×

On asymptotic pointwise contractions in modular metric spaces. (English) Zbl 1292.54020

Summary: In this paper we study and prove some new fixed points theorems for pointwise and asymptotic pointwise contraction mappings in modular metric spaces.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Nakano, H., Modulared Semi-Ordered Linear Spaces (1950), Tokyo, Japan: Maruzen, Tokyo, Japan · Zbl 0041.23401
[2] Chistyakov, V. V., Modular metric spaces. I. Basic concepts, Nonlinear Analysis. Theory, Methods & Applications A, 72, 1, 1-14 (2010) · Zbl 1200.54014 · doi:10.1016/j.na.2009.04.057
[3] Chistyakov, V. V., Modular metric spaces. II. Application to superposition operators, Nonlinear Analysis. Theory, Methods & Applications A, 72, 1, 15-30 (2010) · Zbl 1185.26013 · doi:10.1016/j.na.2009.04.018
[4] Musielak, J., Orlicz Spaces and Modular Spaces. Orlicz Spaces and Modular Spaces, Lecture Notes in Mathematics, 1034 (1983), Berlin, Germany: Springer, Berlin, Germany · Zbl 0557.46020
[5] Orlicz, W., Collected Papers. Part I, II (1988), Warsaw, Poland: PWN—Polish Scientific, Warsaw, Poland · Zbl 0675.01024
[6] Khamsi, M. A.; Kozłowski, W. M.; Reich, S., Fixed point theory in modular function spaces, Nonlinear Analysis. Theory, Methods & Applications A, 14, 11, 935-953 (1990) · Zbl 0714.47040 · doi:10.1016/0362-546X(90)90111-S
[7] Khamsi, M. A.; Kozlowski, W. M., On asymptotic pointwise contractions in modular function spaces, Nonlinear Analysis. Theory, Methods & Applications A, 73, 9, 2957-2967 (2010) · Zbl 1229.47079 · doi:10.1016/j.na.2010.06.061
[8] Khamsi, M. A.; Kozlowski, W. M., On asymptotic pointwise nonexpansive mappings in modular function spaces, Journal of Mathematical Analysis and Applications, 380, 2, 697-708 (2011) · Zbl 1221.47093 · doi:10.1016/j.jmaa.2011.03.031
[9] Belluce, L. P.; Kirk, W. A., Fixed-point theorems for families of contraction mappings, Pacific Journal of Mathematics, 18, 213-217 (1966) · Zbl 0149.10701 · doi:10.2140/pjm.1966.18.213
[10] Belluce, L. P.; Kirk, W. A., Nonexpansive mappings and fixed-points in Banach spaces, Illinois Journal of Mathematics, 11, 474-479 (1967) · Zbl 0149.10702
[11] Browder, F. E., Nonexpansive nonlinear operators in a Banach space, Proceedings of the National Academy of Sciences of the United States of America, 54, 1041-1044 (1965) · Zbl 0128.35801 · doi:10.1073/pnas.54.4.1041
[12] Bruck, R. E., A common fixed point theorem for a commuting family of nonexpansive mappings, Pacific Journal of Mathematics, 53, 59-71 (1974) · Zbl 0312.47045 · doi:10.2140/pjm.1974.53.59
[13] DeMarr, R., Common fixed points for commuting contraction mappings, Pacific Journal of Mathematics, 13, 1139-1141 (1963) · Zbl 0191.14901 · doi:10.2140/pjm.1963.13.1139
[14] Lim, T. C., A fixed point theorem for families on nonexpansive mappings, Pacific Journal of Mathematics, 53, 487-493 (1974) · Zbl 0291.47032 · doi:10.2140/pjm.1974.53.487
[15] Goebel, K.; Reich, S., Uniform Convexity, Hyperbolic Geometry, and Nonexpansive Mappings. Uniform Convexity, Hyperbolic Geometry, and Nonexpansive Mappings, Monographs and Textbooks in Pure and Applied Mathematics, 83 (1984), New York, NY, USA: Marcel Dekker, New York, NY, USA · Zbl 0537.46001
[16] Goebel, K.; Sekowski, T.; Stachura, A., Uniform convexity of the hyperbolic metric and fixed points of holomorphic mappings in the Hilbert ball, Nonlinear Analysis, 4, 5, 1011-1021 (1980) · Zbl 0448.47048 · doi:10.1016/0362-546X(80)90012-7
[17] Kirk, W. A., Fixed point theorems in CAT(0) spaces and \(\mathbb{R} \)-trees, Fixed Point Theory and Applications, 4, 309-316 (2004) · Zbl 1089.54020 · doi:10.1155/S1687182004406081
[18] Kirk, W. A., Fixed points of asymptotic contractions, Journal of Mathematical Analysis and Applications, 277, 2, 645-650 (2003) · Zbl 1022.47036 · doi:10.1016/S0022-247X(02)00612-1
[19] Kirk, W. A., Asymptotic pointwise contractions, plenary lecture, Proceedings of the 8th International Conference on Fixed Point Theory and Its Applications, Chiang Mai University
[20] Hussain, N.; Khamsi, M. A., On asymptotic pointwise contractions in metric spaces, Nonlinear Analysis. Theory, Methods & Applications A, 71, 10, 4423-4429 (2009) · Zbl 1176.54031 · doi:10.1016/j.na.2009.02.126
[21] Kirk, W. A.; Xu, H.-K., Asymptotic pointwise contractions, Nonlinear Analysis. Theory, Methods & Applications A, 69, 12, 4706-4712 (2008) · Zbl 1172.47038 · doi:10.1016/j.na.2007.11.023
[22] Khamsi, M. A.; Kirk, W. A., An Introduction to Metric Spaces and Fixed Point Theory (2001), New York, NY, USA: John Wiley, New York, NY, USA · Zbl 1318.47001 · doi:10.1002/9781118033074
[23] Kozlowski, W. M., Modular Function Spaces. Modular Function Spaces, Monographs and Textbooks in Pure and Applied Mathematics, 122 (1988), New York, NY, USA: Marcel Dekker, New York, NY, USA · Zbl 0661.46023
[24] Kozlowski, W. M., Notes on modular function spaces I, Comment Mathematica, 28, 91-104 (1988)
[25] Kozlowski, W. M., Notes on modular function spaces II, Comment Mathematica, 28, 105-120 (1988)
[26] Boyd, D. W.; Wong, J. S. W., On nonlinear contractions, Proceedings of the American Mathematical Society, 20, 458-464 (1969) · Zbl 0175.44903 · doi:10.1090/S0002-9939-1969-0239559-9
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.