Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A fixed point theorem for the sum of two mappings


Author: Olga Hadžić
Journal: Proc. Amer. Math. Soc. 85 (1982), 37-41
MSC: Primary 47H10
MathSciNet review: 647893
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A generalization of a fixed point theorem of Rzepecki is proved and it is shown that in a paranormed space $ E$ this result yields, under certain circumstances, solutions to the equation $ x = Tx + Sx$ for $ T:E \to E$ either continuous and affine or a generalized contraction, and $ S:K \subseteq E \to E$ compact.


References [Enhancements On Off] (What's this?)

  • [1] O. Hadžić, Fixed point theorems for multivalued mappings in topological vector spaces, Glas. Mat. Ser. III 15(35) (1980), no. 1, 113–119 (English, with Serbo-Croatian summary). MR 586295
  • [2] Shouro Kasahara, On formulations of topological linear spaces by topological semifields, Math. Japon. 19 (1974), 121–134. MR 0367604
  • [3] V. E. Matusov, A generalization of Tihonov’s fixed point theorem, Dokl. Akad. Nauk UzSSR 2 (1978), 12–14 (Russian). MR 0513066
  • [4] A. Meir and Emmett Keeler, A theorem on contraction mappings, J. Math. Anal. Appl. 28 (1969), 326–329. MR 0250291
  • [5] Thomas Riedrich, Vorlesungen über nichtlineare Operatorengleichungen, BSB B. G. Teubner Verlagsgesellschaft, Leipzig, 1976 (German). Mit englischen, französischen und russischen Zusammenfassungen; Teubner-Texte zur Mathematik. MR 0467414
  • [6] Bogdan Rzepecki, Remarks on Schauder’s fixed point principle and its applications, Bull. Acad. Polon. Sci. Sér. Sci. Math. 27 (1979), no. 6, 473–480 (English, with Russian summary). MR 560183
  • [7] K. Zima, On the Schauder’s fixed point theorem with respect to para-normed space, Comment. Math. Prace Mat. 19 (1976/77), no. 2, 421–423. MR 0458260

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47H10

Retrieve articles in all journals with MSC: 47H10


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1982-0647893-X
Keywords: Fixed point, paranormed space, $ \Phi $ paranormed space, generalized contraction
Article copyright: © Copyright 1982 American Mathematical Society