Weak contractions on chains in a generalized metric space with a partial order
详细信息 查看全文
- 作者：Binayak S. Choudhury (1)
Pranati Maity (1) - 关键词：$$G$$ ; metric space ; Partially ordered set ; Weak contraction ; Fixed point ; Orbit ; Monotone property ; 54H25
- 刊名：Afrika Matematika
- 出版年：2014
- 出版时间：September 2014
- 年：2014
- 卷：25
- 期：3
- 页码：745-756
- 全文大小：167 KB
- 参考文献：1. Mustafa, Z., Sims, B.: Some remarks concerning D-metric spaces. Int. Conf. Fixed Point Theory Appl. 22(12), 189鈥?98 (2004)
2. Mustafa, Z., Sims, B.: A new approach to generalized metric spaces. J. Nonlin. Convex. Anal. 7(2), 289鈥?97 (2006)
3. Mustafa, Z., Obiedat, H., Awawdeh, F.: Some of Fixed Point Theorem for Mapping on Complete G-Metric Spaces. Fixed Point Theory Appl. 2008 (2008), Article ID 189870.
4. Abbas, M., Rhoades, B.E.: Common fixed point results for noncommuting mappings without continuity in generalised metric spaces. Appl. Math. Comput. 215, 262鈥?69 (2009) CrossRef
5. Abbas, M., Khan, A.R., Nazir, T.: Coupled common fixed point results in two generalized metric spaces. Appl. Math. Comput. 217, 6328鈥?336 (2011) CrossRef
6. Mustafa, Z., Shatanawi, W., Bataineh, M.: Existence of Fixed Point Result in G-Metric Spaces. Int. J. Math. Math. Sci. 2009 (2009) Article ID 283028.
7. Mustafa, Z., Sims, B.: Fixed Point Theorems for Contractive Mappings in Complete G-metric Space. Fixed Point Theory Appl. 2009 (2009) Article ID 917175.
8. Choudhury, B.S., Maity, P.: Coupled fixed point results in generalized metric spaces. Math. Comput. Model. 54, 73鈥?9 (2011) CrossRef
9. Chugh, R., Kadian, T., Rani, A., Rhoades, B.E.: Property P in G-Metric Spaces. Fixed Point Theory Appl. 2010 (2010), Article ID 401684.
10. Saadati, R., Vaezpour, S.M., Vetro, P., Rhoades, B.E.: Fixed Point Theorems in generalized partially ordered G-metric spaces. Math. Comput. Model. 52, 797鈥?01 (2010) CrossRef
11. Shatanawi, W.: Fixed Point Theory for Contractive Mappings satisfying \(\phi \) -Maps in G-metric Spaces. Fixed Point Theory Appl. 2010 (2010) Article ID 181650.
12. Mustafa, Z., Aydi, H., Karapinar, E.: On common fixed points in G-metric spaces using (E.A) property. Comput. Math. Appl. doi:10.1016/j.camwa.2012.03.051 .
13. Tahat, N., Aydi, H., Karapinar, E., Shatanawi, W.: Common fixed points for single-valued and multi-valued maps satisfying a generalized contraction in G-metric spaces. Fixed Point Theory Appl. 2012, 48 (2012) CrossRef
14. Aydi, H., Karapinar, E., Shatanawi, W.: Tripled coincidence point results for generalized contractions in ordered generalized metric spaces. Fixed Point Theory Appl. 2012, 101 (2012) CrossRef
15. Dehghan Nezhad, A., Mazaheri, H.: A., Mazaheri, H.: New results in G-best approximation in G-metric spaces. Ukrainian Math. J. 62, 648鈥?54 (2010) CrossRef
16. Kada, O., Suzuki, T., Takahashi, W.: Nonconvex minimization theorems and fixed point theorems in complete metric spaces. Math. Japon. 44, 381鈥?91 (1996)
17. Arvanitakis, A.D.: A proof of the generalized Banach contraction conjecture. Proc. Am. Math. Soc. 131, 3647鈥?656 (2003) CrossRef
18. Huang, L.G., Zhang, X.: Cone metric spaces and fixed point theorems of contractive mappings. J. Math. Anal. Appl. 332, 1468鈥?476 (2007) CrossRef
19. Merryfield, J., Rothschild, B.: An application of Ramsey鈥檚 theorem to the Banach contraction principle. Proc. Am. Math. Soc. 130, 927鈥?33 (2002) CrossRef
20. Suzuki, T.: A generalized Banach contraction principle that characterizes metric completeness. Proc. Am. Math. Soc. 136(5), 1861鈥?869 (2008) CrossRef
