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On cone metric spaces: a survey. (English) Zbl 1221.54059
The article is a very useful survey of different results connected with fixed point theorems in cone metric (K-metric) spaces (X,d) with cone metric d(·,·) taking values in a cone P in a Banach space E. In particular, the authors, in a short and easy way, prove that numerous fixed point results in cone metric spaces obtained under the assumptions that the cone P is normal and solid, can be reduced to the corresponding results in metric spaces; however, the similar reduction, in the general case when P is not normal, is not possible (in particular, some assertions of M. A. Khamsi [Fixed Point Theory Appl. 2010, Article ID 315398 (2010; Zbl 1194.54065)] are not true).

MSC:
54H25Fixed-point and coincidence theorems in topological spaces
References:
[1]Huang, L. G.; Zhang, X.: Cone metric spaces and fixed point theorems of contractive mappings, J. mat. Anal. appl. 332, No. 2, 1468-1476 (2007) · Zbl 1118.54022 · doi:10.1016/j.jmaa.2005.03.087
[2]Kantorovich, L. V.: The method of successive approximations for functional equations, Acta math. 71, 63-77 (1939) · Zbl 0021.13604 · doi:10.1007/BF02547750
[3]Kantorovich, L. V.: The majorant principle and Newton’s method, Dokl. akad. Nauk SSSR (N.S.) 76, 17-20 (1951)
[4]Kantorovich, L. V.: On some further applications of the Newton approximation method, Vestnik leningrad univ. Ser. mat. Meh. astr. 12, No. 7, 68-103 (1957) · Zbl 0091.11502
[5]Kirk, W. A.; Kang, B. C.: A fixed point theorem revisited, J. korean math. Soc. 34, No. 2, 285-291 (1972) · Zbl 0883.47071
[6]Chung, Kun-Jen: Nonlinear contractions in abstract spaces, Kodai math. J. 4, 288-292 (1981) · Zbl 0469.47043 · doi:10.2996/kmj/1138036375
[7]Krasnoseljski, M. A.; Zabreiko, P. P.: Geometrical methods in nonlinear analysis, (1984)
[8]Rus, I. A.; Petrusel, A.; Petrusel, G.: Fixed point theory, (2008)
[9]Vetro, P.: Common fixed points in cone metric spaces, Rend. circ. Mat. Palermo ser. II 56, 464-468 (2007) · Zbl 1196.54086 · doi:10.1007/BF03032097
[10]Abbas, M.; Jungck, G.: Common fixed point results for noncommuting mappings without continuity in cone metric spaces, J. math. Anal. appl. 341, 416-420 (2008) · Zbl 1147.54022 · doi:10.1016/j.jmaa.2007.09.070
[11]Ilić, D.; Rakočević, V.: Common fixed points for maps on cone metric space, J. math. Anal. appl. 341, 876-882 (2008) · Zbl 1156.54023 · doi:10.1016/j.jmaa.2007.10.065
[12]Khan, M. S.; Samanipour, M.: Fixed point theorems for some discontinuous operators in cone metric space, Math. morav. 12, No. 2, 29-34 (2008) · Zbl 1199.54222
[13]P. Raja, S.M. Vaezpour, Some extensions of banach’s contraction principle in complete cone metric spaces, Fixed Point Theory Appl. 2008, 11 pages, Article ID 768294, doi:10.1155/2008/768294. · Zbl 1148.54339 · doi:10.1155/2008/768294
[14]Abbas, M.; Rhoades, B. E.: Fixed and periodic point results in cone metric spaces, Appl. math. Lett. 22, No. 4, 511-515 (2009) · Zbl 1167.54014 · doi:10.1016/j.aml.2008.07.001
[15]Th. Abdeljawad, E. Karapinar, Quasicone metric spaces and generalizations of Caristi-Kirk’s theorem, Fixed Point Theory Appl. 2009, 9 pages, Article ID 574387, doi:10.1155/2009/574387. · Zbl 1197.54051 · doi:10.1155/2009/574387
