Some integral type fixed point theorems in Non-Archimedean Menger PM-Spaces with common property (E.A) and application of functional equations in dynamic programming

详细信息    查看全文

• 作者：Sunny Chauhan (1)
  Stojan Radenovi? (2)
  Mohammad Imdad (3)
  Calogero Vetro (4)
  
• 关键词：t ; norm ; Non ; Archimedean Menger PM ; space ; Weakly compatible mappings ; Property (E.A) ; Common property (E.A) ; Fixed point ; 47H10 ; 54H25
• 刊名：Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas
• 出版年：2014
• 出版时间：September 2014
• 年：2014
• 卷：108
• 期：2
• 页码：795-810
• 全文大小：198 KB
• 参考文献：1. Aamri, M., Moutawakil, D.: El: Some new common fixed point theorems under strict contractive conditions. J. Math. Anal. Appl. 270(1), 181-88 (2002) CrossRef
  2. Aliouche, A.: A common fixed point theorem for weakly compatible mappings in symmetric spaces satisfying a contractive condition of integral type. J. Math. Anal. Appl. 322(2), 796-02 (2006) CrossRef
  3. Altun, I., Türko?lu, D., Rhoades, B.E.: Fixed points of weakly compatible maps satisfying a general contractive condition of integral type. Fixed Point Theory Appl. 2007, Article ID 17301, p 9. doi:10.1155/2007/17301.MR2358022
  4. Baskaran, R., Subrahmanyam, P.V.: A note on the solution of a class of functional equations. Appl. Anal. 22, 235-41 (1986) CrossRef
  5. Bellman, R.: Methods of Nonliner Analysis, vol. II, of Mathematics in Science and Engineering. vol. 61, Academic Press, New York (1973)
  6. Bellman, R., Lee, E.S.: Functional equations in dynamic programming. Aequationes Math. 17, 1-8 (1978) CrossRef
  7. Branciari, A.: A fixed point theorem for mappings satisfying a general contractive condition of integral type. Int. J. Math. Math. Sci. 29(9), 531-36 (2002) CrossRef
  8. Chang, S.S.: Fixed point theorems for single-valued and multi-valued mappings in Non-Archimedean Menger probabilistic metric spaces. Math. Japan. 35(5), 875-85 (1990)
  9. Cho, Y.J., Ha, K.S., Chang, S.S.: Common fixed point theorems for compatible mappings of type \((A)\) in Non-Archimedean Menger PM-spaces. Math. Japon. 46(1), 169-79 (1997)
  10. Cho, Y.J., Kang, S.M., Chang, S.S.: Coincidence point theorems for nonlinear hybrid contractions in Non-Archimedean Menger probabilistic metric spaces. Demonstratio Math. 28(1), 19-2 (1995)
  11. Dimri, R.C., Pant, B.D.: Fixed point theorems in non-Archimedean Menger spaces. J. Kyungpook Math. 31(1), 89-5 (1991)
  12. Djoudi, A., Aliouche, A.: Common fixed point theorems of Gregus type for weakly compatible mappings satisfying contractive conditions of integral type. J. Math. Anal. Appl. 329(1), 31-5 (2007) CrossRef
  13. Fang, J.X., Gao, Y.: Common fixed point theorems under strict contractive conditions in Menger spaces. Nonlinear Anal. 70(1), 184-93 (2009) CrossRef
  14. Imdad, M., Ali, J., Tanveer, M.: Coincidence and common fixed point theorems for nonlinear contractions in Menger PM spaces. Chaos Solitons Fractals 42(5), 3121-129 (2009) CrossRef
  15. Istr??escu, I.: On some fixed point theorems with applications to the Non-Archimedean Menger spaces. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 58(3), 374-79 (1975)
  16. Istr??escu, I.: Fixed point theorems for some classes of contraction mappings on Non-Archimedean probablistic metric space. Publ. Math. Debrecen 25(1-), 29-4 (1978)
  17. Istr??escu, I., Babescu, G.: On the completion on Non-Archimedean probabilistic metric spaces. Seminar de spatii metrice probabiliste, Universitatea Timisoara, Nr. 17, (1979)
  18. Istr??escu, I., Crivat, N.: On some classes of Non-Archimedean probabilistic metric spaces. Seminar de spatii metrice probabiliste, Universitatea Timisoara, Nr. 12, (1974)
