Common fixed points for commuting and compatible maps

• Autorzy: Ismat Beg , Akbar Azam
• Języki publikacji: EN

Abstrakty

EN

Fixed point theorems of multivalued hybrid contractions and Meir-Keeler type multivalued maps are obtained in a metric space. Our results generalize corresponding results of Aubin and Siegel, Dube, Dube and Singh, Hadzic, Iseki, Jungck, Kaneko, Nadler, Park and Bae, Reich, Ray and many others.

Słowa kluczowe

EN

fixed point; multivalued mapping; Meir-Keeler type mapping

Kategorie tematyczne

• 47H04: Set-valued operators
• 47H10: Fixed-point theorems
• 54H25: Fixed-point and coincidence theorems

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
• Rocznik: 1996
• Tom: 16
• Numer: 2
• Strony: 121-135

Daty

wydano

1996

Twórcy

autor

Ismat Beg

• Department of Mathematics, Kuwait University, P.O.Box 5969, Safat 13060, Kuwait

autor

Akbar Azam

• Department of Mathematics, F.G. Post Graduate College, Sector H/8, Islamabad, Pakistan

Bibliografia

• [1] J.P. Aubin, Applied Abstract Analysis, John Wiley and Sons, New York 1977.
• [2] J.P. Aubin and J. Siegel, Fixed points and stationary points of dissipative multivalued maps, Proc. Amer. Math. Soc. 78 (1980), 391-398.
• [3] I. Beg and A. Azam, Fixed points of multivalued locally contractive mappings, Boll. U.M.I. 4-A (7) (1990), 227-233.
• [4] I. Beg and A. Azam, Fixed points of asymptotically regular multivalued mappings, J. Austral. Math. Soc. (Series A) 53 (3) (1992), 313-326.
• [5] L.S. Dube, A theorem on common fixed points of multivalued mappings, Annal. Soc. Sci. Bruxells 84 (4) (1975), 463-468.
• [6] L.S. Dube and S.P. Singh, On multivalued contraction mappings, Bull. Math. de la Soc. Sci. Math. de la. R.S. de Roumanie 14 (62) (3) (1970), 307-310.
• [7] O. Hadzic, Common fixed point theorems for family of mappings in complete metric spaces, Math. Japonica 29 (1984), 127-134.
• [8] T. Hu, Fixed points theorems for multivalued mappings, Canad. Math. Bull. 23 (1980), 193-197.
• [9] K. Iseki, Multivalued contraction mappings in complete metric spaces, Rend. Sem. Math. Univ. Padova 53 (1975), 15-19.
• [10] G. Jungck, Commuting mappings and fixed points, Amer. Math. Monthly 83 (1976), 261-263.
• [11] G. Jungck, Common fixed points for commuting and compatible maps on compacta, Proc. Amer. Math. Soc. 103 (3) (1988), 977-983.
• [12] H. Kaneko, Single valued and multivalued f-contractions, Boll. U.M.I. 4A (1985), 29-33.
• [13] A. Meir and E. Keeler, A theorem on contraction mappings, J. Math. Anal. Appl. 2 (1969), 526-529.
• [14] S.B. Nadler, Jr., Multivalued contraction mappings, Pacific J. Math. 30 (1969), 475-488.
• [15] S. Park and J.S. Bae, Extensions of a fixed point theorem of Meir and Keeler, Ark. Math. 19 (1981), 223-228.
• [16] B.K. Ray, On Ciric's fixed point theorem, Fund. Math. 94 (1977), 221-229.
• [17] S. Reich, Some remarks concerning contraction mappings, Canad. Math. Bull. 14 (1971), 121-124.
• [18] B.E. Rhoades, A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc. 226 (1977), 257-290.
• [19] B.E. Rhoades, S. Park and K.B. Moon, On generalization of Meir-Keeler type contraction maps, J. Math. Anal. Appl. 146 (1990), 482-494.
• [20] C.S. Wong, Common fixed points of two mappings, Pacific J. Math. 49 (1) (1973), 299-312.