[16]Altun, I.; Durmaz, G.: Some fixed point theorems on ordered cone metric spaces, Rend. circ. Mat. Palermo 58, 319-325 (2009) · Zbl 1184.54038 · doi:10.1007/s12215-009-0026-y
[17]M. Asadi, H. Soleimani, S.M. Vaezpour, B.E. Rhoades, On T-stability of picard iteration in cone metric spaces, Fixed Point Theory Appl. 2009, 6 pages, Article ID 751090, doi:10.1155/2009/751090. · Zbl 1202.54030 · doi:10.1155/2009/751090
[18]Azam, A.; Arshad, M.; Beg, I.: Banach contraction principle on cone rectangular metric spaces, Appl. anal. Discrete math. 3, 236-241 (2009)
[19]Ilić, D.; Rakočević, V.: Quasi-contraction on a cone metric space, J. math. Anal. appl. 22, 728-731 (2009) · Zbl 1179.54060 · doi:10.1016/j.aml.2008.08.011
[20]Jleli, M.; Samet, B.: The kannan’s fixed point theorem in a cone rectangular metric space, J. nonlinear sci. Appl. 2, No. 3, 161-167 (2009) · Zbl 1173.54321 · doi:http://www.tjnsa.com/no7.htm
[21]E. Karapinar, Fixed point theorems in cone banach spaces, Fixed Point Theory Appl. 2009, 9 pages, Article ID 09281, doi:10.1155/2009/609281. · Zbl 1204.47066 · doi:10.1155/2009/609281
[22]Klim, D.; Wardowski, D.: Dynamic processes and fixed points of set-valued nonlinear contractions in cone metric spaces, Nonlinear anal. TMA 71, 5170-5175 (2009) · Zbl 1203.54042 · doi:10.1016/j.na.2009.04.001
[23]Pathak, H. K.; Shahzad, N.: Fixed point results for generalized quasi-contraction mappings in abstract metric spaces, Nonlinear anal. TMA 71, 6068-6076 (2009) · Zbl 1189.54036 · doi:10.1016/j.na.2009.05.052
[24]Radenović, S.: Common fixed point under contractive conditions in cone metric spaces, Comput. math. Appl. 58, 1273-1278 (2009) · Zbl 1189.65119 · doi:10.1016/j.camwa.2009.07.035
[25]Rezapour, Sh.; Haghi, R. H.: Fixed points of multifunctions on cone metric spaces, Numer. funct. Anal. optim. 30, No. 7–8, 1-8 (2009) · Zbl 1171.54033 · doi:10.1080/01630560903123346
[26]Sahin, I.; Telci, M.: Fixed points of contractive mappings on complete cone metric spaces, Hacet. J. Math. stat. 38, No. 1, 59-67 (2009) · Zbl 1190.47058
[27]Wardowski, D.: Endpoints and fixed points of set-valued contractions in cone metric spaces, Nonlinear anal. TMA 71, 512-516 (2009) · Zbl 1169.54023 · doi:10.1016/j.na.2008.10.089
[28]Wlodarczyk, K.; Plebaniak, R.; Dolinski, M.: Cone uniform, cone locally convex and cone metric spaces, endpoints, set-valued dynamic systems and quasi-asymptotic contractions, Nonlinear anal. TMA 71, 5022-5031 (2009) · Zbl 1203.54051 · doi:10.1016/j.na.2009.03.076
[29]Abdeljawad, Th.: Completion of cone metric spaces, Hacet. J. Math. stat. 39, No. 1, 67-74 (2010) · Zbl 1195.54057
[30]Abdeljawad, Th.; Turkoglu, D.; Abuloha, M.: Some theorems and examples of cone Banach spaces, J. comput. Anal. appl. 12, No. 4, 739-753 (2010) · Zbl 1198.46014
[31]Altun, I.; Rakočević, V.: Ordered cone metric spaces and fixed point results, Comput. math. Appl. 60, 1145-1151 (2010) · Zbl 1201.65084 · doi:10.1016/j.camwa.2010.05.038
[32]I.D. Arandjelović, D.J. Kečkić, A counterexample on a theorem of Khojasteh, Goodarzi and Razani, Fixed Point Theory Appl. 2010, 6 pages, Article ID 470141, doi:10.1155/2010/470141.
