Fixed Point Results for Hardy Roger Type Contraction in Ordered Complete Dislocated G_d Metric Space

Abdullah Shoaib^1, , Muhammad Arshad² and Syed Hussnain Kazmi²

¹Department of Mathematics and Statistics, Riphah International University, Islamabad, Pakistan

²Department of Mathematics, International Islamic University, H-10, Islamabad, Pakistan

Cite this paper:
Abdullah Shoaib, Muhammad Arshad and Syed Hussnain Kazmi. Fixed Point Results for Hardy Roger Type Contraction in Ordered Complete Dislocated G_d Metric Space. Turkish Journal of Analysis and Number Theory. 2017; 5(1):5-12. doi: 10.12691/tjant-5-1-2

Abstract

In this paper we discuss the fixed points of mappings satisfying a contractive condition on a closed ball in an ordered complete dislocated quasi G_d-metric space. The notion of dominated mappings is applied to approximate the unique solution of non linear functional equations. An example is given to show the validity of our work. Our results improve/generalize several well known recent and classical results.

Keywords:
fixed point contractive dominated mappings closed ball crdered complete dislocated quasi G_d-metric spaces

This 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]	M. Abbas and B. E. Rhoades, Common fixed point results for noncommuting mappings without continuity in generalized metric spaces, Appl Maths and Computation, 215(2009), 262-269.
[2]	M. Abbas and S. Z. Nemeth, Finding solutions of implict complementarity problems by isotonicty of metric projection, Nonlinear Anal, 75(2012), 2349-2361.
[3]	R. Agarwal and E. Karapinar, Remarks on some coupled fixed point theorems in G-metric spaces, Fixed Point Theory and Appli, 2013(2013),15pages.
[4]	M. Arshad, A. Shoaib, I. Beg, Fixed point of a pair of contractive dominated mappings on a closed ball in an ordered complete dislocated metric space, Fixed Point Theory and Appl. (2013), 2013:115, 15 pages.
[5]	M. Arshad, A. Shoaib, and P. Vetro, Common Fixed Points Of A Pair Of Hardy Rogers Type Mappings On A Closed Ball In Ordered Dislocated Metric Spaces, Journal of Function Spaces and Appl. 2013 (2013), Article ID 63818.
[6]	M. Arshad, A. Shoaib, M. Abbas and A. Azam, Fixed Points of a pair of Kannan Type Mappings on a Closed Ball in Ordered Partial Metric Spaces, Miskolc Mathematical Notes, 14 (2013), 769-784.
[7]	M. Arshad, A. Azam, M. Abbas and A. Shoaib, Fixed point results of dominated mappings on a closed ball in ordered partial metric spaces without continuity U.P.B. Sci. Bull., Series A, Vol. 76, Iss. 2, 2014.
[8]	A. Azam, S. Hussain and M. Arshad, Common Fixed Points of Kannan Type Fuzzy Mappings on closed balls, Appl. Math. Inf. Sci. Lett. 1, 2 (2013), 7-10.
[9]	A. Azam, S. Hussain and M. Arshad, Common fixed points of Chatterjea type fuzzy mappings on closed balls, Neural Computing & Appl, 21(2012), S313-S317.
[10]	A. Azam, M. Waseem, M. Rashid, Fixed point theorems for fuzzy contractive mappings in quasi-pseudo-metric spaces, Fixed Point Theory Appl, 27(2013) 14pages.
[11]	I. Beg, M. Arshad, A. Shoaib,Fixed Point on a Closed Ball in ordered Dislocated Quasi Metric Space, Article in press, Fixed Point Theory, 2015.
[12]	Lj. Gaji’c and M. Stojakovi’c, On Ciri’c generalization of mappings with a contractive iterate at a point in G-metric spaces, Appl Maths and computation, 219(2012), 435-441.
[13]	H. Hydi, W. Shatanawi, C. Vetro, On generalized weak G-contraction mappings in G-metric spaces, Compute. Math. Appl., 62 (2011), 4223-4229.
[14]	M. Jleli and B. Samet, Remarks on G-metric spaces and fixed point theorems Fixed Point Theory appl, 210 (2012).
[15]	H.K Nashine, Coupled common fixed point results in ordered G-metric spaces, J. Nonlinear Sc. Appl. 1(2012), 1-13.
[16]	J. J. Nieto and R. Rodrigguez-Lopez, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order, 22 (3) (2005), 223-239.
[17]	M. A. Kutbi, J. Ahmad, N. Hussain and M. Arshad, Common Fixed Point Results for Mappings with Rational Expressions, Abstr. Appl. Anal, 2013, Article ID 549518, 11 pages.
[18]	Z. Mustafa and B. Sims, A new approach to generalized metric spaces, Journal of Nonlinear and Convex Anal, 7(2006) 289-297.
[19]	Z. Mustafa, H. Obiedat, and F. Awawdeh, Some fixed point theorem for mappings on a complete G- metric space, Fixed point theory and appl, 2008(2008), 12pages.
[20]	H. Obiedat and Z. Mustafa, Fixed point results on a non symmetric G-metric spaces, Jordan Journal of Maths and Stats, 3(2010), 65-79.
[21]	A.C.M. Ran, M.C.B. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc., 132 (5) (2004), 1435-1443.
[22]	B. Samet, C. Vetro, F. Vetro, Remarks on G-metric spaces, Int. J. Anal., 2013(2013), 6pages.
[23]	W. Shatanawi, Fixed point theory for contractive mappings satisfying Φ-maps in G-metric spaces, Fixed Point Theory and Appl, 2010(2010), 9pages.
[24]	A. Shoaib, M. Arshad and J. Ahmad, Fixed point results of locally cotractive mappings in ordered quasi-partial metric spaces, The Scienti’c World Journal, 2013 (2013), Article ID 194897, 8 pages.
[25]	A. Shoaib, M. Arshad and M. A. Kutbi, Common fixed points of a pair of Hardy Rogers Type Mappings on a Closed Ball in Ordered Partial Metric Spaces, J. Comput. Anal. Appl., 17(2014), 255-264.
[26]	A. Shoaib, M. Arshad and A. Azam, Fixed Points of a pair of Locally Contractive Mappings in Ordered Partial Metric Spaces, Matematiµcki vesnik, 67(1), 2015, 26-38.
[27]	R.K. Vats, A. Kumar, Fixed point theorem for set valued maps in G-metric spaces, Adv. Fixed point theory, 4(2014), 60-68.
[28]	S. Zhou and F.Gu, Some new fixed points in G-metric spaces Journal of Hangzhou Normal University, 11(2010), 47-50.