Fixed points of involution mappings in convex uniform spaces

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  • Joy Chinyere Umudu1,
  • Johnson Olajire Olaleru2,
  • Adesanmi Alao Mogbademu2,
  1. Department of Mathematics Faculty of Natural Sciences University of Jos Jos Plateau State Nigeria
  2. Department of Mathematics Faculty of Science University of Lagos Akoka Lagos State Nigeria

Published in Issue 2025-11-09

How to Cite

Fixed points of involution mappings in convex uniform spaces. (2025). Communications in Nonlinear Analysis, 7(1). https://oiccpress.com/cna/article/view/17926

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Abstract

In this paper, we study some fixed point theorems for self-mappings satisfying certain contraction principles on a $S$-complete convex Hausdorff uniform space, these theorems generalize previously obtained results in convex metric space and convex partial metric space.

Keywords

  • involution mapping,
  • $k$-Lipschitzian mapping,
  • $(k,
  • L)$-Lipschitzian mapping,
  • uniform spaces
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References

  1. [1] M. Aamri and D. El Moutawakil, Common fixed point theorems for E-contractive or E-expansive maps in uniform spaces, Acta Mathematica Academiae Paedagogicae Nyi Regyhaziensis (New Series), 20, 1(2004), 83-89.
  2. [2] I. Beg, Inequalities in metric spaces with application, Topological Methods in Nonlinear Anal., 17 (2001), 183-190.
  3. [3] I. Beg and M. Abbas, Common fixed points and best approximation in convex metric spaces, Soochow Journal of Mathematics, 33, 4(2007), 729-738.
  4. [4] I. Beg and M. Abbas, Fixed-point theorem for weakly inward multivalued maps on a convex metric space, Demonstratio Mathematica, 39, 1(2006), 149-160.
  5. [5] I. Beg and O. Olatinwo, Fixed point of involution mappings in convex metric spaces, Nonlinear Functional Analysis and Applications, 16, 1(2011), 93-99.
  6. [6] V. Berinde, Iterative approximation of fixed points, springer-Verlag Berlin Heidelberg, (2007).
  7. [7] N. Bourbaki, Topologie Generale, Chapitre 1: Structures Topologiques, Chapitre 2: Structures Uniformes. Quatrieme Edition, Actualites Scientiques et Industrielles, Hermann, Paris, France, no. 1142, (1965).
  8. [8] S. S. Chang, J. K. Kim and D. S. Jin, Iterative sequences with errors for asymptotically quasi nonexpansive mappings in convex metric spaces, Arch. Inequal. Appl., 2 (2004), 365-374.
  9. [9] L. Ciric, On some discontinuous fixed point theorems in convex metric spaces, Czech. Math. J., 43, 188(1993),319-326.
  10. [10] X. P. Ding, Iteration processes for nonlinear mappings in convex metric spaces, J. Math. Anal. Appl., 132 (1988),114-122.
  11. [11] K. Goebel and W. A. Kirk, Topics in metric fixed point theory, Cambridge Stud. Adv. Math., Cambridge University Press, London, 28 (1990).
  12. [12] M. Moosaei, Fixed Point Theorems in Convex Metric Spaces, Fixed Point Theory and Applications, 2012,2012:164 doi:10.1186/1687-1812-2012-164.
  13. [13] V. O. Olisama, J. O. Olaleru and H. Akewe, Best proximity points results for some contractive mappings in uniform spaces, Int. J. Anal., 2017, Article ID 6173468 (2017).
  14. [14] T. Shimizu and W. Takahashi, Fixed point theorems in certain convex metric spaces, Math. Japon., 37 (1992),855-859.
  15. [15] Y. X. Tian, Convergence of an Ishikawa type iterative scheme for asymptotically quasi nonexpansive mappings, Computers and Maths. with Applications, 49 (2005), 1905-1912.
  16. [16] W. Takahashi, A convexity in metric spaces and nonexpansive mapping, Kodai Math. Sem. Rep., 22 (1970),142-149.
  17. [17] J. Rodrguez-Montes and J. A. Charris, (electronic), Fixed points for W-contractive or W-expansive maps in uniform spaces: toward a unied approach, Southwest J. Pure Appl. Math., 1 (2001), 93-101.
  18. [18] A. Weil, Surles Espaces a Structure Uniforme et sur la Topologie Generale, Actualites Scientiques et Industrielles, Hermann, Paris, France. 551, (1937).
  19. [19] X. Zhiqun, L. V. Guiwen and B. E. Rhoades, On Equivalence of Some Iterations Convergencefor Quasi-Contraction Maps in Convex Metric Spaces, Fixed Point Theory and Applications, 2010,doi:10.1155/2010/252871.