[33]Azam, A.; Arshad, M.; Beg, I.: Existence of fixed points in complete cone metric spaces, Int. J. Mod. math. 5, No. 1, 91-99 (2010) · Zbl 1203.54034 · doi:http://ijmm.dixiewpublishing.com/Volume5-1.php
[34]Chen, Chi-Ming; Chang, Toni-Huei: Common fixed point theorems for a weaker Meir-Keeler type function in cone metric spaces, Appl. math. Lett. 23, No. 11, 1336-1341 (2010) · Zbl 1196.54067 · doi:10.1016/j.aml.2010.06.027
[35]Chen, Chi-Ming; Chang, Tong-Huei: A common fixed point theorem for the psi-contractive mapping, Tamkang J. Math. 41, No. 1, 25-30 (2010) · Zbl 1221.54053
[36]Choudhry, B. S.; Metiya, N.: Fixed points of weak contractions in cone metric spaces, Nonlinear anal. TMA 72, 1589-1593 (2010) · Zbl 1191.54036 · doi:10.1016/j.na.2009.08.040
[37]Choudhry, B. S.; Metiya, N.: The point of coincidence and common fixed point for a pair of mappings in cone metric spaces, Comput. math. Appl. 60, No. 6, 1686-1695 (2010) · Zbl 1202.54031 · doi:10.1016/j.camwa.2010.06.048
[38]E. Karapinar, D. Turgoklu, Best approximations theorem for a couple in cone banach space, Fixed Point Theory Appl. 2010, 9 pages, Article ID 784578, doi:10.1155/2010/784578. · Zbl 1204.47067 · doi:10.1155/2010/784578
[39]M.A. Khamsi, Remarks on cone metric spaces and fixed point theorems of contractive mappings, Fixed Point Theory Appl. 2010, 7 pages, Article ID 315398, doi:10.1115/2010/315398. · Zbl 1194.54065 · doi:10.1155/2010/315398
[40]Khamsi, M. A.; Hussain, N.: KKM mappings in metric type spaces, Nonlinear anal. TMA 73, 3123-3129 (2010)
[41]F. Khojasteh, Z. Goodarzi, A. Razani, Some fixed point theorems of integral type contraction in cone metric spaces, Fixed Point Theory Appl. 2010, 13 pages, Article ID 189684, doi:10.1155/2010/189684. · Zbl 1188.54020 · doi:10.1155/2010/189684
[42]A. Latif, F.Y. Shaddad, Fixed point results for multivalued maps in cone metric spaces, Fixed Point Theory Appl. 2010, 11 pages, Article ID 941371, doi:10.1155/2010/941371. · Zbl 1197.54066 · doi:10.1155/2010/941371
[43]Morales, J.; Rojas, E.: Cone metric spaces and fixed point theorems of T-kannan contractive mappings, Int. J. Math. anal. 4, No. 4, 175-184 (2010) · Zbl 1197.54068 · doi:http://www.m-hikari.com/ijma/ijma-2010/ijma-1-4-2010/index.html
[44]Pavlović, M.; Radenović, S.; Radojević, S.: Abstract metric spaces and sehgal-guseman-type theorems, Comput. math. Appl. 60, 865-872 (2010) · Zbl 1201.65093 · doi:10.1016/j.camwa.2010.05.033
[45]Radenović, S.; Kadelburg, Z.: Quasi-contractions on symmetric and cone symmetric spaces, Banach J. Math. anal. 5, No. 1, 38-50 (2011)
[46]Rezapour, Sh.; Hamlbarani, R.: Fixed points of multifunctions on regular cone metric spaces, Expo. math. 28, 71-77 (2010) · Zbl 1193.47058 · doi:10.1016/j.exmath.2009.04.001
[47]Sönmez, A.: On paracompactness in cone metric spaces, Appl. math. Lett. 23, 494-497 (2010) · Zbl 1187.54022 · doi:10.1016/j.aml.2009.12.011
[48]Sönmez, A.; Cakalli, H.: Cone normed spaces and weighted means, Math. comput. Modelling 52, No. 9–10, 1660-1666 (2010) · Zbl 1205.40003 · doi:10.1016/j.mcm.2010.06.032
[49]Turkoglu, D.; Abuloha, M.; Abdeljawad, T.: KKM mappings in cone metric spaces and some fixed point theorems, Nonlinear anal. TMA 72, 348-353 (2010) · Zbl 1197.54076 · doi:10.1016/j.na.2009.06.058
[50]Turkoglu, D.; Abuloha, M.: Cone metric spaces and fixed point theorems in diametrically contractive mappings, Acta math. Sin. (Engl. Ser.) 26, No. 3, 489-496 (2010) · Zbl 1203.54049 · doi:10.1007/s10114-010-8019-5
