Document Type : Research Paper


Department of Mathematics, Shirvan Branch, Islamic Azad University, Shirvan, Iran


In this paper, we first introduce some types of generalized $\alpha$-Meir-Keeler contractions in $b$-metric-like spaces and then we establish some fixed point results for these types of contractions. Also, we present a new fixed point theorem for a Meir-Keeler contraction through rational expression. Finally, we give some examples to illustrate the usability of the obtained results.


Main Subjects

[1] M. A. Alghamdi, N. Hussain, P. Salimi, Fixed point and coupled fixed point theorems on b-metric-like spaces, J. Inequal. Appl. 2013, 2013:402.
[2] H. H. Alsulami, S. Gulyaz,˙I. M. Erhan, Fixed points of α-admissible Meir-Keeler contraction mappings on quasi-metric spaces, J. Inequal. Appl. 2015, 2015:84.
[3] A. Amini-Harandi, Metric-like spaces, partial metric spaces and fixed points, Fixed Point Theory Appl. 2012, 2012:204.
[4] H. Aydi, E. Karapinar, S. Rezapour, A generalized Meir-Keeler contraction on partial metric spaces, Abstr. Appl. Anal. 2012, 2012:287127.
[5] S. Banach, Sur les opration dans les ensembles abstraits et leur application aux quations intgrales, Fund. Math. 1 (3) (1922), 133-181.
[6] C. Chan, J. Dong, C. Zhu, Some fixed point theorems in b-metric-like spaces, Fixed Point Theory Appl. 2015, 2015:122.
[7] A. Erduran, M. Imdad, Coupled fixed point theorems for generalized Meir-Keeler contractions in ordered partial metric spaces, J. Nonlinear Anal. Appl. 2012, 2012:00169.
[8] N. Gholamian, M. Khanehgir, Fixed points of generalized Meir-Keeler contraction mappings in b-metric-like spaces, Fixed Point Theory Appl. 2016, 2016:34.
[9] E. Karapinar, P. Kumam, P. Salimi, On (α-ψ)-Meir-Keeler contractive mappings, Fixed Point Theory Appl. 2013, 2013:94.
[10] E. Karapinar, B. Samet, Generalized (α-ψ) contractive type mapping and related fixed point theorems with applications, Abstr. Appl. Anal. 2012, 2012:793486.
[11] A. Meir, E. Keeler, A theorem on contraction mappings, J. Math. Anal. Appl. 28 (1969), 326-329.
[12] N. Hussain, J. R. Roshan, V. Parvaneh, Z. Kadelburg, Fixed point of contractive mapping in b-metric-like spaces, The Sci. World. J. 2014, 2014:471827.
[13] B. Samet, C. Vetro, P. Vetro, Fixed point theorems for α-ψ contractive type mappings, Nonlinear Anal. 75 (4) (2012), 2154-2165.
[14] B. Samet, C. Vetro, H. Yazidi, A fixed point theorem for a Meir-Keeler type contraction through rational expression, J. Nonlinear Sci. Appl. 6 (2013), 162-169.
[15] N. Shobkolaei, S. Sedghi, J. R. Roshan, N. Hussain, Suzuki-type fixed point results in metric-like spaces, J. Funct. Spaces. Appl. 2013, 2013:143686.
[16] S. Shukla, Partial b-metric spaces and fixed points theorems, Mediterr. J. Math. 11 (2) (2014), 703-711.