Fixed Points Results for Graphic Contraction on Closed Ball

Aftab Hussain^{1, 2,}

¹Department of Mathematics, International Islamic University, H-10, Islamabad - 44000, Pakistan

²Department of Mathematical Sciences, Lahore Leads University, Lahore - 54000, Pakistan

Cite this paper:
Aftab Hussain. Fixed Points Results for Graphic Contraction on Closed Ball. Turkish Journal of Analysis and Number Theory. 2016; 4(4):92-97. doi: 10.12691/tjant-4-4-2

Abstract

In this paper, we introduce a new class of ciric fixed point theorem of (α,ψ)-contractive mappings on a closed ball in complete metric space. As an application, we have derived some new fixed point theorems for ciric ψ-graphic contractions defined on a metric space endowed with a graph in metric space. Our results provide extension as well as substantial generalizations and improvements of several well known results in the existing comparable literature.

Keywords:
fixed point α-admissible (αψ)-contraction closed ball

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References:

[1]	M. Abbas and T. Nazir, Common fixed point of a power graphic contraction pair in partial metric spaces endowed with a graph, Fixed Point Theory and Applications 2013, 2013:20.
[2]	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 pp.
[3]	M. Arshad, Fahimuddin, A. Shoaib and A. Hussain, Fixed point results for α-ψ-locally graphic contraction in dislocated qusai metric spaces, Mathematical Sciences, In press.
[4]	T. Abdeljawad, Meir-Keeler α-contractive fixed and common fixed point theorems, Fixed Point Theory and Appl. 2013.
[5]	F. Bojor, Fixed point theorems for Reich type contraction on metric spaces with a graph, Nonlinear Anal., 75 (2012) 3895-3901.
[6]	E. Karapinar and B. Samet, Generalized (α-ψ) contractive type mappings and related fixed point theorems with applications, Abstr. Appl. Anal., (2012) Article id: 793486.
[7]	B. Mohammadi and Sh. Rezapour, On Modified α-φ-Contractions, J. Adv. Math. Stud. 6 (2) (2013), 162-166.
[8]	N. Hussain, M. Arshad, A. Shoaib and Fahimuddin, Common fixed point results for α-ψ-contractions on a metric space endowed with graph, J. Inequal. Appl., 2014, 2014:136.
[9]	N. Hussain, E. Karapınar, P. Salimi and F. Akbar, α-admissible mappings and related fixed point theorems, J. Inequal. Appl. 114 2013 1-11.
[10]	N. Hussain, P Salimi and A. Latif, Fixed point results for single and set-valued α-η-ψ-contractive mappings, Fixed Point Theory and Applications, 2013, 2013:212.
[11]	N. Hussain, E. Karapinar, P. Salimi, P. Vetro, Fixed point results for Gm-Meir-Keeler contractive and G-(α,ψ)-Meir-Keeler contractive mappings, Fixed Point Theory and Applications 2013, 2013:34.
[12]	N. Hussain, S. Al-Mezel and P. Salimi, Fixed points for α-ψ-graphic contractions with application to integral equations, Abstr. Appl. Anal., Article 575869, 2013.
[13]	J. Jachymski, The contraction principle for mappings on a metric space with a graph, Proc. Amer. Math. Soc., 1 (136) (2008) 1359-1373.
[14]	M. A. Kutbi, M. Arshad and A. Hussain, On Modified α-η-Contractive mappings, Abstr. Appl. Anal., (2014) Article ID 657858, 7 pages.
[15]	B. E. Rhoades, A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc. 226 (1977), 257-290.
[16]	B. E. Rhoades, Two fixed-point theorems for mappings satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci., 63 (2003) 4007-4013.
[17]	P. Salimi, A. Latif and N. Hussain, Modified α-ψ-Contractive mappings with applications, Fixed Point Theory Appl., (2013) 2013:151.
[18]	B. Samet, C. Vetro and P. Vetro, Fixed point theorems for α-ψ-contractive type mappings, Nonlinear Anal. 75 (2012) 2154-2165.