Existence of triple best proximity point for a 3-cyclic summing Meir-Keeler contraction
Subject Areas : Statistics
1 - Department of pure Mathematics, Payame Noor University, P. O. Box, Tehran 19395-3697, Iran
Keywords: خاصیت UC, انقباض دوری جمعی مییر-کییلر از مرتبه p, بهترین نقطه تقریبی, نقطه ثابت,
Abstract :
Let , and be nonempty subsets of a matric space . Then the mapping is called cyclic if , and . Consider the following optimization problem Let , certainly if the condition be true for some then it is best answer for optimization problem , that we called it triple best proximity point of .In this paper, first we introduce the notion of 3-cyclic summing Meir-Keeler contractions as a generalization of 3-cyclic summing contractions, then we obtain the conditions for the existence of a triple best proximity point for these class of mappings in the metric spaces with property UC. Our results in this paper are true for a n-cyclic summing Meir-Keeler contraction just we work with order 3 for the simplicity of proofs. Note that, our results are generalizations of some existing theorems with shorter and simpler proofs. Note that, our results are generalizations of some existing theorems with shorter and simpler proofs.
[1] Di Bari, C., Suzuki, T., Vetro, C.: Best proximity points for cyclic Meir-Keeler contractions. Nonlinear Anal. 69(11), 3790-3794 (2008)
[2] Eldred, A. A., Veeramani, P.: Existence and convergence of best proximity points. J. Math. Anal. Appl. 323(2), 1001-1006 (2006)
[3] Fallahi, K., Ghahramani, H., Soleimani-Rad, Gh.: Integral type contractions in partially ordered metric spaces and best proximity point. Iran J Sci Technol Trans Sci. 44, 177-183 (2020)
[4] Felicit, J. M., Eldred, A. A.: Best proximity points for cyclical contractive mappings, Appl. Gen. Topol. 16(2) 119-126 (2015)
[5] Karpagam, S., Agrawal, S.: Best proximity point theorems for p-cyclic Meir-Keeler contractions. Fixed Point Theory Appl. Article ID: 197308 (2009)
[6] Karpagam, S., Agrawal, S.: Existence of best proximity points of p-cyclic contractions. Fixed Point Theory. 13(1), 99-105 (2012)
[7] Karpagam, S., Zlatanov, B.: Best proximity points of p-cyclic orbital Meir-Keeler contraction maps. Nonlinear Anal. 21(6), 790-806 (2016)
[8] Lim, T. C.: On characterizations of Meir-Keeler contractive maps. Nonlinear Anal. 46, 113-120 (2001)
[9] Meir, A., Keeler, E.: A theorem on contraction mappings. J. Math. Anal. Appl. 28(2), 326-329 (1969)
[10] Petric, M. A., Zlatanov, B.: Best proximity points and fixed points for p-summing maps. Fixed Point Theory Appl. (2012)
[11] Safari-Hafshejani, A., Amini-Harandi, A. Fakhar, F.: Best proximity points and fixed points results for noncyclic and cyclic Fisher quasi-contractions. Numer. Funct. Anal. Optim. 40(5), 603-619 (2019)
[12] Suzuki, T.: Some notes on Meir-Keeler contractions and L-functions, Bull. Kyushu Inst. Technol. Pure Appl. Math. 53, 1-13 (2006)
[13] Suzuki, T., Kikkawa, M., Vetro, C.: The existence of best proximity points in metric spaces with the property UC. Nonlinear Anal. 71(7), 2918-2926 (2009)
