Turkish Journal of Analysis and Number Theory
ISSN (Print): 2333-1100 ISSN (Online): 2333-1232 Website: http://www.sciepub.com/journal/tjant
Open Access
Journal Browser
Go
Turkish Journal of Analysis and Number Theory. 2017, 5(2), 69-79
DOI: 10.12691/tjant-5-2-5
Open AccessArticle

Some Fixed Point Theorems for Multivalued Mappings in Banach Algebras and Application to Integral Inclusions

Mohamed Boumaiza1,

1Higher School of Sciences and Technologies of Hammam Sousse, Street Lamin El Abbassi 4011, Hammam Sousse, Tunisia

Pub. Date: April 05, 2017

Cite this paper:
Mohamed Boumaiza. Some Fixed Point Theorems for Multivalued Mappings in Banach Algebras and Application to Integral Inclusions. Turkish Journal of Analysis and Number Theory. 2017; 5(2):69-79. doi: 10.12691/tjant-5-2-5

Abstract

In this paper, we present new multivalued analogues of the krasnoselskii fixed point theorems, for the sum AB+C, where the operators A;B and C are D-set Lipcshitzian with respect to a measure of non-compactness which satisfies condition (m). Our results generalize, prove and extend well-known results in the literature. An application to solving non linear integral inclusion is given.

Keywords:
measure of noncompatness Banach algebras condensing multimap integral equations

Creative CommonsThis work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References:

[1]  A. Aghajani and M. Aliaskari, “Measure of noncompactness in Banach algebra and application to the solvability of integral equation in BC(IR+)'”, Inf. Sci. Lett 4, No 2, 93-99 (2015).
 
[2]  J. Banas and M.A. Taoudi, “Fixed point and solution of operators for the weak topology in Banach algebras”, Taiwainese Journal of Mathematics, 18 (3) (2014), 871-893.
 
[3]  J. Banas M. Lecho, “Fixed point of the product of operators in Banach algebras”, Pan American Math. J., 12 (2002), 101-109.
 
[4]  J. Banas, “Measure on noncompactness in the space of continuous tempered functions”, Demonstration Math. 14 (1981), 127-133.
 
[5]  J. Banas and L. Olszowy, “On a class of measures of noncompactness in Banach algebras and their application to nonlinear integral equations,” Zeitschrift fur Analysis und ihre Anwendungen, vol. 28, no. 4, pp. 475498, 2009.
 
[6]  A. Ben Amar, S. Chouayekh and A. Jerbi, “New fixed point theorems in Banach algebras under weak topology features and application to nonlinear integral equations,” J. Funct. Anal, 259 (9) (2010), 2215-2237.
 
[7]  A. Ben Amar ,S. Chouayekh and A. Jerbi, “Fixed point theory in new class of Banach algebras and application,” Afr. Mat, 24 (2013), 725-724.
 
[8]  A. Ben Amar , M. Boumaiza and D. O'Regan, “Hybrid fixed point theorems for multivalued mappings in Banach algebras under weak topology setting,” J. Fixed Point Theory App, June 2016, Volume 18, Issue 2, pp 327-350.
 
[9]  D W. Boyd and J S W. Wong, “On nonlinear contractions,” Proc. Amer. Math. Soc, 20 (1969), 458-464.
 
[10]  K. Deimling, “Multivalued dfferential equation,” W. de Grayter, 1992.
 
[11]  Dhage B C. “Multivalued operators and fixed point theorems in Banach algebras I,” Taiwainaise Journal of Mathematics, 10 (4) (2006), 1025-1045.
 
[12]  B C. Dhage, “Some generalization of multivalued version of Shauder's fixed point theorem whith application,” CUBO A Mathematical Journal, 12 (03) (2010), 139-151.
 
[13]  B C. Dhage, “On some nonlinear alternatives of Leray-Schauder type and functonal integral equation,” Archivum Mathematicum, Vol. 42 (2006), No. 1, 11-23.
 
[14]  B C. Dhage, “On some variants of Shauder's fixed point principle and application to nonlinear integral equations,” J. Math. Phys. Sci. 25 (1998), 603-611.
 
[15]  B C. Dhage, “On a fixed point theorem in Banach algebra with application,” Applied mathematics Letters 18, 2005, 273-280.
 
[16]  B C. Dhage, “Remarks on two fixed pont theorems involving the sum and the product of two operators,” Comput.Math. Appl. 46 (2003) 1779-1785.
 
[17]  B C. Dhage, “On α-condensing mappings in Banach algebra,” Math Student 63 (1994), 146-152.
 
[18]  B C. Dhage, “Multivalued mappings and fixed point II”, Tamkang Journal of Mathematics, Volume 37, Number 1 (2006).
 
[19]  B C. Dhage, “Local fixed point theory involving three operators in Banach algebra,” Topological Methods in Nonlinear analysis. Volume 24 2004, 377-386.
 
[20]  S. Kakutani, “A generalisation of Brower's fixed point theorems,” Duke Math. J, 8 (1941), 457-459.
 
[21]  W.A. Kirk, B. Sims, “Handbook of Metric fixed point theory,” Kluwer Acad. Publ., Dordrecht, 2001.
 
[22]  D. Kandilakis and N. S. Papageorgiou, On the properties of the Aumann integral with applications to differential inclusions and control systems,” Czechoslovak Math. J. 39 (1989), 1-15.
 
[23]  M.Kamenskii, V.Obukhovskii and P.Zecca, “Condensing multivalued maps and Semilinear Differential inclusion in Banach Spaces,” 2001.
 
[24]  D. O'Regan, “Fixed point theory for closed multifunctios,” Arch. Math (Brno), 34 (1998), 191-197.
 
[25]  E. Zeidler, “Nonlinear Functional Analysis and its application,” Part I Springer Verlag, 1985.
 
[26]  M.Ghiocel, A. Petrusel and G. Petrusel, “Topic in Nonlinear Analyses and application to Matimatical Economics,” Cluj-Napoca 2007.