A Nemytskii-Edelstein type fixed point theorem for partial metric spaces

详细信息    查看全文

• 作者：Naseer Shahzad (1)
  Oscar Valero (2)
  
  1. Department of Mathematics ; King Abdulaziz University ; P.O. Box 80203 ; Jeddah ; 21859 ; Saudi Arabia
  2. Departamento de Ciencias Matem谩ticas e Inform谩tica ; Universidad de las Islas Baleares ; Ctra. de Valldemossa km. 7.5 ; Palma de Mallorca ; 07122 ; Spain
  
• 刊名：Fixed Point Theory and Applications
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：2015
• 期：1
• 全文大小：1,213 KB
• 参考文献：1. Hitzler, P, Seda, AK: Generalized distance functions in the theory of computation. Comput. J. 53, 443-464 (2010) CrossRef
  2. K眉nzi, HPA: Nonsymmetric distances and their associated topologies: about the origins of basic ideas in the area of asymmetric topology. In: Aull, CE, Lowen, R (eds.) Handbook of the History of General Topology, vol.聽3, pp.聽853-968. Kluwer Academic, Dordrecht (2001) CrossRef
  3. Rodr铆guez-L贸pez, J, Romaguera, S: Wijsman and hit-and-miss topologies of quasi-metric spaces. Set-Valued Anal. 11, 323-344 (2003) CrossRef
  4. Romaguera, S, Valero, O: A common mathematical framework for asymptotic complexity analysis and denotational semantics for recursive programs based on complexity spaces. In: Afzal, MT (ed.) Semantics - Advances in Theories and Mathematical Models, vol.聽1, pp.聽99-120. InTech Open Science, Rijeka (2012)
  5. Schellekens, MP: The Smyth completion: a common foundation for denotational semantics and complexity analysis. Electron. Notes Theor. Comput. Sci. 1, 211-232 (1995) CrossRef
  6. Matthews, SG: Partial metric topology. Ann. N.Y. Acad. Sci. 728, 183-197 (1994) CrossRef
  7. Matthews, SG: An extensional treatment of lazy data flow deadlock. Theor. Comput. Sci. 151, 195-205 (1995) CrossRef
  8. Edelstein, M: On fixed and periodic points under contractive mappings. J. Lond. Math. Soc. 37, 74-79 (1962) CrossRef
  9. Kirk, WA: Contraction mappings and extensions. In: Kirk, WA, Sims, B (eds.) Handbook of Metric Fixed Point Theory, pp.聽1-34. Kluwer Academic, Dordrecht (2001) CrossRef
  10. Nemytskii, VV: The fixed point method in analysis. Usp. Mat. Nauk 1, 141-174 (1936) (in Russian)
  11. Reinermann, J, Seifert, GH, Stallbohm, V: Two further applications of the Edelstein fixed point theorem to initial value problems of functional equations. Numer. Funct. Anal. Optim. 1, 233-254 (1979) CrossRef
  12. Shalit, OM: The overdeterminedness of a class of functional equations. Aequ. Math. 74, 242-248 (2007) CrossRef
  13. Stachurski, J: Economic dynamical systems with multiplicative noise. J. Math. Econ. 39, 135-152 (2003) CrossRef
  14. Stratford, B: The topology of language. J. Math. Psychol. 53, 502-509 (2009) CrossRef
  15. Abbas, M, Nazir, T, Romaguera, S: Fixed point results for generalized cyclic contraction mappings in partial metric spaces. Rev. R. Acad. Cienc. Exactas F铆s. Nat., Ser. A Mat. 106, 287-297 (2012) CrossRef
  16. Agarwal, RP, Alghamdi, MA, Shahzad, N: Fixed point theory for cyclic generalized contractions in partial metric spaces. Fixed Point Theory Appl. 2012, Article ID 40 (2012) CrossRef
  17. Alghamdi, MA, Shahzad, N, Valero, O: New results on the Baire partial quasi-metric space, fixed point theory and asymptotic complexity analysis for recursive programs. Fixed Point Theory Appl. 2014, Article ID 14 (2014) CrossRef
  18. Alghamdi, MA, Shahzad, N, Valero, O: Fixed point theorems in generalized metric spaces with applications to computer science. Fixed Point Theory Appl. 2013, Article ID 118 (2013). doi:10.1186/1687-1812-2013-118 CrossRef
  19. Alghamdi, MA, Shahzad, N, Valero, O: On fixed point theory in partial metric spaces. Fixed Point Theory Appl. 2012, Article ID 175 (2012) CrossRef
  20. Altun, I, Erduran, A: Fixed point theorems for monotone mappings on partial metric spaces. Fixed Point Theory Appl. 2011, Article ID 508730 (2011) CrossRef
  21. Aydi, H, Abbas, M, Vetro, C: Common fixed points for multivalued generalized contractions on partial metric spaces. Rev. R. Acad. Cienc. Exactas F铆s. Nat., Ser. A Mat. 108, 483-501 (2014) CrossRef
