-Metric spaces and some fixed point theorems

详细信息    查看全文

• 作者：Zead Mustafa (3)
  Vahid Parvaneh (4)
  Jamal Rezaei Roshan (5)
  Zoran Kadelburg (6)
  
  3. Department of Mathematics ; Physics and Statistics ; Qatar University ; Doha ; Qatar
  4. Young Researchers and Elite Club ; Kermanshah Branch ; Islamic Azad University ; Kermanshah ; Iran
  5. Department of Mathematics ; Qaemshahr Branch ; Islamic Azad University ; Qaemshahr ; Iran
  6. Faculty of Mathematics ; University of Belgrade ; Beograd ; Serbia
  
• 关键词：b ; metric space ; 2 ; metric space ; partially ordered set ; fixed point ; generalized contractive map
• 刊名：Fixed Point Theory and Applications
• 出版年：2014
• 出版时间：December 2014
• 年：2014
• 卷：2014
• 期：1
• 全文大小：413 KB
• 参考文献：1. Czerwik, S (1993) Contraction mappings in b-metric spaces. Acta Math. Inform. Univ. Ostrav 1: pp. 5-11
  2. Czerwik, S (1998) Nonlinear set-valued contraction mappings in b-metric spaces. Atti Semin. Mat. Fis. Univ. Modena 46: pp. 263-276
  3. G盲hler, VS (1963) 2-metrische R盲ume und ihre topologische Struktur. Math. Nachr 26: pp. 115-118 CrossRef
  4. Hussain, N, Parvaneh, V, Roshan, JR, Kadelburg, Z (2013) Fixed points of cyclic weakly -contractive mappings in ordered b-metric spaces with applications. Fixed Point Theory Appl.
  5. Dung, NV, Le Hang, VT (2013) Fixed point theorems for weak C-contractions in partially ordered 2-metric spaces. Fixed Point Theory Appl.
  6. Naidu, SVR, Prasad, JR (1986) Fixed point theorems in 2-metric spaces. Indian J. Pure Appl. Math 17: pp. 974-993
  7. Aliouche, A, Simpson, C (2012) Fixed points and lines in 2-metric spaces. Adv. Math 229: pp. 668-690 CrossRef
  8. Deshpande, B, Chouhan, S (2011) Common fixed point theorems for hybrid pairs of mappings with some weaker conditions in 2-metric spaces. Fasc. Math 46: pp. 37-55
  9. Freese, RW, Cho, YJ, Kim, SS (1992) Strictly 2-convex linear 2-normed spaces. J. Korean Math. Soc 29: pp. 391-400
  10. Iseki, K (1975) Fixed point theorems in 2-metric spaces. Math. Semin. Notes 3: pp. 133-136
  11. Iseki, K (1976) Mathematics on 2-normed spaces. Bull. Korean Math. Soc 13: pp. 127-135
  12. Lahiri, BK, Das, P, Dey, LK (2011) Cantor鈥檚 theorem in 2-metric spaces and its applications to fixed point problems. Taiwan. J.聽Math 15: pp. 337-352
  13. Lai, SN, Singh, AK (1978) An analogue of Banach鈥檚 contraction principle in 2-metric spaces. Bull. Aust. Math. Soc 18: pp. 137-143 CrossRef
  14. Popa, V, Imdad, M, Ali, J (2010) Using implicit relations to prove unified fixed point theorems in metric and 2-metric spaces. Bull. Malays. Math. Soc 33: pp. 105-120
  15. Ahmed, MA (2009) A common fixed point theorem for expansive mappings in 2-metric spaces and its application. Chaos Solitons Fractals 42: pp. 2914-2920 CrossRef
  16. Geraghty, M (1973) On contractive mappings. Proc. Am. Math. Soc 40: pp. 604-608 CrossRef
  17. 脨uki膰, D, Kadelburg, Z, Radenovi膰, S (2011) Fixed points of Geraghty-type mappings in various generalized metric spaces. Abstr. Appl. Anal.
  18. Berinde, V (2003) On the approximation of fixed points of weak contractive mappings. Carpath. J. Math 19: pp. 7-22
  19. Berinde, V (2004) Approximating fixed points of weak contractions using the Picard iteration. Nonlinear Anal. Forum 9: pp. 43-53
  20. Berinde, V (2008) General contractive fixed point theorems for 膯iri膰-type almost contraction in metric spaces. Carpath. J.聽Math 24: pp. 10-19
  21. Berinde, V (2009) Some remarks on a fixed point theorem for 膯iri膰-type almost contractions. Carpath. J. Math 25: pp. 157-162
  22. Babu, GVR, Sandhya, ML, Kameswari, MVR (2008) A note on a fixed point theorem of Berinde on weak contractions. Carpath. J. Math 24: pp. 8-12
  23. Roshan, JR, Parvaneh, V, Sedghi, S, Shobkolaei, N, Shatanawi, W (2013) Common fixed points of almost generalized -contractive mappings in ordered b-metric spaces. Fixed Point Theory Appl.
  24. 膯iri膰, L, Abbas, M, Saadati, R, Hussain, N (2011) Common fixed points of almost generalized contractive mappings in ordered metric spaces. Appl. Math. Comput 217: pp. 5784-5789 CrossRef
  25. Khan, MS, Swaleh, M, Sessa, S (1984) Fixed point theorems by altering distances between the points. Bull. Aust. Math. Soc 30: pp. 1-9 CrossRef
  26. Fathollahi, S, Hussain, N, Khan, LA (2014) Fixed point results for modified weak and rational 伪-蠄-contractions in ordered 2-metric spaces. Fixed Point Theory Appl.
  
• 刊物主题：Analysis; Mathematics, general; Applications of Mathematics; Differential Geometry; Topology; Mathematical and Computational Biology;
• 出版者：Springer International Publishing
• ISSN：1687-1812

文摘

The aim of this paper is to establish the structure of -metric spaces, as a generalization of 2-metric spaces. Some fixed point results for various contractive-type mappings in the context of ordered -metric spaces are presented. We also provide examples to illustrate the results presented herein, as well as an application to integral equations. MSC: 47H10, 54H25.