An Extension of Fixed Point Theorems in TVS- Valued Cone Metric Spaces

S.K.Tiwari; Leena Mahar

doi:https://doi.org/10.14445/22315373/IJMTT-V45P513

International Journal of Mathematics Trends and Technology

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Volume 45 | Number 2 | Year 2017 | Article Id. IJMTT-V45P513 | DOI : https://doi.org/10.14445/22315373/IJMTT-V45P513

An Extension of Fixed Point Theorems in TVS- Valued Cone Metric Spaces

S.K.Tiwari, Leena Mahar

Abstract

the purpose of this is to obtain common fixed point theorems for contractive mappings in the setting of topological vector space-valued cone metric spaces. Our results generalize some well- known recent results the literature of [29].

Keywords

common fixed point, contractive mapping, TVS-Valued cone metric space.

References

[1]. Deza, M.M. and Deza, E. , Encyclopedia of Distances ( Springer- Verlag 2009).
[2]. Frechet, M. Sur quelques points du calcul functional. Rendi. Circ. Mat. Palermo,22(1906), 1-74.
[3]. Housdorff, F. Grundzuge der Mengenlehre, Verlag Von Veit & Company, Leipzig (1914). Reprinted by Chelsea Publishing company, New York (1949).
[4]. Kurepa,D.R. Tableaux ramifies d’ensembles. Espaces pseudo-distancies, C.R. Acad Sci.Paris, 198(1934), 1563-1565. [5]. Perov, A.I. On Cauchy problem for a system of ordinary differential equations, Pviblizhen. Met. Reshen. Differ. Uvavan.,2(1964),115-134.
[6]. Proinov, P.D. “ A unified theory of cone metric spaces and its applications to the fixed point,“ In press, http://arxiv.org/abs/1111.4920.
[7]. Zabrejko, P.P. “ K- metric and K-normed linear spaces: survey ,” Collectanea Mathematica, 48(4-6) (1997), 825-859.
[8]. Huang, L.G. and Zhang, X. Cone Metric spaces and Fixed Point Theorems of Contractive mapping,J. Math. Anal. Appl. , 332(2007), 1467-1475.
[9]. Beg, I. Azam, A. and Arshad, M. Common fixed points for maps on topological vector space valued cone metric spaces, Internal. J. Math. Math. Science, 2009(2009).
[10]. Du, W.S. A note on conev metric fixed point theory and its equivalence, Nonliniear Analysis, 72 (5) (2010), 2259-2261.
[11]. Vandergraft, J.S. “ Newton’s method for convex operator in partially ordered spaces,” SIAM Journal on Numerical Analysis, 4 (1967), 406-432.
[12]. Abbas, M. and Jungck, G. “ Common fixed point results for non-commuting mappings without continuity in cone metric spaces,” Journal of Mathematical Analysis and Applications, vol. 341, no. 1, pp. 416-421, 2008.
[13]. Altun, I. Damjanovic, B. and Djoric, D. “ Fixed point and common fixed point theorems on ordered cone metric spaces,” Applied Mathematics Letters, vol. 23, pp. 310-316, 2010.
[14]. Arshad, M. Azam, A. and Vetro, P. “ Some common fixed point results in cone metric spaces,” Fixed point theory and Applications, vol. 2009, Article ID 493965, 11 pages, 2009.
[15]. Azam, A. and Arshad, M. “ Common fixed points of generalized contractive maps in cone metric spaces,” Bulletion of the Iranian Mathematical Society, vol. 35, no. 2, pp. 255-264, 2009.
[16]. Azam, A. and Arshad, M. and Beg, I. “ Common fixed points of two maps in cone metric spaces,” Rendiconti del Circolo Matematico di Palermo, vol. 57, no. 3, pp. 433- 441, 2008.
[17]. Azam, A. and Arshad, M. and Beg, I. “ Banach contraction principle on cone rectangular metric spaces,” Application Analysis and Discrete Mathematics, vol. 3, no. 2, pp. 236-241, 2009.
[18]. Cevik, C. and Altun, I. “ Vector metric spaces and some properties, “ Topological Mathods in Nonlinear Analysis, vol.34, no. 2, pp. 375-382,2009.
[19]. Choudhury, B. S. and Metiya, N. “ Fixed point of weak contractions in cone metric spaces,” Non-linear Analysis: Theory Methods & Applications, vol. 72, no. 3-4, pp.1589-1593, 2010.
[20]. Huang, L.G. and Zhang, X. Cone Metric spaces and Fixed Point Theorems of Contractive mapping, J. of Math. Anal. Appl. ,vol. 332, no. 2 , 1468-1476, 2007.
[21]. Illic, D. and Rakocevic, V. “ Common fixed point for maps on cone metric spaces,” J. of Math. Anal. Appl. ,vol. 341, no. 2 , 876-882, 2008.
[22]. Jankovic, S. Kadelburg, Z. Radenoviv, S. and Rhoades, B.E. “ Assad Kirk-type fixed point theorems for a pair of nonself mappings on cone metric spaces, “ Fixed point theory and Application vol. 2009, Article ID 761086, 16 pages, 2009.
[23]. Kadelburg, Z. Radenovic, S. and Rosic, B. “ Strict contractive condition and common fixed point theorems in cone metric spaces,” Fixed point theory and Application vol. 2009, Article ID 173838, 14 pages, 2009.
[24]. Raja, P. and Vaezpour, S.M. “ Some extensions of Banach’s contraction principle in complete cone metric spaces,” Fixed point theory and Application vol. 2008, Article ID 768294, 11 pages, 2008.
[25]. Radenovic, S. common fixed point theorems in cone metric spaces, ” Computers &Mathematics with Application vol. 58, no. 6 pp. 1273-1278, 2009.
[26]. Rezapour, Sh. And Hamlbarani, R. “ Some notes on the paper” Cone metric spaces and fixed point theorems of contractive mapping”, ,” J. of Math. Anal. Appl. ,vol. 345, no. 2 , pp. 719-724, 2008.
[27]. Vetro, P. “Common fixed point in cone metric spaces,” Rendiconti del Circolo Matematico di Palermo, vol. 56, no. 3 , pp. 464-468, 2007.
[28]. Akabar Azam and B.E.Rhoades, Common fixed point theorems in TVS-Valued cone metric spaces, proceeding of the world congress on engineering 2012 vol.1,4-6.
[29]. Akbar Azam, Ismat Beg and M.Arshad, Fixed point in topological vector space- valued cone metric spaces, Fixed point theory and applications, vol.2010, Article ID6040, 9 pages.
[30]. Topological Vector Space-Valued Cone Metric Spaces and Fixed Point Theorems, Fixed point theory and applications, vol.2010, Article ID170253, 17 pages.

Citation :

S.K.Tiwari, Leena Mahar, "An Extension of Fixed Point Theorems in TVS- Valued Cone Metric Spaces," International Journal of Mathematics Trends and Technology (IJMTT), vol. 45, no. 2, pp. 79-85, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V45P513