Asymptotic Behavior of Generalized CR−iteration Algorithm and Application to Common Zeros of Accretive Operators

Authors

  • Aadil MUSHTAQ Department of Mathematics, Maulana Azad National Urdu University, Hyderabad, India. Email: aadilmuhtaq456@gmail.com. https://orcid.org/0000-0002-4029-4694
  • Khaja MOINUDDIN Department of Mathematics, Maulana Azad National Urdu University, Hyderabad, India. Email: kmoinuddin71@gmail.com. https://orcid.org/0000-0003-4028-9876
  • Nisha SHARMA Pt. J.L.N. Govt. College, Department of Higher Education, Harayana, India. Email: nnishaa.bhardwaj@gmail.com.
  • Anita TOMAR Pt.L.M.S. Campus, Sridev Suman Uttarakhand University, Rishikesh, Uttarakhand, India. Email: anitatmr@yahoo.com. https://orcid.org/0000-0001-8033-856X

DOI:

https://doi.org/10.24193/subbmath.2024.2.10

Keywords:

Fixed point, CR−iterative algorithm, nonself QNEMs

Abstract

The purpose of this study is to provide a generalized CRiteration algorithm for finding common fixed points (CFPs) for nonself quasi-nonexpansive mappings (QNEMs) in a uniformly convex Banach space. The suggested algorithm’s convergence analysis is analyzed in uniformly convex Banach spaces.

Mathematics Subject Classification (2010): 37C25, 47H10.

Received 28 October 2021; Accepted 12 January 2023

References

Agarwal, R.P., O’Regan, D., Sahu, D.R., Fixed Point Theory for Lipschitzian-Type Map- pings With Applications, Springer, New York, 2009.

Babu, G.V.R., Satyanarayana, G., Convergence of CR−iteration procedure for a nonlinear quasi contractive map in convex metric spaces, Commun. Nonlinear Anal., 7(2019), 82-88.

Bauschke, H.H., Combettes, P.L., Convex Analysis and Monotone Operator Theory in Hilbert Spaces, Springer, Berlin, 2011.

Browder, F.E., Semicontractive and semiaccretive nonlinear mappings in Banach spaces, Bull. Amer. Math. Soc. (N.S), 74(1968), 660-665.

Chang, R., Kumar, V., Kumar, S., Chan, C.K., Strong convergence of a new three step iterative scheme in Banach spaces, Am. J. Comput. Math., 2(2012), 345-357.

Chang, S.S., Wang, L., Joseph Lee, H.W., Chan, C.K., Strong and convergence for mixed type total asymptotically nonexpansive mappings in CAT(0) spaces, Fixed Point Theory Appl., 122(2013), 1-16.

Ciorănescu, I., Geometry of Banach Spaces, Duality Mapping and Nonlinear Problems, Kluwer, Amsterdam, 1990.

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

Karakaya, V., Gürsoy, F., Dogan, K., Ertürk, M., Data dependence results for multistep and CR−iterative schemes in the class of contractive-like operators, Abstr. Appl. Anal., 2013(2013), 1-7.

Kim, J.K., Tuyen, T.M., Approximation common zero of two accretive operators in Banach spaces, Appl. Math. Comput., 283(2016), 265-281.

Kwan, Y.C., Shahid, A.A., Nazeer, W., Abbas, M., Kang, S.M., Fractal generation via

CR−iteration scheme with s-convexity, IEEE Access., 7(2019), 69986-69997.

Li, D., Shahid, A.A., Tassaddiq, A., Khan, A., Guo, X., Ahmad, M., CR−Iteration in generation of antifractals with s-convexity, IEEE Access., 8(2020), 61621-61630.

Mann, W.R., Mean value methods in iteration, Proc. Amer. Math. Soc., 6(1953), 506- 510.

Martinet, B., Régularisation d’inéquations variationelles par approximations successives, Rev. Fr. Inform. Rech. Oper., 4(1970), 154-158.

Martinet, B., Détermination approchée d’un point fixe d’une application pseudo- contractante, C.R. Math. Acad. Sci. Paris., 274(1972), 163-165.

Picard, E., Mémoire sur la théorie des équations aux dérivés partielles et la méthode des approximations successive, J. Math. Pures et Appl., 6(1890), 145-210.

Rockafellar, R.T., Monotone operators and the proximal point algorithm, SIAM J. Control Optim., 14(1976), 877-898.

Rockafellar, R.T., Augmented Lagrangians and applications of the proximal point algorithm in convex programming, Math. Oper. Res., 1(1976), 97-116.

Sahu, D.R., Applications of the S-iterative algorithm to constrained minimization problems and split feasibility problems, Fixed Point Theory, 12(2011), no. 1, 187-204.

Sahu, D.R., Ansari, Q.H., Yao, J.C., The prox-Tikhonov-like forward-backward method and applications, Taiwanese J. Math., 19(2015), 481-503.

Xu, H.K., Inequalities in Banach spaces with applications, Nonlinear Anal., 16(1991), 1127-1138.

Xu, H.K., Iterative algorithms for nonlinear operators, J. Lond. Math. Soc., 66(2002), no. 2, 240-256.

Xu, H.K., Strong convergence of an iterative method for nonexpansive and accretive operators, J. Math. Anal. Appl., 314(2006), 631-643.

Zegeye, H., Shahzad, N., Strong convergence theorems for a common zero of a finite family of maccretive mappings, Nonlinear Anal., 66(2007), 1161-1169.

Zhang, Q.N., Song, Y.S., Halpern type proximal point algorithm of accretive operators, Nonlinear Anal., 75(2012), 1859-1868.

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Published

2024-06-18

How to Cite

MUSHTAQ, A. ., MOINUDDIN, K. ., SHARMA, N. ., & TOMAR, A. . (2024). Asymptotic Behavior of Generalized CR−iteration Algorithm and Application to Common Zeros of Accretive Operators. Studia Universitatis Babeș-Bolyai Mathematica, 69(2), 399–413. https://doi.org/10.24193/subbmath.2024.2.10

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