Common fixed point results with applications in convex metric space

• Autorzy: Abbas M.
• Języki publikacji: EN

Abstrakty

EN

Sufficient conditions for the existence of a common fixed point for uniformly Cq— commuting mappings satisfying a generalized contractive conditions in the framework of a convex metric space are obtained. As an application, related results on best approximation are derived. Our results generalize various known results in the literature.

Słowa kluczowe

EN

convex metric space; common fixed point; uniformly Cq; commuting mapping; asymptotically S; nonexpansive mapping; best approximation

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2008
• Tom: Nr 39
• Strony: 6--15
• Opis fizyczny: Bibliogr. 21 poz.

Twórcy

autor

Abbas M.

• Department of Mathematics, Indiana University Bloomington, IN 47405-7106, Centre for Advanced Studies in Mathematics and Department of Mathematics, Lahore University of Management Sciences, 54792-Lahore, Pakistan,

Bibliografia

• [1]AL-THAGAFI M . A . , Common fixed points and best approximation, J. Approx.Theory, 85(1996), 318-320.
• [2]AL-THAGAFI M . A . , SHAHZAD N., Noncommuting self maps and invariant approximations, Nonlinear Anal, 64(12)(2006), 2778-2786.
• [3]BEG I., SAHU D.R., DIWAN S.D., Approximation of fixed points of uniformly R- subweakly commuting mappings, J. Math. Anal Appl, 324(2006), 1105-1114.
• [4]BEG I ., ABBAS M., Fixed-point theorems for weakly inward multivalued maps on a convex metric space, Demonstratio Math., 39(1)(2006), 149-160.
• [5]BEG I., ABBAS M., Common fixed points and best approximation in convex metric spaces, Soochow J. Math., to appear.
• [6]BEG I., ABBAS M., KIM J.K., Convergence theorems of the iterative schemes in convex metric spaces, Nonlinear Fund. Anal, and Appl, 3(2006), 421-436.
• [7]CHUGH R., KUMAR S., Common fixed points for weakly compatible maps, Proc. Indian Acad. Sci. (Math. Sci.), 111(2)(2001), 241-247.
• [8]CLRLC L., On some discontinuous fixed point theorems in convex metric spaces, Czech. Math. J., 188(43)(1993), 319-326.
• [9]DING X.P., Iteration process for nonlinear mappings in convex metric spaces, J. Math. Anal. Appl, 132(1988), 114-122.
• [10]GOEBEL K . , KIRK W . A . , Topics in Metric Fixed Point Theory, Cambridge University Press, Cambridge 1990.
• [11]GUAY M . D . , SINGH K . L . , WHITFIELD J . H . M . , Fixed point theorems for nonexpansive mappings in convex metric spaces, Proceedings, Conference on Nonlinear Analysis, Marcel Dekker Inc., New York 80(1982), 179-189.
• [12]JUNGCK G . , Common fixed points for commuting and compatible mappings on compacta, Proc. Amer. Math. Soc., 103(1988), 977-983.
• [13]HUSSAIN N., JUNGCK G., Common fixed point and invariant approximation results for noncommuting generalized (/, g) nonexpansive maps, J. Math. Anal Appl, 321(2006), 851-861.
• [14]HUSSAIN N., O'REGAN D., AGARWAL R.P., Common fixed point and invariant approximation results on non-star shaped domains, Georgian Math. J., 12(2005), 659-669.
• [15]HUSSAIN N., RHOADES B.E., Cg-commuting maps and invariant approximations, Fixed Point Theory and Appl., 2006(2006), pp 9.
• [16]MEINARDUS G., Invarianz bei linearn Approximation, Arch. Rat. Mech. Anal, 14(1963), 301-303.
• [17]PANT R . P . , Common fixed points of noncommuting mappings, J. Math. Anal. Appl., 188(1994), 436-440.
• [18]SHAHZAD N., Invariant approximations and R-subweakly commuting maps, J. Math. Anal. Appl, 257(2001), 39-45.
• [19]SHARMA S., DESPNADE B., Discontinuity and weak compatibility in fixed point consideration of Gregus type in convex metric spaces, Fasc. Math.,36(2005), 91-102.
• [20]SINGH S.P., Application of a fixed point theorem to approximation theory, J. Approx. Theory, 25(1979), 88-89.
• [21]TAKAHASHI W., A convexity in metric spaces and nonexpansive mappings I, Kodai Math. Sem. Rep., 22(1970), 142-149.