Two theorems characterizing increasing k-set contraction mappings
Singh, Kanhaya Lal
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti, Tome 59 (1975), p. 749-757 / Harvested from Biblioteca Digitale Italiana di Matematica

Vengono caratterizzati certi tipi di contrazioni, facendone fra l'altro applicazione per ritrovare alcuni risultati di Yamamuro [9].

Publié le : 1975-12-01
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     author = {Kanhaya Lal Singh},
     title = {Two theorems characterizing increasing k-set contraction mappings},
     journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti},
     volume = {59},
     year = {1975},
     pages = {749-757},
     zbl = {0349.47053},
     mrnumber = {0482413},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RLINA_1975_8_59_6_749_0}
}
Singh, Kanhaya Lal. Two theorems characterizing increasing k-set contraction mappings. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti, Tome 59 (1975) pp. 749-757. http://gdmltest.u-ga.fr/item/RLINA_1975_8_59_6_749_0/

[1] Kuratowskii, C. (1966) - Topology, Volume 1 (Section 34), Academic Press. New York. | MR 217751

[2] Darbo, G. (1955) - Punti Uniti in Transformazioni a Codomino Noncompatto, «Rend. Sem. Mat. Padova», 24, 84-92. | MR 70164 | Zbl 0064.35704

[3] Furi, M. and Vignoli, A. (1970) - On α-nonexpansive Mappings and Fixed point Theorems, «Accad. Naz. Lincei», (8), 48, 131-134. | MR 279792

[4] Nussbaum, R. D. (1969) - k-set Contractions, Ph. D. Dissertation, University of Chicago.

[5] Sadovskii, B. N. (1972) - Limit Compact and Condensing Operators, «Russian Mathematical Survey», 27, 85-155. | MR 428132 | Zbl 0243.47033

[6] Petryshyn, W. V. (1975) - Fredholm Alternatives for nonlinear k-ball Contraction Mappings with Applications, «Jour. Differential Equations», 17, 82-95. | MR 355713

[7] Petryshyn, W. V. (1973) - Fixed point Theorems for Various class of 1-set Contractions and 1-ball Contractions in Banach spaces, «Trans. Amer. Math. Soc.», 182, 323-352. | MR 328688

[8] Petryshyn, W. V. (1971) - Structure of Fixed point sets of k-set Contractions, «Arch. Rat. Mech. and Anal.», 40, 312-328. | MR 273480 | Zbl 0218.47028

[9] Yamamuro, Sadayuki (1965) - Monotone Mappings in Topological Linear Spaces, «Jour. Australian Math. Soc.», 5, 25-35. | MR 180842

[10] Nussbaum, R. D. (1971) - Estimates of the Number of Solutions of Operatr Equations, «Applicable Analysis», 1, 183-200. | MR 296780

[11] Yamamuro, Sadayuki (1974) - Differential Calculus in Topological Linear Spaces, Lecture Note No. 374, Spinger Verlag. | MR 488118 | Zbl 0276.58001

[12] Singh, K. L. (1968) - Contraction Mappings and Fixed Point Theorems, «Annales de la Société Scientifique de Bruxelles», 83, 34-44. | MR 246177 | Zbl 0188.55402

[13] Singh, K. L. (1969) - A remark on a Paper by V. V. Bryant, «Amer. Math. Montly», 89.

[14] Singh, K. L. (1969) - Some Fixed Theorems, «Riv. Mat. Univ. Parma», (2) 10, 13-21. | MR 293612

[15] Singh, K. L. (1969) - Some Further Extensions of Banach's Contraction Principles, «Riv. Mat. Univ. Parma» (2), 10, 139-155. | MR 296929 | Zbl 0216.19404

[16] Singh, K. L. (1970) - Nonexpansive Mappings in Banach Spaces, II, «Bull. Math. Rumania», 14 (2), 237-246. | MR 326513

[17] Singh, K. L. - Fixed Point Theorems in Banach Spaces, I, Banaras Hindu University Scientific Journal (In Press).

[18] Singh, K. L. and Srivastava, S. (1971) - On Some Fixed Point Theorems, «Nanta Mathematica» (In Press). | MR 454956

[19] Singh, K. L., Ded, S. and Gardner, B. (1971) - On Contraction Mappings, «Rivista Mat. Univ. Parma», (2), 12. | MR 362281

[20] Singh, K. L. and Singh, B. P. - Proximate Solutions of Nonlinear Functional Equations and a Converse o f Banach's Contraction Principle, «Bharat Ganita» (Submitted). | MR 239069

[21] Singh, K. L. and Singh, B. P. - Quasi-nonexpansive Mappings and Common Fixed Points, «Boll. Un. Mat. Ital.» (Submitted). | MR 530455

[22] Singh, K. L. (1972) - Fixed Point Theorems for Densifying Mappings, I, «The Math. Students», 40, (3), 283-288. | MR 423140

[23] Singh, K. L. - Fixed Point Theorems for Densifying Mappings, «Riv. Mat. Univ. Parma» (accepted). | MR 540680

[24] Singh, K. L. - Construction of Fixed Point Theorems for Densifying Mappings, «Riv. Mat. Univ. Parma» (accepted). | MR 540680

[25] Singh, K. L. - Eigenvalues of Densifying Mappings, «Accad. Naz. dei Lincei» (accepted). | MR 448178

[26] Singh, K. L. - Some Applications of Darbo's Theorems, «Bull. Math. Rumania» (submitted). | MR 435955

[27] Krasnoselskii, M. A. (1964) - Topological Methods for the study of Nonlinear Integral Equations, Pergamon Press, New York.

[28] Vainberg, M. M. (1964) - Variational Methods for the study of Nonlinear Operator Equations, Holden—Day Publishing Co., San Francisco. | MR 176364

[29] Granas, Andrej (1961) - Introduction to the Topology of Function Spaces, Lecture Note, University of Chicago, Spring.

[30] Singh, K. L. - An Invariance of Domain Theorem for Increasing Densifying Mappings, «Fundamenta Mathematica» (submitted).