Fixed points of α-Θ-Geraghty type and Θ-Geraghty graphic type contractions

Wudthichai Onsod, Poom Kumam, Yeol Je Cho


In this paper, by using the concept of the α-Garaghty contraction, we introduce the new notion of the α-Θ-Garaghty type contraction and prove some fixed point results for this contraction in partial metric spaces. Also, we give some examples and applications to illustrate the main results.


α-Θ-Garaghty type contraction; Θ-Geraghty graphic type contractions; partial order; partial metric spaces; common fixed points

Subject classification

47H09; 47H10; 54H25; 37C25

Full Text:



T. Abdeljawad, Meir-Keeler α-contractive fixed and common fixed point theorems, Fixed Point Theory Appl. 19 (2013).

T. Abdeljawad and D. Gopal, Erratum to Meir-Keeler $alpha$-contractive fixed and common fixed point theorems, Fixed Point Theory Appl. 110 (2013).

H. Alikhani, D. Gopal, M. A. Miandaragh, Sh. Rezapour and N. Shahzad, Some endpoint results for β-generalized weak contractive multifunctions, The Scientific World Journal (2013), Article ID 948472.

S. Banach, Sur les operations dans les ensembles abstraits et leur applications aux equations integrales, Fund. Math. 3 (1922), 133-181.

I. Beg, A. R. Butt and S. Radojevic, The contraction principle for set value mappings on a metric space with a graph, Comput. Math. Appl. 60 (2010), 1214-1219.

A. Branciari, A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces, Publ. Math. (Debr.) 57 (2000), 31-37.

S. H. Cho, J. S. Bae and E. Karapinar, Fixed point theorems for α-Geraghty contraction type maps in metric spaces, Fixed Point Theory Appl. 329 (2013).

S. Chondok, Some fixed point theorems for (α, β)-admissible Geraghty type contractive maooings and related results, Math. Sci. 9 (2015), 127-135.

M. Geraghty, On contractive mappings, Proc. Amer. Math. Soc. 40 (1973), 604-608.

D. Gopal, Fixed points of α-type F-contractive mappings with an application to nonlinear fractional differential equation, Acta Mathematica Scientia 2016, no. 36 (2016), 957-970.

M. E. Gordji, M. Ramezani, Y. J. Cho and S. Pirbavafa, A generalization of Geraghty's theorem in partially ordered metric spaces and applications to ordinary differential equations, Fixed Point Theory Appl. 74 (2012).

N. Hussian, M. Arshad, A. Shoaib and Fahimuddin, Common fixed point results for α-ψ-contractions on a metric space endowed with a graph, J. Inequal. Appl. 136 (2014).

N. Hussain, E. Karapinar, P. Salimi and F. Akbar, α-admissible mappings and related fixed point theorems, J. Inequal. Appl. 114 (2013).

N. Hussain, P. Salimi and A. Latif, Fixed point results for single and set-valued α-η-ψ-contractive mappings, Fixed Point Theory Appl. 212 (2013).

M. Jleli, E. Karapinar and B. Samet, Further generalizations of the Banach contraction principle. J. Inequal. Appl. 439 (2014). M. Jleli and B. Samet, A new generalization of the Banach contraction principle, J. Inequal. Appl. 38 (2014).

E. Karapinar, P. Kumam and P. Salimi, On α-ψ -Meir-Keeler contractive mappings, Fixed Point Theory Appl. (2013), Article ID 94.

M. A. Kutbi, M. Arshad and A. Hussain, On modified α-η-contractive mappings, Abstr. Appl. Anal. (2014), Article ID 657858.

J. Jachymski, The contraction principle for mappings on a metric space with a graph, Proc. Amer. Math. Soc. 136 (2008), 1359-1373.

X. D. Liu, S. S. Chang, Y. Xiao and L. C. Zhao, Existence of fixed points for Θ-type contraction and Θ-type Suzuki contraction in complete metric spaces, Fixed Point Theory Appl. 8 (2016).

J. Martinez-Moreno, W. Sintunavarat and Y. J. Cho, Common fixed point theorems for Geraghty's type contraction mappings using the monotone property with two metrics, Fixed Point Theory Appl. 174 (2015).

S. G. Mathews, Partial metric topology, in Proceedings of the 11th Summer Conference on General Topology and Applications 728 (1995), 183-197, The New York Academy of Sci.

C. Mongkolkehai, Y. J. Cho and P. Kumam, Best proximity points for Geraghty's proximal contraction mappings, Fixed Point Theory Appl. 180 (2013).

W. Onsod and P. Kumam, Common fixed point results for φ-ψ-weak contraction mappings via f-α-admissible Mappings in intuitionistic fuzzy metric spaces, Communications in Mathematics and Applications 7 (2016), 167-178.

V. L. Rosa and P. Vetro, Fixed point for Geraghty-contractions in partial metric spaces, J. Nonlinear Sci. Appl. 7 (2014), 1-10.

P. Salimi, A. Latif and N. Hussain, Modified α-ψ-contractive mappings with applications, Fixed Point Theory Appl. 151 (2013).

B. Samet, C. Vetro and P. Vetro, Fixed point theorems for α-ψ-contractive type mappings, Nonlinear Anal. 75 (2012), 2154-2165.

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