Common fixed point and best approximation for Banach operator pairs in non-starshaped domain

• Autorzy: Nashine H.
• Języki publikacji: EN

Abstrakty

EN

Common fixed point results for Banach operator pair with generalized nonexpansive mappings in non-starshaped domain of metric space have been obtained in the present work. As application, more general best approximation results in normed space have also been determined. These results extend and generalize various existing known results with the aid of Banach operator pair and without starshaped condition of domain.

Słowa kluczowe

EN

common fixed point; Banach operator; domain

PL

metoda punktu stałego; operator Banacha; dziedzina

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2009
• Tom: Vol. 42, nr 4
• Strony: 797--807
• Opis fizyczny: Bibliogr. 27 poz.

Twórcy

autor

Nashine H.

• Departmet of Mathematics Disha Institute of Management and Technology Satya Vihar, Vidhansabha-Chandrahhuri Marg (Baloda Bazar Road), Mandir Hasaud, Raipur-492101 (Chhattisgarh), India,

Bibliografia

• [1] M. A. Al-Thagafi, Common fixed points and best approximation, J. Approx. Theory, 85 (3) (1996), 318-323.
• [2] B. Brosowski, Fixpunktsätze in der Approximationstheorie, Mathematica (Cluj) 11 (1969), 165-220.
• [3] J. Chen, Z. Li, Common fixed points for Banach operator pairs in best approximation, J. Math. Anal. Appl. 336 (2) (2007), 1466-1475.
• [4] W. G. Dotson, Fixed point theorems for nonexpasive mappings on starshaped subsets of Banach space, J. London Math. Soc. 4 (2) (1972), 408-410.
• [5] W. G. Dotson, On fixed point of nonexpansive mappings in nonconvex sets, Proc. Amer. Math. Soc. 38 (1) (1973), 155-156.
• [6] L. Habiniak, Fixed point theorems and invariant approximations, J. Approx. Theory, 6 (1989), 241-244.
• [7] T. L. Hicks, M. D. Humphries, A note on fixed point theorems, J. Approx. Theory, 34 (1982), 221-225.
• [8] N. Hussain, A. R. Khan, Common fixed point results in best approximation theory, Appl. Math. Lett. 16 (2003), 575-580.
• [9] N. Hussain, D. O’Regan , R. P. Agarwal, Common fixed point and invariant approximation results on non-starshaped domains, Georgian Math. J. 12 (2005), 659-669.
• [10] G. Jungck, Common fixed points for commuting and compatible maps on compacta, Proc. Amer. Math. Soc. 103 (1988), 977-983.
• [11] G. Jungck, Common fixed point theorems for compatible self maps of Hausdorff topological spaces, Fixed Point Theory Appl. 3 (2005), 355-363.
• [12] G. Jungck, N. Hussain, Compatible maps and invariant approximations, J. Math. Anal. Appl. 325 (2007), 1003-1012.
• [13] G. Jungck, S. Sessa, Fixed point theorems in best approximation theory, Math. Japon. 42 (1995), 249-252.
• [14] L. A. Khan, A. R. Khan, An extention of Brosowski-Meinardus theorem on invariant approximations, Approx. Theory Appl. 11 (1995), 1-5.
• [15] A. R. Khan, N. Hussain, A. B. Thaheem, Application of fixed point theorems to invariant approximation, Approx. Theory Appl. 16 (3) (2000), 48-55.
• [16] A. R. Khan, A. Latif, A. Bano, N. Hussain, Some results on common fixed points and best approximation, Tamkang J. Math. 36 (1) (2005), 33-38.
• [17] G. Meinardus, Invarianze bei linearen approximationen, Arch. Rational Mech. Anal. 14 (1963), 301-303.
• [18] H. K. Nashine, Common fixed points versus invariant approximation for noncommutative mappings in a q-normed space, An. Univer. de Vest, Timi. Seria Mat. Infor. 43 (2) (2005), 101-110.
• [19] H. K. Nashine, Invariant approximations, noncommuting, generalized I-nonexpansive mappings and non-starshaped set in q-normed space, Nonlinear Funct. Anal. Appl. (12 (1) (2007), 363-375.
• [20] H. K. Nashine, Invariant approximations, generalized I-nonexpansive mappings and non-convex domain, Tamkang J. Math. 39 (1) (2007), 53-62.
• [21] D. O’Regan, N. Hussain, Generalized I-contractions and pointwise R-subweakly commuting maps, Acta Math. Sinica 23 (8) (2007), 1505-1508.
• [22] S. A. Sahab, M. S. Khan, S. Sessa, A result in best approximation theory, J. Approx. Theory 55 (1988), 349-351.
• [23] N. Shahzad, Invariant approximations and R-subweakly commuting maps, J. Math. Anal. Appl. 257 (2001), 39-45.
• [24] N. Shahzad, Invariant approximations, generalized I-contractions, and R-subweakly commuting maps, Fixed Point Theory Appl. 1 (2005), 79-86.
• [25] S. P. Singh, An application of fixed point theorem to approximation theory, J. Approx. Theory 25 (1979), 89-90.
• [26] A. Smoluk, Invariant approximations, Mat. Stos. 17 (1981), 17-22.
• [27] P. V. Subrahmanyam, An application of a fixed point theorem to best approximation, J. Approx. Theory 20 (1977), 165-172.