[51]K. Wlodarczyk, R. Plebaniak, Maximality principle and general results of Ekeland and Caristi types without lower semicontinuity assumptions in cone uniform spaces with generalized pseudodistances, Fixed Point Theory Appl. 2010, 37 pages, Article ID 175453, doi:10.1155/2010/175453. · Zbl 1201.54039 · doi:10.1155/2010/175453
[52]K. Wlodarczyk, R. Plebaniak, Periodic point, endpoint, and convergence theorems for dissipative set-valued dynamic systems with generalized pseudodistances in cone uniform and uniform spaces, Fixed Point Theory Appl. 2010, 32 pages, Article ID 864536, doi:10.1155/2010/864536. · Zbl 1193.37101 · doi:10.1155/2010/864536
[53]Wlodarczyk, K.; Plebaniak, R.; Obczynski, C.: Convergence theorems, best approximation and best proximity for set-valued dynamic system of relatively quasi-asymptotic contractions in cone uniform spaces, Nonlinear anal. TMA 72, 794-805 (2010) · Zbl 1185.54020 · doi:10.1016/j.na.2009.07.024
[54]Krein, M.: Propriétés fondamentales des ensembles coniques normaux dans l’espace de Banach, CR (Doklady) acad. Sci. URSS (N.S.) 28, 13-17 (1940) · Zbl 0024.12202
[55]Azam, A.; Arshad, M.; Beg, I.: Common fixed points of two maps in cone metric spaces, Rend. circ. Mat. Palermo 57, 433-441 (2008) · Zbl 1197.54056 · doi:10.1007/s12215-008-0032-5
[56]Di Bari, C.; Vetro, P.: ϕ-pairs and common fixed points in cone metric spaces, Rend. circ. Mat. Palermo 57, 279-285 (2008) · Zbl 1164.54031 · doi:10.1007/s12215-008-0020-9
[57]Rezapour, Sh.; Hamlbarani, R.: Some notes on the paper cone metric spaces and fixed point theorems of contractive mappings, J. math. Anal. appl. 345, 719-724 (2008) · Zbl 1145.54045 · doi:10.1016/j.jmaa.2008.04.049
[58]M. Arshad, A. Azam, P. Vetro, Some common fixed point results in cone metric spaces, Fixed Point Theory Appl. 2009, 11 pages, Article ID 493965, doi:10.1155/2009/493965. · Zbl 1167.54313 · doi:10.1155/2009/493965
[59]M. Asadi, H. Soleimani, S.M. Vaezpour, An order on subsets of cone metric spaces and fixed points of set-valued contractions, Fixed Point Theory Appl. 2009, 8 pages, Article ID 723203, doi:10.1155/2009/723203. · Zbl 1187.47041 · doi:10.1155/2009/723203
[60]Azam, A.; Arshad, M.; Beg, I.: Common fixed point theorems in cone metric spaces, J. nonlinear sci. Appl. 2, No. 4, 204-213 (2009) · Zbl 1173.54317 · doi:http://www.tjnsa.com/no8.htm
[61]I. Beg, A. Azam, M. Arshad, Common fixed points for maps on topological vector space valued cone metric spaces, Int. J. Math. Math. Sci. 2009, 8 pages, Article ID 560264, doi:10.1155/2009/560264. · Zbl 1187.54032 · doi:10.1155/2009/560264
[62]J.O. Olaleru, Some generalizations of fixed point theorems in cone metric spaces, Fixed Point Theory Appl. 2009, 10 pages, Article ID 657914, doi:10.1155/2009/657914. · Zbl 1203.54043 · doi:10.1155/2009/657914
[63]F. Sabetghadam, H.P. Masiha, A.H. Sanatpour, Some coupled fixed point theorem in cone metric spaces, Fixed Point Theory Appl. 2009, 8 pages, Article ID 125426, doi:10.1155/2009/125426. · Zbl 1179.54069 · doi:10.1155/2009/125426
[64]Cakić, N.; Kadelburg, Z.; Radenović, S.; Razani, A.: Common fixed point results in cone metric spaces for family of weakly compatible maps, Advances appl. Math. sci. 1, No. 1, 183-207 (2009) · Zbl 1218.54032
