Best Proximity Point Results via Simulation Functions in Metric-Like Spaces


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Authors: G. V. V. J. RAO, H. K. NASHINE AND Z. KADELBURG

DOI: 10.46793/KgJMat2003.401R

Abstract:

In this paper, we discuss the existence of best proximity points of certain mappings via simulation functions in the frame of complete metric-like spaces. Some consequences and examples are given of the obtained results.

Keywords:

Z-contraction, best proximity point, simulation function, admissible mapping.

References:

[1]   H. H. Alsulami, E. Karapinar, F. Khojasteh and A. F. R.-L. de Hierro, A proposal to the study of contractions in quasi-metric spaces, Discrete Dyn. Nat. Soc. 2014 (2014), Article ID 269286.

[2]   A. Amini-Harandi, Metric-like spaces, partial metric spaces and fixed points, Fixed Point Theory Appl. 2012(204) (2012), 10 pages.

[3]   N. Bilgili, E. Karapinar and B. Samet, Generalized α-ψ-contractive mappings in quasi-metric spaces and related fixed-point theorems, J. Inequal. Appl. 2014(36) (2014), 15 pages.

[4]   S. Chandok and M. Postolache, Fixed point theorem for weakly Chatterjea-type cyclic contractions, Fixed Point Theory Appl. 2013(28) (2013), 9 pages.

[5]   A. F. R.-L. de Hierro, E. Karapinar, C. R.-L. de Hierro and J. Martínez-Moreno, Coincidence point theorems on metric spaces via simulation functions, J. Comput. Appl. Math. 75 (2015), 345–355.

[6]   M. Jleli, E. Karapinar and B. Samet, Best proximity points for generalized α-ψ-proximal contractive type mappings, J. Appl. Math. 2013 (2013), Article ID 534127, 10 pages.

[7]   E. Karapinar, Fixed points results via simulation functions, Filomat 30(8) (2016), 2343–2350 .

[8]   E. Karapinar, H. H. Alsulami and M. Noorwali, Some extensions for Geraghty type contractive mappings, J. Inequal. Appl. 2015(303) (2015), 22 pages.

[9]   E. Karapinar and F. Khojasteh, An approach to best proximity points via simulation functions, J. Fixed Point Theory Appl. 19 (2017), 1983–1995.

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

[11]   E. Karapinar and P. Salimi, Dislocated metric space to metric spaces with some fixed point theorems, Fixed Point Theory Appl. 2013 (2013), Article ID 222.

[12]   E. Karapinar and B. Samet, Fixed point theorems for generalized α-ψ contractive type mappings and applications, Abstr. Appl. Anal. 2012 (2012), 17 pages.

[13]   F. Khojasteh, S. Shukla and S. Radenović, A new approach to the study of fixed point theorems via simulation functions, Filomat 29 (2015), 1189–1194.

[14]   S. Radenović, Z. Kadelburg, D. Jandrlić and A. Jandrlić, Some results on weak contraction maps, Bull. Iranian Math. Soc. 38 (2012), 625–645.

[15]   B. Samet, Best proximity point results in partially ordered metric spaces via simulation functions, Fixed Point Theory Appl. 2015(232) (2015), 15 pages.

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