# Convergence results for modified SP-iteration in uniformly convex metric spaces

Volume 26, Issue 2, pp 162--171
Publication Date: November 05, 2021 Submission Date: April 17, 2021 Revision Date: August 21, 2021 Accteptance Date: September 17, 2021
• 196 Views

### Authors

P Sukprasert - Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi, Pathumthani, 12110, Thailand. V. Yang - Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi, Pathumthani, 12110, Thailand. R. Khunprasert - Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi, Pathumthani, 12110, Thailand. W. Khuangsatung - Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi, Pathumthani, 12110, Thailand.

### Abstract

In this paper, we prove a strong convergence theorem of a Modified SP-iteration for finding a common fixed point of the combination of a finite family of nonexpansive mappings in a convex metric space. Moreover, we give some numerical example for supporting our main theorem and compare convergence rate between the modified SP-iteration and the Ishikawa iteration.

### Share and Cite

##### ISRP Style

P Sukprasert, V. Yang, R. Khunprasert, W. Khuangsatung, Convergence results for modified SP-iteration in uniformly convex metric spaces, Journal of Mathematics and Computer Science, 26 (2022), no. 2, 162--171

##### AMA Style

Sukprasert P, Yang V., Khunprasert R., Khuangsatung W., Convergence results for modified SP-iteration in uniformly convex metric spaces. J Math Comput SCI-JM. (2022); 26(2):162--171

##### Chicago/Turabian Style

Sukprasert, P, Yang, V., Khunprasert, R., Khuangsatung, W.. "Convergence results for modified SP-iteration in uniformly convex metric spaces." Journal of Mathematics and Computer Science, 26, no. 2 (2022): 162--171

### Keywords

• Convergence theorem
• SP-iteration
• convex metric space

•  47H09
•  47H10

### References

• [1] K. Aoyama, K. Eshita, W. Takahashi, Iteration processes for nonexpansive mappings in convex metric spaces, In: Nonlinear analysis and convex analysis, 2007 (2007), 31--39

• [2] F. E. Browder, W. V. Petryshyn, Construction of fixed points of nonlinear mappings in Hilbert spaces, J. Math. Anal. Appl., 20 (1967), 197--228

• [3] H. Fukhar-ud-din, One step iterative scheme for a pair of nonexpansive mappings in a convex metric space, Hacet. J. Math. Stat., 44 (2015), 1023--1031

• [4] B. Gündüz, Fixed Points of a Finite Family of I-Asymptotically Quasi-Nonexpansive Mappings in a Convex Metric Space, Filomat, 31 (2017), 2175--2182

• [5] B. Halpern, Fixed points of nonexpanding maps, Bull. Amer. Math. Soc., 73 (1967), 957--961

• [6] S. Ishikawa, Fixed points by a new iteration method, Proc. Amer. Math. Soc., 44 (1974), 147--150

• [7] A. Kangtunyakarn, On convergence theorem of a finite family of nonlinear mappings in uniformly convex metric spaces, J. Comput. Anal. Appl., 24 (2018), 382--391

• [8] A. R. Khan, M. A. Khamsi, H. Fukhar-ud-din, Strong convergence of a general iteration scheme in $CAT(0)$-spaces, Nonlinear Anal., 74 (2011), 783--791

• [9] W. A. Mann, Mean value methods in iteration, Proc. Amer. Math. Soc., 4 (1953), 506--510

• [10] M. A. Noor, New approximation schemes for general variational inequalities, J. Math. Anal. Appl., 251 (2000), 217--229

• [11] G. A. Okeke, Convergence theorems for $G$-nonexpansive mappings in convex metric spaces with a directed graph, Rend. Circ. Mat. Palermo (2), 70 (2021), 907--922

• [12] M. O. Osilike, Implicit iteration process for common fixed points of a finite family of strictly pseudocontractive maps, J. Math. Anal. Appl., 294 (2004), 73--84

• [13] 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 (2011), 3006--3014

• [14] W. Phuengrattana, S. Suantai, Strong Convergence Theorems for a Countable Family of Nonexpansive Mappings in Convex Metric Spaces, Abstr. Appl. Anal., 2011 (2011), 18 pages

• [15] W. Phuengrattana, S. Suantai, Existence and convergence theorems for generalized hybrid mappings in uniformly convex metric spaces, Indian J. Pure Appl. Math., 45 (2014), 121--136

• [16] T. Shimizu,, A convergence theorem to common fixed points of families of nonexpansive mappings in convex metric spaces, In: Nonlinear analysis and convex analysis, 2007 (2007), 575--585

• [17] K. Siriyan, A. Kangtunyakarn, Fixed point results in convex metric spaces, J. Fixed Point Theory Appl., 21 (2019), 12 pages

• [18] W. Takahashi, A convexity in metric space and nonexpansive mappings, I, Kōdai Math. Sem. Rep., 22 (1970), 142--149