

Details

Primary Language English
Journal Section Research Articles
Authors

Esra Yolacan 0000-0002-1655-0993

Project Number -
Publication Date June 30, 2023
Submission Date January 30, 2023
Published in Issue Year 2023 Issue: 053

Cite

IEEE E. Yolacan, “ITERATION SCHEME FOR APPROXIMATING FIXED POINTS OF G-NONEXPANSIVE MAPS ON BANACH SPACES VIA A DIGRAPH”, JSR-A, no. 053, pp. 28–40, June 2023, doi: 10.59313/jsr-a.1244484.