Advances in Operator Theory

On different type of fixed point theorem for multivalued mappings via measure of noncompactness

Nour El Houda Bouzara and Vatan Karakaya

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


In this paper by using the measure of noncompactness concept, we present new fixed point theorems for multivalued maps. In further we introduce a new class of mappings which are general than Meir-Keeler mappings. Finally, we use these results to investigate the existence of weak solutions to an Evolution differential inclusion with lack of compactness.

Article information

Adv. Oper. Theory Volume 3, Number 2 (2018), 326-336.

Received: 23 April 2017
Accepted: 11 September 2017
First available in Project Euclid: 15 December 2017

Permanent link to this document

Digital Object Identifier

Primary: 47H10: Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30]
Secondary: 47H08: Measures of noncompactness and condensing mappings, K-set contractions, etc. 34G25: Evolution inclusions 34A60: Differential inclusions [See also 49J21, 49K21]

fixed point measure of noncompactness evolution inclusions


Bouzara, Nour El Houda; Karakaya, Vatan. On different type of fixed point theorem for multivalued mappings via measure of noncompactness. Adv. Oper. Theory 3 (2018), no. 2, 326--336. doi:10.15352/AOT.1704-1153.

Export citation


  • N. U. Ahmed, Semigroup theory with applications to systems and control, Harlow John Wiley & Sons Inc. New York, 1991.
  • P. R. Akmerov, M. I. Kamenskiĭ, A. S. Potapov, A. E. Rodkina, and B. N. Sadovskiĭ, Measures of noncompactness and condensing operators, Translated from the 1986 Russian original by A. Iacob. Operator Theory: Advances and Applications, 55. Birkhäuser Verlag, Basel, 1992.
  • J. Banas and K. Goebel, Measure of noncompactness in Banach spaces, Lecture Notes in Pure and Applied Mathematics, 60. Marcel Dekker, Inc., New York, 1980.
  • C. Castaing and M. Valadier, Convex analysis and measurable multifunction, Lecture Notes in Math. 580, Springer-Verlag New York, 1977.
  • K. Deimling, Multivalued differential equations, De Gruyter Series in Nonlinear Analysis and Applications, 1, Walter de Gruyter & Co., Berlin, 1992.
  • B. C. Dhage, Some generalizations of multivalued version of Schauder's fixed point theorem with applications, Cubo 12 (2010), no. 3, 139–151.
  • K. J. Engel and R. Nagel, One-parameter semigroups for linear evolution equations, With contributions by S. Brendle, M. Campiti, T. Hahn, G. Metafune, G. Nickel, D. Pallara, C. Perazzoli, A. Rhandi, S. Romanelli and R. Schnaubelt, Graduate Texts in Mathematics, 194, Springer-Verlag, New York, 2000.
  • K. Fan, Fixed-point and minimax theorems in locally convex topological linear spaces, Proc. Nat. Acad. Sei. U.S.A. 38 (1952), 121–126.
  • L. Górniewicz, Topological fixed point theory of multivalued mappings, Mathematics and its Applications 495, Kluwer Academic Publishers Dordrecht, 1999.
  • M. Kamenskii, V. Obukhovskii, and P. Zecca, Condensing multivalued maps and semilinear differential inclusions in Banach spaces, Walter de Gruyter, Berlin-New York, 2001.
  • M. Kisielewicz, Differential inclusions and optimal control, Kluwer Dordrecht The Netherlands, 1991.
  • A. Meir and E. Keeler, A theorem on contraction mappings, J. Math. Anal. Appl. 28 (1969), 326–329.
  • A. Pazy, Semigroups of linear operators and applications to partial differential equations, Springer-Verlag New York, 1983.
  • A. Samadia and M. B. Ghaemia, An extension of Darbo fixed point theorem and its applications to coupled fixed point and integral equations, Filomat 28 (2014), no. 4, 879–886.
  • H. Thiems, Integrated semigroup and integral solutions to abstract Cauchy problem, J. Math. Anal. Appl. 152 (1990), 416–447.