21. Alber, Ya.I., Guerre-Delabriere, S.: Principles of weakly contractive maps in Hilbert spaces, in:I. Gohberg, Yu. Lyubich(Eds.), New Results in Operator Theory. In : Advances and Appl. 98, Birkh盲user, Basel, 7鈥?2 (1997)
22. Rhoades, B.E.: Some theorems on weakly contractive maps. Nonlin. Anal. TMA 47, 2683鈥?693 (2001) CrossRef
23. Chidume, C.E., Zegeye, H., Aneke, S.J.: Approximation of fixed points of weakly contractive nonself maps in Banach spaces. J. Math. Anal. Appl. 270, 189鈥?99 (2002) CrossRef
24. Choudhury, B.S., Metiya, N.: Fixed points of weak contractions in cone metric spaces. Nonlin. Anal. TMA 72(3鈥?), 1589鈥?593 (2010) CrossRef
25. Choudhury, B.S., Konar, P., Rhoades, B.E., Metiya, N.: Fixed point theorems for generalized weakly contractive maps. Nonlin. Anal. TMA 74(6), 2116鈥?126 (2011) CrossRef
26. Doric, D.: Common fixed point for generalized \((\Psi,\Phi )\) -weak contractions. Appl. Math. Lett. 22(12), 1896鈥?900 (2009) CrossRef
27. Dutta, P. N., Choudhury, B.S.: A Generalisation of Contraction Principle in Metric Spaces. Fixed Point Theory Appl. 2008 (2008), Article ID 406368, p. 8
28. Song, Y.: Coincidence points for noncommuting f-weakly contractive mappings. Int. J. Comput. Appl. Math. (IJCAM) 2(1), 51鈥?7 (2007)
29. Zhang, Q., Song, Y.: Fixed point theory for generalized \(\phi -\) weak contractions. Appl. Math. Lett. 22(1), 75鈥?8 (2009) CrossRef
30. Ciric, L., Cakic, N., Rajovic, M., Ume, J. S.: Monotone generalized nonlinear contractions in partially ordered metric spaces. Fixed Point Theory Appl. 2008 (2008), Article ID 131294.
31. Gnana Bhaskar, T., Lakshmikantham, V.: Fixed point theorems in partially ordered metric spaces and applications. Nonlin. Anal. TMA 65, 1379鈥?393 (2006) CrossRef
32. Harjani, J., Sadarangani, K.: Fixed point theorems for weakly contractive mappings in partially ordered sets. Nonlin. Anal. 71, 3403鈥?410 (2009) CrossRef
33. Nieto, J.J., Rodriguez-Lopez, R.: Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations. Order 22, 223鈥?39 (2005) CrossRef
34. Nieto, J.J., Lopez, R.R.: Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations. Acta. Math. Sinica. (Engl. Ser.) 23(12), 2205鈥?212 (2007) CrossRef
35. Ran, A.C.M., Reurings, M.C.B.: A fixed point theorem in partially ordered sets and some applications to matrix equations. Pror. Am. Math. Soc. 132, 1435鈥?443 (2004) CrossRef
36. Ciric, L.: On some maps with a nonunique fixed point. Publications De L鈥檌nstitut Mathematique 17(31), 52鈥?8 (1974) - 作者单位：Binayak S. Choudhury (1)
Pranati Maity (1)
1. Department of Mathematics, Bengal Engineering and Science University, Shibpur, P.O. - B. Garden, Howrah, 聽711103, West Bengal, India - ISSN：2190-7668
文摘
Weak contraction mapping principle is a generalization of the Banach contraction mapping principle. Weakly contractive mappings are intermediate to contraction mappings and nonexpansive mappings. They have been studied in several contexts. Metric fixed point theory in partially ordered spaces have rapidly developed in recent times. In this paper we extend the concept of weak contraction to subset of a partially ordered generalized metric space which are chains by themselves. It is noted that this weak contraction is different from weak contraction on the whole space. We prove here that under certain assumptions the weakly contractive mapping on certain chains will have a fixed point. Two illustrative examples are given.