Turkish Journal of Analysis and Number Theory
ISSN (Print): 2333-1100 ISSN (Online): 2333-1232 Website: http://www.sciepub.com/journal/tjant
Open Access
Journal Browser
Go
Turkish Journal of Analysis and Number Theory. 2017, 5(2), 57-62
DOI: 10.12691/tjant-5-2-3
Open AccessArticle

Fixed Point Theorems for Expansive Mappings in G-metric Spaces

Rahim Shah1, and Akbar Zada1

1Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan

Pub. Date: February 15, 2017

Cite this paper:
Rahim Shah and Akbar Zada. Fixed Point Theorems for Expansive Mappings in G-metric Spaces. Turkish Journal of Analysis and Number Theory. 2017; 5(2):57-62. doi: 10.12691/tjant-5-2-3

Abstract

In this paper we prove some fixed point theorems for contractive as well as for expansive mappings in G-metric space by using integral type contraction. Finally, we present an example.

Keywords:
G-metric space fixed point integral type contractive mapping expansive mapping

Creative CommonsThis work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References:

[1]  R. Agarwal, E, Karapinar, Remarks on some coupled fixed point theorems in G-metric spaces, Fixed Point Theory Appl., 2013, 2 (2013).
 
[2]  H. Aydi, M. Postolache, W. Shatanawi, Coupled fixed point results for (ϕ-ψ)-weakly contractive mappings in ordered G-metric spaces, Comput. Math. Appl., vol. 63(1), 2012, pp. 298-309.
 
[3]  H. Aydi, W. Shatanawi, C. Vetro, On generalized weakly G-contraction mappings in G-metric spaces, Comput. Math. Appl., vol. 62, 2011, pp. 4222-4229.
 
[4]  H. Aydi, B. Damjanovic, B. Samet, W. Shatanawi, Coupled fixed point theorems for nonlinear contractions in partially ordered G-metric spaces, Math. Comput. Model., vol. 54, 2011, pp. 2443-2450.
 
[5]  H. Aydi, E. Karapinar, W. Shatanawi, Tripled fixed point results in generalized metric spaces, J. Appl. Math., 2012, Article ID 314279.
 
[6]  H. Aydi, E. Karapinar, Z. Mustafa. On common fixed points in G-metric spaces using (E.A) property, Comput. Math. Appl., vol. 64(6), 2012, pp. 1944-1956.
 
[7]  H. Aydi, E. Karapinar, W. Shatanawi, Tripled common fixed point results for generalized contractions in ordered generalized metric spaces, Fixed Point Theory Appl., 2012, 101 (2012).
 
[8]  A. Branciari. A fixed point theorem for mappings satisfying a general contractive condition of integral type. International Journal of Mathematics and Mathematical Sciences, vol. 29, no. 9, 2002, pp. 531-536.
 
[9]  A. Mehdi, K. Erdal, S. Peyman, A new approach to G-metric and related fixed point theorems, J. Ineq. Apps., 2013, 2013:454.
 
[10]  Z. Mustafa, B. Sims, A new approach to generalized metric spaces, J. Nonlinear Convex Anal., vol. 7 (2), 2006, pp. 289-297.
 
[11]  Z. Mustafa, A new structure for generalized metric spaces with applications to fixed point theory, PhD thesis, The University of Newcastle, Australia, 2005.
 
[12]  Z. Mustafa, M. Khandaqji, W. Shatanawi, Fixed point results on complete G-metric spaces, Studia Sci. Math. Hung., vol. 48, 2011, pp. 304-319.
 
[13]  Z. Mustafa, H. Aydi, E. Karapinar, Mixed g-monotone property and quadruple fixed point theorems in partially ordered metric space, Fixed Point Theory Appl., 2012, 71.
 
[14]  Z. Mustafa, Common fixed points of weakly compatible mappings in G-metric spaces, Appl. Math. Sci., vol. 6(92), 2012, pp. 4589-4600.
 
[15]  Z. Mustafa, Some new common fixed point theorems under strict contractive conditions in G-metric spaces, J. Appl. Math., 2012, Article ID 248937.
 
[16]  Z. Mustafa, Mixed g-monotone property and quadruple fixed point theorems in partially ordered G-metric spaces using (ϕ-ψ) contractions, Fixed Point Theory Appl., 2012, 199.
 
[17]  Z. Mustafa, W. Shatanawi, M. Bataineh, Existence of fixed point results in G-metric spaces, Int. J. Math. Math. Sci., 2009, Article ID 283028 (2009).
 
[18]  R. Shah, A. Zada and I. Khan, Some fixed point theorems of integral type contraction in cone b-metric spaces, Turkish. J. Ana. Num. Theor., vol. 3(6), 2105, 165-169.
 
[19]  R. Shah et al., New common coupled fixed point results of integral type contraction in generalized metric spaces, J. Ana. Num. Theor., vol. 4(2), 2106, 1-8.
 
[20]  K. P. R. Rao, L. Bhanu, Z. Mustafa, Fixed and related fixed point theorems for three maps in G-metric space, J. Adv. Stud. Topol., vol. 3(4), 2012, pp. 12-19.
 
[21]  W. Shatanawi, Z. Mustafa, On coupled random fixed point results in partially ordered metric spaces, Mat. Vesn., vol. 64, 2012, pp. 139-146.
 
[22]  A. Zada, R. Shah, T. Li, Integral Type Contraction and Coupled Coincidence Fixed Point Theorems for Two Pairs in G-metric Spaces, Hacet. J. Math. Stat., vol. 45(5), 2016, pp. 1475-1484.