[65]S. Janković, Z. Kadelburg, S. Radenović, B.E. Rhoades, Assad-Kirk-type fixed point theorems for a pair of nonself mappings on cone metric spaces, Fixed Point Theory Appl. 2009, 16 pages, Article ID 761086, doi:10.1155/2009/761086. · Zbl 1186.54035 · doi:10.1155/2009/761086
[66]G. Jungck, S. Radenović, S. Radojević, V. Rakočević, Common fixed point theorems for weakly compatible pairs on cone metric spaces, Fixed Point Theory Appl. 2009, 13 pages, Article ID 643840, doi:10.1155/2009/643840. · Zbl 1190.54032 · doi:10.1155/2009/643840
[67]Kadelburg, Z.; Radenović, S.; Rakočević, V.: Remarks on ”quasi-contraction on a cone metric space”, Anal. math. Lett. 22, 1674-1679 (2009) · Zbl 1180.54056 · doi:10.1016/j.aml.2009.06.003
[68]Z. Kadelburg, S. Radenović, B. Rosić, Strict contractive conditions and common fixed point theorems in cone metric spaces, Fixed Point Theory Appl. 2009, 14 pages, Article ID 173838, doi:10.1155/2009/173838. · Zbl 1179.54062 · doi:10.1155/2009/173838
[69]Radenović, S.; Rhoades, B. E.: Fixed point theorem for two non-self mappings in cone metric spaces, Comput. math. Appl. 57, 1701-1707 (2009) · Zbl 1186.65073 · doi:10.1016/j.camwa.2009.03.058
[70]Abbas, M.; Khan, M. Ali; Radenović, S.: Common coupled fixed point theorems in cone metric spaces for w-compatible mappings, Appl. math. Comput. 217, 195-202 (2010) · Zbl 1197.54049 · doi:10.1016/j.amc.2010.05.042
[71]Abbas, M.; Rhoades, B. E.; Nazir, T.: Common fixed points for four maps in cone metric spaces, Appl. math. Comput. 216, 80-86 (2010) · Zbl 1197.54050 · doi:10.1016/j.amc.2010.01.003
[72]Altun, I.; Damjanović, B.; Dorić, D.: Fixed point and common fixed point theorems on ordered cone metric spaces, Appl. math. Lett. 23, 310-316 (2010) · Zbl 1197.54052 · doi:10.1016/j.aml.2009.09.016
[73]Gajić, Lj.; Ilić, D.; Rakočević, V.: On ćirić maps with a generalized contractive iterate at a point and Fisher’s quasi-contractions in cone metric spaces, Appl. math. Comput. 216, No. 8, 2240-2247 (2010) · Zbl 1201.54032 · doi:10.1016/j.amc.2010.03.010
[74]Xianjiu Huang, Chuanxi Zhu, Xi Wen, Common fixed point theorem for four non-self mappings in cone metric spaces, Fixed Point Theory Appl. 2010, Article ID 983802, doi:10.1155/2010/983802. · Zbl 1194.54063 · doi:10.1155/2010/983802
[75]Izadi, Z.; Nourouzi, K.: Fixed points of correspondences defined on cone metric spaces, Comput. math. Appl. 60, No. 3, 653-659 (2010) · Zbl 1201.54033 · doi:10.1016/j.camwa.2010.05.013
[76]Janković, S.; Golubović, Z.; Radenović, S.: Compatible and weakly compatible mappings in cone metric spaces, Math. comput. Modelling 52, No. 9–10, 1728-1738 (2010) · Zbl 1205.54041 · doi:10.1016/j.mcm.2010.06.043
[77]Kadelburg, Z.; Pavlović, M.; Radenović, S.: Common fixed point theorems for ordered contractions and quasi-contractions in ordered cone metric spaces, Comput. math. Appl. 59, 3148-3159 (2010) · Zbl 1193.54035 · doi:10.1016/j.camwa.2010.02.039
[78]Z. Kadelburg, S. Radenović, V. Rakočević, Topological vector space valued cone metric spaces and fixed point theorems, Fixed Point Theory Appl. 2010, 17 pages, Article ID 170253, doi:10.1155/2010/170253. · Zbl 1197.54063 · doi:10.1155/2010/170253
[79]Karapinar, E.: Couple fixed point theorems for nonlinear contractions in cone metric spaces, Comput. math. Appl. 59, 3656-3668 (2010) · Zbl 1198.65097 · doi:10.1016/j.camwa.2010.03.062
[80]Rezapour, Sh.; Haghi, R. H.; Shahzad, N.: Some notes on fixed points of quasi-contraction maps, Appl. math. Lett. 23, 498-502 (2010) · Zbl 1206.54061 · doi:10.1016/j.aml.2010.01.003