  19. Jungck, G.: Compatible mappings and common fixed points. Int. J. Math. Math. Sci. 9(4), 771-79 (1986)
  20. Jungck, G., Rhoades, B.E.: Fixed points for set valued functions without continuity. Indian J. Pure Appl. Math. 29(3), 227-38 (1998)
  21. Khan, M.A.: Sumitra: A common fixed point theorem in Non-Archimedean Menger PM-spaces. Novi Sad J. Math. 39(1), 81-7 (2009)
  22. Kutukcu, S., Sharma, S.: A common fixed point theorem in Non-Archimedean Menger PM-spaces. Demonstratio Math. XLII(4), 837-49 (1996)
  23. Liu, Y., Wu, J., Li, Z.: Common fixed points of single-valued and multi-valued maps. Internat. J. Math. Math. Sci. 19, 3045-055 (2005) CrossRef
  24. Mishra, U., Nashine, H.K., Samet, B., Vetro, C.: Semi-compatible and reciprocally continuous maps in weak Non-Archimedean Menger PM-spaces. Filomat 26(4), 783-92 (2012) CrossRef
  25. Pant, R.P.: Common fixed point theorems for contractive maps. J. Math. Anal. Appl. 226(1), 251-58 (1998) CrossRef
  26. Pathak, H.K., López, R.R., Verma, R.K.: A common fixed point theorem using implicit relation and property (E.A) in metric spaces. Filomat 21(2), 211-34 (2007)
  27. Rao, K.P.R., Ramudu, E.T.: Common fixed point theorem for four mappings in Non-Archimedean Menger PM-spaces. Filomat 20(2), 107-13 (2006) CrossRef
  28. Rhoades, B.E.: Two fixed-point theorems for mappings satisfying a general contractive condition of integral type. Internat. J. Math. Math. Sci. 63, 4007-013 (2003) CrossRef
  29. Schweizer, B., Sklar, A.: Statistical metric spaces. Pacific J. Math. 10, 313-34 (1960) CrossRef
  30. Sehgal, V.M., Bharucha-Reid, A.T.: Fixed points of contraction mappings on probabilistic metric spaces. Math. Syst. Theo. 6(97), 102 (1972)
  31. Sherwood, H.: Complete probabilistic metric spaces. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 20, 117-28 (1971/72)
  32. Singh, B., Jain, A., Agarwal, P.: Semi-compatibility in Non-Archimedean Menger PM-space. Comment. Math 49(1), 15-5 (2009)
  33. Singh, S.L., Pant, B.D.: Common fixed points of weakly commuting mappings on Non-Archimedean Menger PM-spaces. Vikram J. Math. 6, 27-1 (1987)
  34. Singh, S.L., Pant, B.D., Chauhan, S.: Fixed point theorems in Non-Archimedean Menger PM-spaces. J. Nonlinear Anal. Optim. Theory Appl. 3(2), 153-60 (2012)
  35. Suzuki, T.: Meir-Keeler contractions of integral type are still Meir-Keeler contractions. Int. J. Math. Math. Sci. Article ID 39281, (2007)
  36. Vetro, C.: On Branciari’s theorem for weakly compatible mappings. Appl. Math. Lett. 23, 700-05 (2010) CrossRef
  37. Vijayaraju, P., Rhoades, B.E., Mohanraj, R.: A fixed point theorem for a pair of maps satisfying a general contractive condition of integral type. Int. J. Math. Math. Sci. 15, 2359-364 (2005) CrossRef
  
• 作者单位：Sunny Chauhan (1)
  Stojan Radenovi? (2)
  Mohammad Imdad (3)
  Calogero Vetro (4)
  
  1. R. H. Government Postgraduate College, (U. S. Nagar), 244713, Kashipur, Uttarakhand, India
  2. Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120, Beograd, Serbia
  3. Department of Mathematics, Aligarh Muslim Univeristy, Aligarh, 202002, India
  4. Dipartimento di Matematica e Informatica, Università degli Studi di Palermo, via Archirafi 34, 90123, Palermo, Italy
  
• ISSN：1579-1505

文摘

In this paper, we prove some integral type common fixed point theorems for weakly compatible mappings in Non-Archimedean Menger PM-spaces employing common property (E.A). Some examples are furnished which demonstrate the validity of our results. We extend our main result to four finite families of self-mappings employing the notion of pairwise commuting. Moreover, we give an application which supports the usability of our main theorem.