The extension of quadrupled fixed point results in K-metric spaces
محورهای موضوعی : History and biography
1 - Young Researchers and Elite club, Central Tehran Branch,
Islamic Azad University, Tehran, Iran
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Department of Mathematics, Faculty of Science, Islamic Azad University,
Central Tehran Branch, PO. Code 13185-768, Tehran, Iran.
کلید واژه: K-metric spaces, T-contraction, Sequentially, Quadrupled fixed point,
چکیده مقاله :
Recently, Rahimi et al. [Comp. Appl. Math. 2013, In press] defined the conceptof quadrupled fied point in K-metric spaces and proved several quadrupled fixed pointtheorems for solid cones on K-metric spaces. In this paper some quadrupled fixed point resultsfor T-contraction on K-metric spaces without normality condition are proved. Obtainedresults extend and generalize well-known comparable results in the literature.
[1] M. Abbas, B.E. Rhoades, Fixed and periodic point results in cone metric spaces, Appl. Math. Lett. 22 (2009), pp. 511-515.
[2] S. Banach, Sur les oprations dans les ensembles abstraits et leur application aux quations intgrales, Fund. Math. J. 3 (1922), pp. 133-181.
[3] V. Berinde, M. Borcut, Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces, Nonlinear Anal. 74 (2011), pp. 4889-4897.
[4] T. Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. 65 (2006), pp. 1379-1393.
[5] M. Filipovic, L. Paunovic, S. Radenovic, M. Rajovic, Remarks on Cone metric spaces and fixed point theorems of T-Kannan and T-Chatterjea contractive mappings", Math. Comput. Modelling. 54 (2011), pp. 1467-1472.
[6] K. Deimling, Nonlinear Functional Analysis, Springer-Verlag, 1985.
[7] G.E. Hardy, T.D. Rogers, A generalization of a fixed point theorem of Reich, Canad. Math. Bull. 1 (6) (1973), pp. 201-206.
[8] L.G. Huang, X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 332 (2007), pp. 1467-1475.
[9] E. Karapinar, N.V. Luong, Quadruple fixed point theorems for nonlinear contractions, Comput. Math. Appl. 64 (6) (2012) pp. 1839-1848.
[10] J.R. Morales, E. Rojas, Cone metric spaces and fixed point theorems of T-Kannan contractive mappings, Int. J. Math. Anal. 4 (4) (2010), pp. 175-184.
[11] E.M. Mukhamadiev, V.J. Stetsenko, Fixed point principle in generalized metric space, Izvestija AN Tadzh. SSR, z.-mat.igeol.-chem.nauki. 10 (4) (1969), pp. 8-19 (in Russian).
[12] A.I. Perov, The Cauchy problem for systems of ordinary differential equations, Approximate Methods of Solving Differential Equations. Kiev. Naukova Dumka. (1964), pp. 115-134 (in Russian).
[13] H. Rahimi, S. Radenovic, G. Soleimani Rad, P. Kumam, Quadrupled fixed point results in abstract metric spaces, Comp. Appl. Math. (2013), DOI 10.1007/s40314-013-0088-5.
[14] H. Rahimi, B.E. Rhoades, S. Radenovic, G. Soleimani Rad, Fixed and periodic point theorems for T-contractions on cone metric spaces, Filomat. 27 (5) (2013), pp. 881{888 (DOI 10.2298/FIL1305881R).
[15] H. Rahimi, G. Soleimani Rad, Common xed point theorems and c-distance in ordered cone metric spaces, Ukrainian Mathematical Journal, (2013), to appear.
[16] H. Rahimi, G. Soleimani Rad, Fixed point theory in various spaces, Lambert Academic Publishing, Germany, 2013.
[17] H. Rahimi, G. Soleimani Rad, New fixed and periodic point results on cone metric spaces, Journal of Linear and Topological Algebra 1 (1) (2012), pp. 33-40.
[18] H. Rahimi, G. Soleimani Rad, Note on Common fixed point results for noncommuting mappings without continuity in cone metric spaces", Thai. J. Math. 11 (3) (2013), pp. 589-599.
[19] H. Rahimi, G. Soleimani Rad, Some fixed point results in metric type space, J. Basic Appl. Sci. Res. 2 (9)(2012), pp. 9301-9308.
[20] H. Rahimi, G. Soleimani Rad, P. Kumam, Coupled common fixed point theorems under weak contractions in cone metric type spaces , Thai. J. Math, In press.
[21] H. Rahimi, P. Vetro, G. Soleimani Rad, Some common fixed point results for weakly compatible mappings in cone metric type space, Miskolc Math. Notes. 14 (1) (2013), pp. 233-243.
[22] S. Rezapour, R. Hamlbarani, Some note on the paper cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 345 (2008), pp. 719-724.
[23] B.E. Rhoades, A comparison of various denition of contractive mappings, Trans. Amer. Math. Soc. 266 (1977), pp. 257-290.
[24] B. Samet, C. Vetro, Coupled fixed point, f-invariant set and fixed point of N-order, Ann. Funct. Anal. 1 (2) (2010), pp. 46-56.
[25] P. P. Zabrejko, K-metric and K-normed linear spaces: survey, Collect. Math. 48 (4-06)(1997), pp. 825-859.