Turkish Journal of Analysis and Number Theory
ISSN (Print): 2333-1100 ISSN (Online): 2333-1232 Website: https://www.sciepub.com/journal/tjant
Open Access
Journal Browser
Go
Turkish Journal of Analysis and Number Theory. 2015, 3(6), 165-169
DOI: 10.12691/tjant-3-6-5
Open AccessArticle

Some Fixed Point Theorems of Integral Type Contraction in Cone b-metric Spaces

Rahim Shah1, , Akbar Zada1 and Ishfaq Khan1

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

Pub. Date: December 31, 2015

Cite this paper:
Rahim Shah, Akbar Zada and Ishfaq Khan. Some Fixed Point Theorems of Integral Type Contraction in Cone b-metric Spaces. Turkish Journal of Analysis and Number Theory. 2015; 3(6):165-169. doi: 10.12691/tjant-3-6-5

Abstract

In the present paper, we introduces the concept of integral type contraction with respect to cone b-metric space. Also we proved some fixed point results of integral type contractive mapping in cone b-metric space. We give an example to support our main result.

Keywords:
cone b-metric space fixed point integral type contractive 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]  A. Azam, M. Arshad, Kannan fixed point theorems on generalized metric spaces, J. Nonlinear Sci. Appl., vol. 1, 2008, pp. 45-48.
 
[2]  A. Azam, M. Arshad, I. Beg, Banach contraction principle on cone rectengular metric spaces, Applicable Anal. Discrete Math., vol. 3, 2009, pp. 236-241.
 
[3]  I. A. Bakhtin, The contraction mapping principle in almost metric spaces, Func. Anal. Gos. Ped. Inst. Unianowsk, vol. 30, 1989, pp. 26-37.
 
[4]  S. Banach, Sur les operations dans les ensembles abstrait et leur application aux equations, integrals, Fundan. Math., vol. 3, 1922, pp. 133-181.
 
[5]  M. Boriceanu, Strict fixed point theorems for multivalued operators in b-metric spaces, Intern. J. Modern Math., vol. 4(3), 2009, pp. 285-301.
 
[6]  M. Boriceanu, M. Bota, A. Petrusel, Multivalued fractals in b-metric spaces, Cent. Eur. J. Math., vol. 8(2), 2010, pp. 367-377.
 
[7]  M. Bota, A. Molnar, V. Csaba, On Ekeland's variational principal in b-metric spaces, Fixed Point Theory, vol. 12, 2011, pp. 21-28.
 
[8]  A. Branciari, A _xed 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]  S. Czerwik, Cotraction mapping in b-metric spaces, Acta. Math. Inform. Univ. Ostraviensis, vol. 1, 1993, pp. 5-11.
 
[10]  P. Das, B.K. Lahiri, Fixed point of cotractive mappings in generalized metric space, Math. Slovaca., vol. 59, 2009, pp. 499-501.
 
[11]  K. Deimling, Nonlinerar Functional Analysis, Springer, 1985.
 
[12]  I.M. Erhan, E. Karapinar, T. Sekulic, Fixed points of (ψ, φ) contractions on generalized metric space, Fixed Point Theory Appl., 2012, 220, (2012).
 
[13]  R. George, B. Fisher, Some generalized results in cone b-metric space, Math. Moravica., vol. 17(2), 2013, pp. 39-50.
 
[14]  H. H. Haung, S. Xu, Fixed point theorems of contractive mappings in cone b-metric spaces and applications, Fixed Point Theory Appl., 2012(220), 2012.
 
[15]  L. G. Haung, X. Zhang, Cone metric space and _xed point theorems of contractive mappings, J. Math. Anal., Apal, vol. 332(2), 2007, pp. 1468-1476.
 
[16]  N. Hussain, MH. Shah, KKM mapping in cone b-metric spaces, Comput. Math. Appl., vol.62, 2011, pp. 1677{1684.
 
[17]  M. Jleli, B. Zhang, The Kannan's fixed point theorem in a cone rectengular metric space, J. Nonlinear Sci. Apal., vol. 2(3), 2009, pp. 161-167.
 
[18]  Z. Kadelburg, S. Radenović, On generalized metric space, TWMS J. Pure. Appl. Math., vol. 5(1), 2014, pp. 03-13.
 
[19]  F. Khojasteh, Z. Goodarzi, A. Razani, Some Fixed Point Theorems of Integral Type Contraction in Cone Metric Spaces, Fixed Point Theory Appl., vol. 2010, Article ID 189684, 13 pages, 2010.
 
[20]  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.