[81]F. Sabetghadam, H.P. Masiha, Common fixed points for genralized ϕ-pairs of mappings on cone metric spaces, Fixed Point Theory Appl. 2010, 8 pages, Article ID 718340, doi:10.1155/2010/718340. · Zbl 1188.54023 · doi:10.1155/2010/718340
[82]Song, Guangxing; Sun, Xiaoyan; Zhao, Yian; Wang, Guotao: New common fixed point theorems for maps on cone metric space, Appl. math. Lett. 23, No. 9, 1033-1037 (2010) · Zbl 1195.54089 · doi:10.1016/j.aml.2010.04.032
[83]R. Sumitra, V.R. Uthariaraj, R. Hemavathy, P. Vijayaraju, Common fixed point theorem for non-self mappings satisfying generalized Ćirić type contraction condition in cone metric space, Fixed Point Theory Appl. 2010, 17 pages, Article ID 408086, doi:10.1155/2010/408086. · Zbl 1194.54071 · doi:10.1155/2010/408086
[84]Du, Wei-Shih: A note on cone metric fixed point theory and its equivalence, Nonlinear anal. TMA 72, 2259-2261 (2010) · Zbl 1205.54040 · doi:10.1016/j.na.2009.10.026
[85]Wei-Shih Du, Nonlinear contractive conditions for coupled cone fixed point theorems, Fixed Point Theory Appl. 2010, 20 pages, Article ID 190606, doi:10.1155/2010/190606. · Zbl 1220.54022 · doi:10.1155/2010/190606
[86]Amini-Harandi, A.; Fakhar, M.: Fixed point theory in cone metric spaces obtained via the scalarization method, Comput. math. Appl. 59, 3529-3534 (2010) · Zbl 1197.54055 · doi:10.1016/j.camwa.2010.03.046
[87]Kadelburg, Z.; Radenović, S.; Rakočević, V.: A note on the equivalence of some metric and cone metric fixed point results, Appl. math. Lett. 24, 370-374 (2011) · Zbl 1213.54067 · doi:10.1016/j.aml.2010.10.030
[88]Khani, M.; Pourmahdian, M.: On the metrizability of cone metric spaces, Topology appl. 158, No. 2, 190-193 (2011) · Zbl 1206.54026 · doi:10.1016/j.topol.2010.10.016
[89]Feng, Y.; Mao, W.: The equivalence of cone metric spaces and metric spaces, Fixed point theory 11, No. 2, 259-264 (2010) · Zbl 1221.54055 · doi:http://www.math.ubbcluj.ro/~nodeacj/vol__11(2010)_no_2.php
[90]Wong, Yau-Chuen; Ng, Kung-Fu: Partially ordered topological vector spaces, (1973) · Zbl 0269.46007
[91]Vandergraft, J. S.: Newton’s method for convex operators in partially ordered spaces, SIAM J. Numer. anal. 4, No. 3, 406-432 (1967) · Zbl 0161.35302 · doi:10.1137/0704037
[92]Deimling, K.: Nonlinear functional analysis, (1985) · Zbl 0559.47040
[93]Schaefer, H. H.: Topological vector spaces, (1970)
[94]Mohebi, H.: Topical functions and their properties in a class of ordered Banach spaces, part II of the book, , 343-361 (2005) · Zbl 1124.90048
[95]Aliprantis, C. D.; Tourky, R.: Cones and duality, Graduate studies in mathematics 84 (2007)
[96]Drenkoweski, Z.; Migorski, S.; Papagergiou, N. S.: An introduction to nonlinear analysis: applications, (2003)
[97]Krein, M. G.; Rutman, M. A.: Linear operators leaving invariant a cone in a Banach spaces, Uspekhi math. Nauk (N.S.) 3, No. 1, 3-95 (1948) · Zbl 0030.12902 · doi:http://mi.mathnet.ru/eng/umn/v3/i1/p3
[98]Zabreiko, P. P.: K-metric and K-normed linear spaces: survey, Collect. math. 48, No. 4–6, 825-859 (1997) · Zbl 0892.46002
[99]Meir, A.; Keeler, E.: A theorem on contraction mappings, J. math. Anal. appl. 28, 326-329 (1969) · Zbl 0194.44904 · doi:10.1016/0022-247X(69)90031-6
[100]Y. Qing, B.E. Rhoades, T-stability of picard iteration in metric spaces, Fixed Point Theory Appl. 2008, 4 pages, Article ID 418971, doi:10.1155/2008/418971. · Zbl 1145.54328 · doi:10.1155/2008/418971