COINCIDENCE AND COMMON FIXED POINT THEOREMS FOR SINGLE-VALUED AND SET-VALUED MAPPINGS
0
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
In the present paper, we prove common fixed point theorems for single-valued and set-valued occasionally weakly compatible mappings in Menger spaces. Our results improve and extend the results of Chen and Chang [Chi-Ming Chen and Tong-Huei Chang, {\it Common fixed point theorems in Menger spaces}, Int. J. Math. Math. Sci. {\bf (2006)}, Article ID 75931, Pages 1--15].
Abstract
In the present paper, we prove common fixed point theorems for single-valued and set-valued occasionally weakly compatible mappings in Menger spaces. Our results improve and extend the results of Chen and Chang [Chi-Ming Chen and Tong-Huei Chang, {\it Common fixed point theorems in Menger spaces}, Int. J. Math. Math. Sci. {\bf (2006)}, Article ID 75931, Pages 1--15].
참고문헌 (50)
- C. T. Aage, "On fixed point theorems in fuzzy metric spaces", Int. J. Open Probl. Comput. Sci. Math, 3(2), pp.123~131 (2010)
- M. Abbas, "Common fixed point theorems for hybrid pairs of occasion- ally weakly compatible mappings satisfying generalized contractive condition of integral type", Fixed Point Theory Appl, 2007, pp.9~ (2007)
- M. Abbas, "Common fixed point theorems for hybrid pairs of occasionally weakly compatible mappings defined on symmetric spaces", Panamer. Math. J, 18(1), pp.55~62 (2008)
- A. Aliouche, "General common fixed point theorems for occasionally weakly compatible hybrid mappings and applications", Novi Sad J. Math, 39(1), pp.89~109 (2009)
- M. A. Al-Thagafi, "Generalized I-nonexpansive selfmaps and invariant approximations", Acta Math. Sinica, 24(5), pp.867~876 (2008)
- I. Altun, "A fixed point theorem for multi-maps satisfying an implicit relation on metrically convex metric spaces", Math. Commun, 11(1), pp.17~23 (2006)
- G. V. R. Babu, "Common fixed point theorems for occasionally weakly compatible maps satisfying property (E.A) using an inequality involving quadratic terms", Appl. Math. Lett, 24(6), pp.975~981 (2011)
- A. Bhatt, "Common fixed point theorems for occasionally weakly compatible mappings under relaxed conditions", Nonlinear Anal, 73(1), pp.176~182 (2010)
- H. Bouhadjera, "A unique common fixed point theorem for occasionally weakly compatible maps", Surv. Math. Appl, 3, pp.177~182 (2008)
- H. Bouhadjera, "A unique common fixed point theorem for occasionally weakly compatible maps", Bull. Allahabad Math. Soc, 24(1), pp.1~6 (2009)
- H. Bouhadjera, "Common fixed point theorems for occasionally weakly compatible maps", Acta Math. Vietnam, 36(1), pp.1~17 (2011)
- J. Caristi, "Fixed point theorems for mappings satisfying inwardness conditions", Trans. Amer. Math. Soc, 215, pp.241~251 (1976)
- H. Chandra, "Fixed point theorems for occasionally weakly compatible maps in probabilistic semi-metric space", Int. J. Math. Anal, 3(9-12), pp.563~570 (2009)
- S. S. Chang, "Fixed Point theory with applications" (1984), Chongqing Publishing House
- T.-H. Chang, "Common fixed point theorems for multivalued mappings", Math. Japon, 41(2), pp.311~320 (1995)
- S. S. Chang, "Nonlinear Operator Theory in Probabilistic Metric Spaces" (2001), Nova Science Publishers, Inc
- S. S. Chang, "Common fixed point theorems for multi-valued mappings in Menger PM-spaces", Math. Japon, 40(2), pp.289~293 (1994)
- S. Chauhan, "Fixed points of occasionally weakly compatible mappings in fuzzy metric spaces", Scientia Magna, 7(2), pp.22~31 (2011)
- S. Chauhan, "Common fixed point theorem for weakly compatible mappings in Menger space", J. Adv. Res. Pure Math, 3(2), pp.107~119 (2011)
- S. Chauhan, "Common fixed point theorems for occasionally weakly compatible mappings using implicit relation", J. Indian Math. Soc, 77(1-4), pp.13~21 (2010)
- C.-M. Chen, "Common fixed point theorems in Menger spaces", Int. J. Math. Math. Sci, 2006, pp.1~15 (2006)
- S. Chuan, "Caristi type hybrid fixed point theorems in Menger probabilistic metric space", Appl. Math. Mech, 18(2), pp.201~209 (1997)
