Fixed point theorems for weakly commuting and compatible multi-valued mappings

• Autorzy: Miczko A. , Palczewski B.
• Języki publikacji: EN

Abstrakty

EN

In this paper some common fixed point theorems for single- and multivalued contractive mappings with weak commutativity and compatibility conditions are given. Assumed that single-valued T and S are self-mappings on a generalized (in the sense of Jung [8]) metric space (X,d). Multi-valued mappings F,G : -Cl(X) have values in a space (Cl(X),H) of all nonempty and closed subsets of X, where H is a generalized Hausdorff metric in Cl(X).

Słowa kluczowe

EN

fixed point theorems; metric space; compatible mappings; rational inequality; multivalued functions

PL

twierdzenie o punkcie stałym; przestrzeń metryczna; multifunkcje

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2004
• Tom: Vol. 37, nr 4
• Strony: 803--821
• Opis fizyczny: Bibliogr. 18 poz.

Twórcy

autor

Miczko A.

• Faculty of Applied Physics and Mathematics, Technical University of Gdańsk, G. Narutowicza 11/12, 80-952 Gdańsk, Poland

autor

Palczewski B.

• Faculty of Applied Physics and Mathematics, Technical University of Gdańsk, G. Narutowicza 11/12, 80-952 Gdańsk, Poland

Bibliografia

• [1] Abdalla J. Asad and Zaheer Ahmad, Common fixed point of multivalued mappings with weak commutativity conditions, Radovi Matematicki, 1 (1999), (1), 119-124.
• [2] A. Azam, I. Berg, Coincidence points of compatible multivalued mappings, Demonstratio Math. 29 (1996), 17-22.
• [3] J. G. Borisovitz, B. D. Gelmann, A. D. Myschkis, V. V. Obukhovski, Introduction to multivalued mappings, Voronesh, (1986) (in Russian).
• [4] H. Covitz and S. B. Nadler jr, Multivalued contraction mappings in generalized metric spaces, Israel J. Math. 8 (1970), 5-11.
• [5] S. Czerwik, Fixed point theorems and special solutions of functional equations, Prace Nauk. Uniw. Śląsk. 428, Katowice, (1980).
• [6] J. Dugundji, A. Granas, Fixed Point Theory, PWN, Warszawa 1982.
• [7] B. Fisher, Mapping satisfying rational inequality, Nanta Math. 12 (1979), 195-199.
• [8] C. K. Jung, On generalized complete metric spaces, Bull. Amer. Math. Soc. (1969), 113-116.
• [9] G. Jungck, Compatible mappings and common fixed points, Int. J. Math. & Math. Sci., 9 (4) (1986), 771-779.
• [10] H. Kaneko, A common fixed point of weakly commuting multivalued mappings, Math. Japan. 33 (5) (1988), 741-744.
• [11] H. Kaneko, S. Sessa, Fixed point theorems for compatible multivalued and single valued mappings, Internat. J. Math. Sci. 12 (1989), 257-262.
• [12] T. Kubiak, Two coincidence theorems for contractive type multivalued mappings, Studia Univ. Babes-Bolyai, Mathematica, XXX (1985), 65-68.
• [13] T. Kubiak, Fixed point theorems for contractive type multivalued mappings, Math. Japonica, 30, 1 (1985), 89-101.
• [14] S. B. Nadler jr, Multivalued contraction mappings, Pacific J. Math., 30 (2) (1969), 475-488.
• [15] V. Popa, A coincidence theorem for multifunctions, Review of Research Faculty of Science, Math. Series, 18 (1) (1988), 149-156.
• [16] V. Popa, A general coincidence theorem for compatible multivalued mappings satisfying an implicit relation, Demonstratio Math. 33 (1) (2000), 159-164.
• [17] S. Sessa, On a weak commutativity condition in fixed point considerations, Publ. Inst. Math. (Beograd) 32 (46) (1982), 149-153.
• [18] R. Węgrzyk, Fixed-point theorems for multi-valued functions and their applications to functional equations, Dissertationes Math. 201, PWN, Warszawa (1982).