Fixed Point Results for Generalized Non-linear Operators with Convergence Analysis

Ravi Parkash Bhokal

B.R.S. Govt. College Dujana (Jhajjar), India.

Manoj Kumar *

Department of Mathematics, Baba Masthnath University, Asthal Bohar, Rohtak, India.

Ashish Kumar

Department of Mathematics, Baba Masthnath University, Asthal Bohar, Rohtak, India.

*Author to whom correspondence should be addressed.


The purpose of this research article is to introduce a new iteration scheme and to prove J-iterationconvergence and stability results for it. We also claim the newly introduced iterative scheme  has better efficiency than some of the existing iterations in the literature. Our claim is supported by numerical example.

Keywords: J-iteration, Suzuki generalized non expansive mapping, stability

How to Cite

Bhokal, R. P., Kumar, M., & Kumar, A. (2023). Fixed Point Results for Generalized Non-linear Operators with Convergence Analysis. Asian Research Journal of Mathematics, 19(11), 95–103.


Download data is not yet available.


Bhutia JD, Tiwari K. New iteration process for approximating fixed points in Banach spaces. Journal of linear and topological algebra. 2019;8(4):237-250.

Erturk M, Gursoy F. Some convergence, stability and data dependency results for Picard-S iteration method of quasi-strictly contractive operators, Mathematica Bohemica. 2019;144:69-83.

Hussain N, Ullah K, Arshad M. Fixed point approximation for Suzuki generalized nonexpansive mappings via new iteration process. J. Nonlinear Convex Anal. 2018;19(8):1383-1393.

Thakur BS, Thakur D, Postolache M. A new iterative scheme for numerical reckoning fixed points of Suzuki’s generalized nonexpansive mappings. Appl. Math. Comp. 2016;275:147-155.

Thakur BS, Thakur D, Postolache M. A new iterative scheme for approximating fixed points of non-expansive mappings. Filomat. 2016;30:2711-2720.

Shanjit L, Rohen Y, Chandok S, Devi MB. Some results on iterative proximal convergence and chebyshev center. Journal of Function Spaces. 2021;Article ID 8863325:1-8.

Shanjit L, Rohen Y, Singh KA. Cyclic relatively nonexpansive mappings with respect to orbits and best proximity point theorems. Journal of Mathematics. 2021;Article ID 6676660:1-7.

Shanjit L, Rohen Y. Non-convex proximal pair and relatively nonexpansive maps with respect to orbits. Journal of Inequalities and Applications. 2021;2021:124.

Ullah K, Arshad M. On different results for new three step iteration process in Banach Spaces. Springer Plus. 2016;1-15.

Ullah K, Arshad M. New iteration process and numerical reckoning fixed point in Banach space. U.P.B.sci. bull. (Series A). 2017;79(4):113-122.

Ullah K, Arshad M. Numerical reckoning fixed point for Suzuki’s generalized non-expansive mappings via new iterative process. Filomat. 2018;32:187-196.

Ullah K, Arshad M. New three-step iteration process and fixed point approximation in Banach Spaces. Journal of linear and topological algebra. 2018;7(2):87-100.

Suzuki T. Fixed point theorems and convergence theorems for some generalized non-expansive mappings, J.Math. Anal. 2008;340(2):1088-1095.

Harder AM. Fixed point theory and stability results for fixed point iteration procedure, University of Missouri-Rolla, Missouri; 1987.

Berinde V. Iterative approximation of fixed points, Springer, Berlin; 2007.

Soltuz SM, Grosan T. Data dependence for Ishikawa iteration when dealing with contractive like operators. Fixed point theory and applications; 2008.

Schu J. Weak and strong convergence to fixed points of asymptotically non expansive mappings. Bull. Aust. Math. Soc. 1991;43:153-159.

Abbas M, Nazir T. A new faster iteration process applied to constrained minimization and feasibility problems. Mater. Vesn. 2014;66:223-234.

Agarwal RP, O’Regan D, Sahu DR. Iterative construction of fixed points of nearly asymptotically non-expansive mappings. J. Nonlinear Convex Anal. 2007;8:61-79.

Ali J, Ali F, Kumar P. Approximation of fixed points for Suzuki’s generalized non expansive mappings, Mathemaics. 2019;1-11.

Mann WR. Mean value methods in iteration, Proc. Am. Math. Soc. 1953;4:506-510.

Noor MA. New approximation schemes for general variational inequalities. Journal of Mathematical Analysis and Applications. 2000;251:217–229.