- Lj. B, "´Ciri´c, R. P. Agarwal, and B. Samet, Mixed monotone-generalized contractions in partially ordered probabilistic metric spaces", Fixed Point Theory Appl, 56, pp.13~ (2011)
- Lj. B, "´Ciri´c, B. Samet, and C. Vetro, Common fixed point theorems for families of occasionally weakly compatible mappings", Math. Comput. Modelling, 53(5-6), pp.631~636 (2011)
- O. Hadˇzi´c, "Fixed point theorems for multivalued mappings in probabilistic metric spaces", Mat. Vesnik, 3(2), pp.125~133 (1979)
- O. Hadˇzi´c, "Fixed point theorems in fuzzy metric and probabilistic metric spaces", Zb. Rad. Prirod.-Mat. Fak. Ser. Mat, 24(2), pp.197~209 (1994)
- O. Hadˇzi´c, "Fixed Point Theory in Probabilistic Metric Spaces, In Mathematics and its Applications" (2001), Kluwer Academic Publishers
- O. Hadˇzi´c, "Probabilistic multi-valued contractions and decomposable measures", Internat. J. Uncertain. Fuzziness Knowledge-Based Systems, 10, pp.59~74 (2002)
- O. Hadˇzi´c, "A fixed point theorem for multivalued mappings in probabilistic metric spaces and an application in fuzzy metric spaces", Fuzzy Sets and Systems, 127(2), pp.333~344 (2002)
- G. Jungck, "Compatible mappings and common fixed points", Int. J. Math. Math. Sci, 9(4), pp.771~779 (1986)
- G. Jungck, "Fixed points for set valued functions without continuity", Indian J. Pure Appl. Math, 29(3), pp.227~238 (1998)
- G. Jungck, "Fixed point theorems for occasionally weakly compatible mappings", Fixed Point Theory, 7(2), pp.287~296 (2006)
- M. A. Khan, "Common fixed point theorems for occasionally weakly com- patible maps in fuzzy metric spaces", Far East J. Math. Sci, 41(2), pp.285~293 (2010)
- K. Menger, "Statistical metrics", Proc. Nat. Acad. Sci. U.S.A, 28, pp.535~537 (1942)
- D. Mihet, "Multivalued generalizations of probabilistic contractions", J. Math. Anal. Appl, 304(2), pp.464~472 (2005)
- S. N. Mishra, "Common fixed points of compatible mappings in PM-spaces", Math. Japon, 36(2), pp.283~289 (1991)
- D. O’Regan, "Nonlinear contraction theorems in probabilistic spaces", Appl. Math. Comput, 195(1), pp.86~93 (2008)
- B. D. Pant, "Common fixed point theorem for occasionally weakly com- patible mappings in Menger space", Surv. Math. Appl, 6, pp.1~7 (2011)
- B. D. Pant, "Fixed point theorems for families of occasionally weakly compatible mappings", J. Indian Math. Soc, 79(1-4), pp.127~138 (2012)
- E. Pap, "A fixed point theorem in probabilistic metric spaces and an application", J. Math. Anal. Appl, 202(2), pp.433~449 (1996)
- H. K. Pathak, "Coincidence point theorems for multi-valued and single-valued mappings in Menger PM-spaces", Tamkang J. Math, 26(4), pp.313~319 (1995)
- K. P. R. Sastry, "A critical look at fixed point theorems for occasionally weakly compatible maps in probabilistic semi-metric spaces", Int. J. Math. Anal, 4(27), pp.1341~1348 (2010)
- B. Schweizer, "Probabilistic Metric Spaces, In North-Holland Series in Probability and Applied Mathematics" (1983), North-Holland Publishing Co
- V. M. Sehgal, "Fixed points of contraction mappings on probabilistic metric spaces", Math. Systems Theory, 6, pp.97~102 (1972)
- B. Singh, "A fixed point theorem in Menger space through weak compatibility", J. Math. Anal. Appl, 301(2), pp.439~448 (2005)
- M. Stojakovic, "Coincidence point for multivalued mappings in probabilistic space", Math. Japon, 40(2), pp.283~288 (1994)
- C. Vetro, "Some fixed point theorems for occasionally weakly compatible mappings in probabilistic semi-metric spaces", Int. J. Modern Math, 4(3), pp.277~284 (2009)
- S. Zhang, "On the theory of probabilistic metric spaces with applications", Acta Math. Sinica, 1(4), pp.366~377 (1985)
- S. Zhang, "A set-valued Caristi’s theorem in probabilistic metric spaces", Sichuan Daxue Xuebao, 30(1), pp.12~16 (1993)
- T. ˘Ziki´c-Do˘senovi´c, "A multivalued generalization of Hicks C-contraction", Fuzzy Sets and Systems, 151(3), pp.549~562 (2005)