  22. Aydi, H, Abbas, M, Vetro, C: Partial Hausdorff metric and Nadler鈥檚 fixed point theorem on partial metric spaces. Topol. Appl. 159, 3234-3242 (2012) CrossRef
  23. Aydi, H, Karap谋nar, E, Vetro, C: On Ekeland鈥檚 variational principle in partial metric spaces. Appl. Math. Inf. Sci. 9, 257-262 (2015) CrossRef
  24. Kumam, P, Vetro, C, Vetro, F: Fixed points for weak alpha-psi-contractions in partial metric spaces. Abstr. Appl. Anal. 2013, Article ID 986028 (2013)
  25. Paesano, D, Vetro, C: Multi-valued / F-contractions in 0-complete partial metric spaces with application to Volterra type integral equation. Rev. R. Acad. Cienc. Exactas F铆s. Nat., Ser. A Mat. 108, 1005-1020 (2014) CrossRef
  26. Paesano, D, Vetro, P: Suzuki鈥檚 type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces. Topol. Appl. 164, 125-137 (2014) CrossRef
  27. Romaguera, S: Matkowski鈥檚 type theorems for generalized contractions on (ordered) partial metric spaces. Appl. Gen. Topol. 12, 213-220 (2011)
  28. Romaguera, S: Fixed point theorems for generalized contractions on partial metric spaces. Topol. Appl. 159, 194-199 (2012) CrossRef
  29. Rus, IA: Fixed point theory in partial metric spaces. An. Univ. Vest. Timi艧., Ser. Mat.-Inform. 56, 149-160 (2008)
  30. Samet, B, Vetro, C, Vetro, F: From metric spaces to partial metric spaces. Fixed Point Theory Appl. 2013, Article ID 5 (2013) CrossRef
  31. Shahzad, N, Valero, O: On 0-complete partial metric spaces and quantitative fixed point techniques in denotational semantics. Abstr. Appl. Anal. 2013, Article ID 985095 (2013) CrossRef
  32. Vetro, F, Radenovic, S: Nonlinear psi-quasi-contractions of 膯iri膰-type in partial metric spaces. Appl. Math. Comput. 219, 1594-1600 (2012) CrossRef
  33. Vetro, C, Vetro, F: Metric or partial metric spaces endowed with a finite number of graphs: a tool to obtain fixed point results. Topol. Appl. 159, 911-920 (2012) CrossRef
  34. Kirk, WA, Shahzad, N: Fixed Point Theory in Distance Spaces. Springer, New York (2014) CrossRef
  35. Hitzler, P, Seda, AK: Mathematical Aspects of Logic Programming Semantics. CRC, Boca Raton (2011)
  36. Haghi, RH, Rezapour, S, Shazhad, N: Be careful on partial metric fixed point results. Topol. Appl. 160, 450-454 (2013) CrossRef
  37. Oltra, S, Romaguera, S, S谩nchez-P茅rez, EA: Bicompleting weightable quasi-metric spaces and partial metric spaces. Rend. Circ. Mat. Palermo 51, 151-162 (2002) CrossRef
  38. O鈥橬eill, SJ: Two topologies are better than one. Technical Report 283, Department of Computer Science, University of Warwick (1995)
  39. Romaguera, S, Schellekens, MP: On the structure of the dual complexity space: the general case. EM 13, 249-253 (1998)
  40. Romaguera, S, Schellekens, MP: Quasi-metric properties of complexity spaces. Topol. Appl. 98, 311-322 (1999) CrossRef
  41. Aliprantis, CD, Border, KC: Infinite Dimensional Analysis: A Hitchhiker鈥檚 Guide. Springer, Heidelberg (1999) CrossRef
  
• 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

In 1994, Matthews obtained an extension of the celebrated Banach fixed point theorem to the partial metric framework (Ann. N.Y. Acad. Sci. 728:183-197, 1994). Motivated by the Matthews extension of the Banach theorem, we present a Nemytskii-Edelstein type fixed point theorem for self-mappings in partial metric spaces in such a way that the classical one can be retrieved as a particular case of our new result. We give examples which show that the assumed hypothesis in our new result cannot be weakened. Moreover, we show that our new fixed point theorem allows one to find fixed points of mappings in some cases in which the Matthews result and the classical Nemytskii-Edelstein one cannot be applied. Furthermore, we provide a negative answer to the question about whether our new result can be retrieved as a particular case of the classical Nemytskii-Edelstein one whenever the metrization technique, developed by Hitzler and Seda (Mathematical Aspects of Logic Programming Semantics, 2011), is applied to partial metric spaces.