Waek Sub-sequential Continuous Maps in Non Arhimedean Manger PM Space
Abstract
In this paper , we established some common xed point theoremsfor two pairs of self maps by using the more weaker notion of weak sub se-quential continuity (wsc) with compatibility of type (E) in non Archimedean Menger PM space. We improve some earlier results in this line.
References
[1] Achari, J. Fixed Point theorems for a class of mappings on non-Archimedean probabilistic metric spaces. Mathematica, 25(1983), 5-9.
[2] Bouhadjera, H. and Thobie, C.G. Common xed point for pair of sub-compatible maps.
Available online at http://arxiv.org/pdf/0906.3159.pdf
[3] Beloul, S. Common fixed point theorems for weakly sub-sequentially continuous generalized contractions with applications. App. Math. E-notes, 15(2015), 173-186.
[4] Chang, S.S. On some fixed point theorems in probabilistic metric spaces and its applications. Z. Wahrshch. Verw. Gebiete, 63(1983), 463-474.
[5] Chang, S.S. On the theory of probabilistic metric spaces with applications. Acta Math., Sinica, New Series, 1(4)(1985), 366-377.
[6] Chang, S.S. Probabilistic metric spaces and fixed point theorems for mappings. J. Math. Research Expos., 3(1985), 23-28.
[7] Chang, S.S. Fixed point theorems for single-valued and multi-valued mappings in non-Archimedean Menger probabilistic metric spaces. Math. Japonica, 35(5)(1990), 875-885.
[8] Chang, S.S. Probabilistic contractor and the solutions for nonlinear operator equations in PN-spaces, Chinese Sci. Bull., 35(19)(1990), 1451-1454. (In Chinese)
[9] Chang, S.S. and Che, S.B. The metrization of probabilistic metric spaces and fixed points. Chinese Quarterly J. Math., 2(3)(1987), 54-60.
[10] Ciric, Lj. B. On fixed points of generalized contractions of probabilistic metric spaces. Publ. Inst. Math. Beograd, 18(32)(1975), 71-78.
[11] Chang, S. S., Chen, Y. Q. and Guo, J. L. Ekeland's variational principle and Caristi's fixed point theorems in probabilistic metric spaces. Acta Math. Appl. Sincica, 7(3)(1991), 217-229.
[12] Cho, Y. J., Ha, K.S. and Chang, S. S. Common fixed point theorems for compatible mappings of type (A) in non-Archimedean Menger PM-spaces. Math. Japonica, 46(1)(1997), 169-179.
[13] Chang , S.S., Kang, S. and Huang, N. Fixed point theorems for mappings in probabilistic metric spaces with applications. J. Chengdu Univ. Sci. Tech., 57(3)(1991), 1-4.
[14] Hadzic, O. Some theorems on the fixed points in probabilistic metric and Random normed spaces. Boll. Un. Mat. Ital., 13(5)(1981), 1-11.
[15] Hadzic, O. Common fixed point theorems for families of mappings in complete metric space. Math. Japon., 29(1)(1984), 127-134.
[16] Istratescu, V.I. Fixed point theorems for some classes of contraction mappings on non-Archimedean probablistic spaces. Publ. Math. (Debrecen), 25(1-2)(1978), 29-34.
[17] Istratescu, V. I. On common fixed point theorems with applications to the non-Archimedean Menger spaces. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 58(3)(1975), 374-379.
[18] Istratescu, V.I. and Crivat, N. On some classes of non-Archimedean probabilistic metric spaces. Seminar de spatii metrice probabiliste, Univ. Timisoara, Nr. 12(1974).
[19] Jungck, G. Compatible mappings and common fixed points. Internat. J. Math. Math. Sci., 9(4)(1986), 771-779.
[20] Jungck, G. and Rhoades, B. E. Fixed point for set valued functions without continuity. Ind. J. Pure Appl. Maths., 29(3)(1998), 227-238.
[21] Menger, K. Statistical Metrics. Pro. Nat. Acad. Sci. USA, 28(12)(1942), 535- 537.
[22] Mishra, S.N. Common fixed points of compatible mappings in PM- spaces. Math. Japonica, 36(2)(1991), 283-289.
[23] Radu, V. On some contraction principle in Menger spaces. An Univ. Timisoara, Ser. Math., 22(1-2)(1984), 83-88.
[24] Schweizer, B. and Sklar, A. Statistical metric spaces. Pacific. J. Math., 10(1)(1960), 313-334.
[25] Sehgal, V. M. and Bharucha-Reid, A.T. Fixed points of contraction mappings on probabilistic metric spaces. Math. Systems Theory, 6(1)(1972), 97-102.
[26] Schweizer, B. and Sklar, A. Probabilistic metric spaces. North Hollend, Amsterdam 1983.
[27] Singh, S. L. and Pant, B. D. Fixed point theorems for commuting mappings in probabilistic metric space. Honam Math. J., 5(1983), 139-150.
[28] Stojakovic, M. Fixed point theorem in probabilistic metric spaces. Kobe J. Math., 2(1985), 1-9.
[29] Stojakovic, M. Common fixed point theorem in complete metric and probabilistic metric spaces, Bull. Austral. Math. Soc., 36(1987), 73-88.
[30] Stojakovic, M. A common fixed point theorem in probabilistic metric spaces and its applications. Glasnik Math., 23(43)(1988), 203-211.
[31] Sessa, S. On a weak commutativity condition of mappings in a fixed point considerations. Publ. Inst. Math., 32(46)(1986), 149-153.
[32] Singh, M.R. and Mahendra Singh, Y. Compatible mappings of type (E) and common fixed point theorems of Meir-Keller type. Int. J. Math. Sci. Engg. Appl., 1(2) (2007), 299-315.
