Common fixed point of four mappings satisfying implicit generalized weak contractive type condition

• Autorzy: Sedghi S. , Shobe N. , Abbas M.
• Języki publikacji: EN

Abstrakty

EN

In this paper, common fixed point for four maps using an implicit contractive condition in a complete metric space is proved. Some periodic point results for such mappings are also obtained. These results extend and generalize several comparable results in the current literature.

Słowa kluczowe

EN

fixed point; weakly compatible mappings; implicit contractive condition

PL

punkt stały; odwzorowanie zgodne

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2014
• Tom: Vol. 47, nr 2
• Strony: 396--410
• Opis fizyczny: Bibliogr. 22 poz.

Twórcy

autor

Sedghi S.

• Department of Mathematics, Qaemshahr Branch Islamic Azad University, Qaemshahr, Iran

autor

Shobe N.

• Department of Mathematics, Islamic Azad University-Babol Branch, Iran

autor

Abbas M.

• Department of Mathematics, Lahore University of Management Sciences, 54792-Lahore, Pakistan
• School of Mathematics, The University of Birmingham, The Watson Building Edgbaston, Birmingham B152tt, UK

Bibliografia

• [1] M. Abbas, D. Doric, Common fixed point theorem for four mappings satisfying generalized weak contractive condition, Filomat 24(2) (2010), 1–10.
• [2] M. A. Ahmed, Common fixed point theorems for weakly compatible mappings, Rocky Mountain J. Math. 33(4) (2003), 1189–1203.
• [3] Ya. I. Alber, S. Guerre-Delabriere, Principle of weakly contractive maps in Hilbert spaces in New Results in Operator Theory and Its Applications, I. Gohberg and Y. Lyubich Eds., vol. 98 of Operator Theory: Advances and Applications, 7–22, Birkhäuser, Basel, Switzerland, 1997.
• [4] M. A. Al-Thagafi, N. Shahzad, Noncommuting self maps and invariant approximations, Nonlinear Anal. 64 (2006), 2778–2786.
• [5] I. Beg, M. Abbas, Coincidence point and invariant approximation for mapping satisfying generalized weak contractive condition, Fixed Point Theory and Applications, vol. 2006, Article ID 74503, 7 pages, 2006.
• [6] R. Chugh, S. Kumar, Common fixed points for weakly compatible maps, Proc. Indian Acad. Sci. Math. Sci. 111(2) (2001), 241–247.
• [7] Lj. B. Ciric, J. S. Ume, Some common fixed point theorems for weakly compatible mappings, J. Math. Anal. Appl. 314(2) (2006), 488–499.
• [8] D. Doric, Common fixed point for generalized (ψ, φ)-weak contractions, Appl. Math. Lett., in press.
• [9] P. N. Dutta, B. S. Choudhury, A generalization of contraction principle in metric spaces, Fixed Point Theory and Applications, vol. 2008, Article ID 406368, 8 pages.
• [10] J. Gornicki, B. E. Rhoades, A general fixed point theorem for involutions, Indian J. Pure Appl. Math. 27 (1996), 13–23.
• [11] N. Hussain, G. Jungck, Common fixed point and invariant approximation for noncommuting generalized (f, g)-nonexpansive maps, J. Math. Anal. Appl. 321 (2006), 851–861.
• [12] G. Jungck, Compatible mappings and common fixed points, Int. J. Math. Math. Sci. 9(4) (1986), 771–779.
• [13] G. Jungck, Common fixed points for non-continuous non-self maps on non metric spaces, Far East J. Math. Sci. 4(2) (1996), 199–215.
• [14] G. Jungck, B. E. Rhoades, Fixed points for set valued functions without continuity, Indian J. Pure Appl. Math. 29(3) (1998), 227–238.
• [15] G. S. Jeong, B. E. Rhoades, Maps for which F(T) = F(Tⁿ), Fixed Point Theory Appl. 6 (2006), 72–105.
• [16] M. S. Khan, M. Swaleh, S. Sessa, Fixed point theorems by altering distances between the points, Bull. Austral. Math. Soc. 30(1) (1984), 1–9.
• [17] B. E. Rhoades, Some theorems on weakly contractive maps, Nonlinear Anal. 47 (2001), 2683–2693.
• [18] B. E. Rhoades, M. Abbas, Maps satisfying a contractive condition of integral type for which fixed point and periodic point coincide, Int. J. Pure Appl. Math. 45(2) (2008), 225–231.
• [19] S. Sessa, On a weak commutativity condition of mappings in fixed point consideration, Publ. Inst. Math. Soc. 32 (1982), 149–153.
• [20] N. Shahzad, Invariant approximations, generalized I-contractions and R-weakly commuting maps, Fixed Point Theory Appl. 1 (2005), 79–86.
• [21] V. Popa, A general fixed point theorem for four weakly compatible mappings satisfying an implicit relation, Filomat 19 (2005), 45–51.
• [22] Q. Zhang, Y. Song, Fixed point theory for generalized φ-weak contractions, Appl. Math. Lett. 22 (2009), 75–78.