American Journal of Applied Mathematics and Statistics
ISSN (Print): 2328-7306 ISSN (Online): 2328-7292 Website: https://www.sciepub.com/journal/ajams Editor-in-chief: Mohamed Seddeek
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American Journal of Applied Mathematics and Statistics. 2023, 11(2), 61-62
DOI: 10.12691/ajams-11-2-3
Open AccessArticle

Unique Fixed Points on OWC for Self-Maps with Generalized Contractive Type Conditions in CMS

K. Prudhvi1,

1Department of Mathematics, University College of Science, Saifabad, Osmania University, Hyderabad, Telangana State, India

Pub. Date: April 24, 2023

Cite this paper:
K. Prudhvi. Unique Fixed Points on OWC for Self-Maps with Generalized Contractive Type Conditions in CMS. American Journal of Applied Mathematics and Statistics. 2023; 11(2):61-62. doi: 10.12691/ajams-11-2-3

Abstract

In this paper, we obtain fixed point theorem for OWC (Occasionally Weakly Compatible) self-mappings satisfying a generalized contractive type condition in CMS (Cone Metric Space). Our results are generalizing and improving some of the well known comparable results existing in this literature.

Keywords:
fixed point occasionally weakly compatible cone metric space normal cone

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References:

[1]  L.G. Huang, X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings J. Math. Anal. Appl. 332(2) (2007), 1468-1476.
 
[2]  M. Abbas and G. Jungck, Common fixed point results for non commuting mappings without continuity in cone metric spaces, J. Math. Anal. Appl. 341(2008) 416-420.
 
[3]  M. Abbas, B. E. Rhoades, Fixed and periodic point results in cone metric spaces, Appl. Math. Lett. 21(2008): 511-515.
 
[4]  I. Altun, B. Durmaz, Some fixed point theorems on ordered cone metric spaces, Rend. Circ. Mat. Palermo 58(2009), 319-325.
 
[5]  M.A.Al-Thagafi and Naseer Shahzad, Generalized I-non expansive self maps and invariant approximations, Acta Mathematica Sinica, 24(2008), 867-876
 
[6]  Arvind Bhatt and Harish Chandra, Occasionally weakly compatible mappings in cone metric space, Applied Mathematical Sciences, Vol. 6, no. 55, (2012), 2711-2717.
 
[7]  Guangxing Song, Xiaoyan Sun, Yian Zhao, Guotao Wang, New common fixed point theorems for maps on cone metric spaces, Appl. Math. Lett. 32(2010) 1033-1037.
 
[8]  G.Jungck and B.E. Rhoades, Fixed point theorems for occasionally weakly compatible mappings, Fixed Point Theory, 7(2006), 286-296.
 
[9]  G.Jungck and B.E. Rhoades, Fixed point theorems for occasionally weakly compatible mappings, Erratum, Fixed Point Theory, 9(2008), 383-384.
 
[10]  Ö. Özer, A. Shatarah, A kind of fixed point theorem on the complete C*- Algebra valued s-metric spaces, Asia Mathematika, vol.4., Iisue .1, (2020), 53-62.
 
[11]  K. Prudhvi, A Unique Common Fixed Point Theorem for a Metric Space with the Property (E.A), American Journal of Applied Mathematics and Statistics, Vol.11., No.1, (2023), 11-12.