[33] Singh, M. R. and Mahendra Singh, Y. On various types of compatible maps and fixed point theorems of Meir-Keller type. Hacet. J. Math. Stat., 40(4)(2011), 503-513.
[2] Bouhadjera, H. and Thobie, C.G. Common xed point for pair of sub-compatible maps.
Available online at http://arxiv.org/pdf/0906.3159.pdf
[3] Beloul, S. Common fixed point theorems for weakly sub-sequentially continuous generalized contractions with applications. App. Math. E-notes, 15(2015), 173-186.
[4] Chang, S.S. On some fixed point theorems in probabilistic metric spaces and its applications. Z. Wahrshch. Verw. Gebiete, 63(1983), 463-474.
[5] Chang, S.S. On the theory of probabilistic metric spaces with applications. Acta Math., Sinica, New Series, 1(4)(1985), 366-377.
[6] Chang, S.S. Probabilistic metric spaces and fixed point theorems for mappings. J. Math. Research Expos., 3(1985), 23-28.
[7] Chang, S.S. Fixed point theorems for single-valued and multi-valued mappings in non-Archimedean Menger probabilistic metric spaces. Math. Japonica, 35(5)(1990), 875-885.
[8] Chang, S.S. Probabilistic contractor and the solutions for nonlinear operator equations in PN-spaces, Chinese Sci. Bull., 35(19)(1990), 1451-1454. (In Chinese)
[9] Chang, S.S. and Che, S.B. The metrization of probabilistic metric spaces and fixed points. Chinese Quarterly J. Math., 2(3)(1987), 54-60.
[10] Ciric, Lj. B. On fixed points of generalized contractions of probabilistic metric spaces. Publ. Inst. Math. Beograd, 18(32)(1975), 71-78.
[11] Chang, S. S., Chen, Y. Q. and Guo, J. L. Ekeland's variational principle and Caristi's fixed point theorems in probabilistic metric spaces. Acta Math. Appl. Sincica, 7(3)(1991), 217-229.
[12] Cho, Y. J., Ha, K.S. and Chang, S. S. Common fixed point theorems for compatible mappings of type (A) in non-Archimedean Menger PM-spaces. Math. Japonica, 46(1)(1997), 169-179.
[13] Chang , S.S., Kang, S. and Huang, N. Fixed point theorems for mappings in probabilistic metric spaces with applications. J. Chengdu Univ. Sci. Tech., 57(3)(1991), 1-4.
[14] Hadzic, O. Some theorems on the fixed points in probabilistic metric and Random normed spaces. Boll. Un. Mat. Ital., 13(5)(1981), 1-11.
[15] Hadzic, O. Common fixed point theorems for families of mappings in complete metric space. Math. Japon., 29(1)(1984), 127-134.
[16] Istratescu, V.I. Fixed point theorems for some classes of contraction mappings on non-Archimedean probablistic spaces. Publ. Math. (Debrecen), 25(1-2)(1978), 29-34.
[17] Istratescu, V. I. On common fixed point theorems with applications to the non-Archimedean Menger spaces. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 58(3)(1975), 374-379.
[18] Istratescu, V.I. and Crivat, N. On some classes of non-Archimedean probabilistic metric spaces. Seminar de spatii metrice probabiliste, Univ. Timisoara, Nr. 12(1974).
[19] Jungck, G. Compatible mappings and common fixed points. Internat. J. Math. Math. Sci., 9(4)(1986), 771-779.
[20] Jungck, G. and Rhoades, B. E. Fixed point for set valued functions without continuity. Ind. J. Pure Appl. Maths., 29(3)(1998), 227-238.
[21] Menger, K. Statistical Metrics. Pro. Nat. Acad. Sci. USA, 28(12)(1942), 535- 537.
[22] Mishra, S.N. Common fixed points of compatible mappings in PM- spaces. Math. Japonica, 36(2)(1991), 283-289.
[23] Radu, V. On some contraction principle in Menger spaces. An Univ. Timisoara, Ser. Math., 22(1-2)(1984), 83-88.
[24] Schweizer, B. and Sklar, A. Statistical metric spaces. Pacific. J. Math., 10(1)(1960), 313-334.
[25] Sehgal, V. M. and Bharucha-Reid, A.T. Fixed points of contraction mappings on probabilistic metric spaces. Math. Systems Theory, 6(1)(1972), 97-102.
[26] Schweizer, B. and Sklar, A. Probabilistic metric spaces. North Hollend, Amsterdam 1983.
[27] Singh, S. L. and Pant, B. D. Fixed point theorems for commuting mappings in probabilistic metric space. Honam Math. J., 5(1983), 139-150.
[28] Stojakovic, M. Fixed point theorem in probabilistic metric spaces. Kobe J. Math., 2(1985), 1-9.
[29] Stojakovic, M. Common fixed point theorem in complete metric and probabilistic metric spaces, Bull. Austral. Math. Soc., 36(1987), 73-88.
[30] Stojakovic, M. A common fixed point theorem in probabilistic metric spaces and its applications. Glasnik Math., 23(43)(1988), 203-211.
[31] Sessa, S. On a weak commutativity condition of mappings in a fixed point considerations. Publ. Inst. Math., 32(46)(1986), 149-153.
[32] Singh, M.R. and Mahendra Singh, Y. Compatible mappings of type (E) and common fixed point theorems of Meir-Keller type. Int. J. Math. Sci. Engg. Appl., 1(2) (2007), 299-315.
[33] Singh, M. R. and Mahendra Singh, Y. On various types of compatible maps and fixed point theorems of Meir-Keller type. Hacet. J. Math. Stat., 40(4)(2011), 503-513.
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2016-12-31
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