Fixed points of involution mappings in convex uniform spaces

Document Type: Original Article

Authors

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

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

[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] I. Beg, Inequalities in metric spaces with application, Topological Methods in Nonlinear Anal., 17 (2001), 183-190.

[3] I. Beg and M. Abbas, Common fi xed points and best approximation in convex metric spaces, Soochow Journal of Mathematics, 33, 4(2007), 729-738.

[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] 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] V. Berinde, Iterative approximation of fi xed points, springer-Verlag Berlin Heidelberg, (2007). 

[7] N. Bourbaki, Topologie Generale, Chapitre 1: Structures Topologiques, Chapitre 2: Structures Uniformes. Quatrieme Edition, Actualites Scienti ques et Industrielles, Hermann, Paris, France, no. 1142, (1965). 

[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] L. Ciric, On some discontinuous fixed point theorems in convex metric spaces, Czech. Math. J., 43, 188(1993),319-326. 
[10] X. P. Ding, Iteration processes for nonlinear mappings in convex metric spaces, J. Math. Anal. Appl., 132 (1988),114-122. 
[11] K. Goebel and W. A. Kirk, Topics in metric fixed point theory, Cambridge Stud. Adv. Math., Cambridge University Press, London, 28 (1990).
[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] 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] T. Shimizu and W. Takahashi, Fixed point theorems in certain convex metric spaces, Math. Japon., 37 (1992),855-859.
[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] W. Takahashi, A convexity in metric spaces and nonexpansive mapping, Kodai Math. Sem. Rep., 22 (1970),142-149. 
[17] J. Rodrguez-Montes and J. A. Charris, (electronic), Fixed points for W-contractive or W-expansive maps in uniform spaces: toward a uni ed approach, Southwest J. Pure Appl. Math., 1 (2001), 93-101.
[18] A. Weil, Surles Espaces a Structure Uniforme et sur la Topologie Generale, Actualites Scienti ques et Industrielles, Hermann, Paris, France. 551, (1937). 
[19] X. Zhiqun, L. V. Guiwen and B. E. Rhoades, On Equivalence of Some Iterations Convergence
for Quasi-Contraction Maps in Convex Metric Spaces, Fixed Point Theory and Applications, 2010,
doi:10.1155/2010/252871.