Existence and Convergence of Fixed points of Generalized alpha non-expensive mappings in metric spaces

Existence and Convergence of Fixed points of Generalized alpha non-expensive mappings

  • Ali Asghar Department of Mathematics, Institute of Southern Punjab, Multan, Pakistan
  • Mohammad Showkat Rahim Chowdhury Department of Mathematics and Statistics, Faculty of Science, The University of Lahore, Lahore, Pakistan
  • Noor Muhammad Department of Mathematics, Institute of Southern Punjab, Multan, Pakistan
  • Muhammad Suhail Aslam Department of Mathematics and Statistics, Faculty of Science, The University of Lahore, Lahore, Pakistan
Keywords: convergence, condition (C), fixed point, non-expansive mapping, opial property, α-non-expansive

Abstract

Abstract Views: 245

We give certain conditions about different kinds of mappings. These conditions will be median of non-expansive mappings and quasi-non-expansive mappings. We will establish some fixed point results of some generalized non-expansive mappings in metric spaces. Moreover, we will also establish few existence and convergence results about generalization of non-expansive mappings. Finally, we present some useful lemmas and propositions.

Downloads

Download data is not yet available.

References

Connell EH. Properties of fixed point spaces. Proc Amer Math Soc.1959;10(6):974-979. https://doi.org/10.2307/2033633

Subrahmanyam PV. Completeness and fixed-points. Monatsh Math. 1975;80:325-330. https://doi.org/10.1007/BF01472580

Ishtiaq U, Saleem N, Uddin F, Sessa S, Ahmad K, di Martino F. Graphical views of intuitionistic fuzzy double-controlled metric-like spaces and certain fixed-point results with application. Symmetry. 2022;14(11):e2364. http://doi.org/10.3390/sym14112364

Browder FE. Fixed-point theorems for noncompact mapping in Hilbert space. Proc. Natl. Acad. Sci. USA. 1965;53(6):1272-1276. https://doi.org/10.1073/pnas.53.6.1272

Gohde D. Zum Prinzip def kontraktiven Abbildung. Math Nachr.1965;30(3-4):251-258. https://doi.org/10.1007/978-3-322-94888-5_2

Goebel K, Kirk WA. Iteration processes for non-expansive mappings. Contempt. Math. 1983;21:115-123.

Kirk WA. A fixed point theorem for mappings which do not increase distances. Amer Math Monthly. 1965;72:1004-1006. https://doi.org/10.2307/2313345

Browder FE. Non-expansive nonlinear operators in a Banach space. Proc Natl Acad Sci. 1965;54(6):1041-1044. https://doi.org/10.1073/pnas.54.4.1041

Saleem, N, Agwu IK, Ishtiaq U. Radenovi´c, S. Strong convergence theorems for finite family of enriched strictly pseudocontractive mappings and φT-Enriched lipschitizian mappings using a new modified mixed- type ishikawa iteration scheme with error. Symmetry. 2022;14(5):e1032. https://doi.org/10.3390/sym14051032

Suzuki T. Krasnoselskii and Mann’s type sequence and Ishikawa’s strong convergence theorem. Paper presented at W. Taka- hashi, T. Tanaka, eds., Proceedings of the third international conference on Nonlinear Analysis and convex Analysis; 2004, Yokohama.

Suzuki T. Strong convergence of Krasnoselskii and Mann,s type sequence for one parameter non-expansive semigroup without Bochner integrals. J Math Anal Appl. 2005;305(1):227-239. https://doi.org/10.1016/j.jmaa.2004.11.017

Dulst DV. Equivalent norms and the fixed point property for non-expansive mappings. J London Math Soc. 1982;25:139-144. https://doi.org/10.1112/jlms/s2-25.1.139

Suzuki T. Strong convergence theorems for infinite family of non-expansive mappings in general Banach spaces. Fixed Point Theory Appl. 2005;2005:e685918. https://doi.org/10.1155/FPTA.2005.103

Suzuki T. Fixed point theorems and convergence theorems for some generalized non expansive mappings. J Math Anal Appl. 2008;340(2):1088-1095. https://doi.org/10.1016/j.jmaa.2007.09.023

Shukla R, Pant R, De la Sen M. Generalized α non-expansive mappings in Banach Spaces. Fixed Point Theory Appl. 2017:4. https://doi.org/10.1186/s13663-017-0597-9

Edelstein M, Brien RCO. Non-expansive mappings, asymptotic regularity and successive approximations. J London Math Soc. 1978;s-217(3):547-554. https://doi.org/10.1112/jlms/s2-17.3.547

Goebel K, Kirk WA. Topics in metric fixed point theory. Cambridge University Press; 1990.

Prus S. Geometrical background of metric fixed point theory. In: Kirk WA, Sims B, eds. Handbook of metric fixed point theory. Kluwer Academic Publishers; 2001:93-132.

Bailon JB. Quelques aspects de la theory des points fixes dans les spaces de Banach-II. Paper presented at: Seminar d, Analysis fonctionnelle. Ecole Polytech, Palaiseau; 1979. http://www.numdam.org/item/SAF_1978-1979____A7_0.pdf

Diaz JB, Metcalf FT. On the structure of the set of sub sequential limit points of successive approximations. Bull Amer Math Soc. 1967;73(4):516-519.

Muhammad N, Asghar A, Irum S, Akgul A, Khalil EM, Mustaffa. Approximation of fixed point of generalized non-expansive mapping via faster iterative scheme in metric domain [J]. Aims Math. 2023;8(2):2856-2870. https://doi.org/10.3934/math.2023149

Ishikawa S. Fixed points and iteration of non-expansive mappings in a Banach space. Proc Amer Math Soc. 1976;59:65-71.

Asghar A, Qayyum A, Muhammad N. Different types of topological structures by graphs. Eur J Math Anal. 2023;3:e3. https://doi.org/10.28924/ada/ma.3.3

Opial Z. Weak convergence of the sequence of successive approximations for non-expansive mappings. Bull Amer Math Soc. 1967;73:591-597.

Kirk WA. Caristi’s fixed point theorem and metric convexity. Colloq Math. 1976; 36:81-86.

Usman A, Haifa AA, Umar I, Khalil A, Shajib A. Solving nonlinear fractional differential equations for contractive and weakly compatible mappings in neutrosophic metric spaces. J Func Spac. 2022;2022:e1491683. https://doi.org/10.1155/2022/1491683

Published
2022-09-15
How to Cite
1.
Asghar A, Chowdhury MSR, Muhammad N, Aslam MS. Existence and Convergence of Fixed points of Generalized alpha non-expensive mappings in metric spaces. Sci Inquiry Rev. [Internet]. 2022Sep.15 [cited 2024Dec.22];6(3):1-18. Available from: https://journals.umt.edu.pk/index.php/SIR/article/view/3104
Section
Orignal Article