Ben Amar, A., Tlili, A. (2017). Critical fixed point theorems in Banach algebras under weak topology features. Bulletin of the Iranian Mathematical Society, 43(5), 995-1015.

A. Ben Amar; A. Tlili. "Critical fixed point theorems in Banach algebras under weak topology features". Bulletin of the Iranian Mathematical Society, 43, 5, 2017, 995-1015.

Ben Amar, A., Tlili, A. (2017). 'Critical fixed point theorems in Banach algebras under weak topology features', Bulletin of the Iranian Mathematical Society, 43(5), pp. 995-1015.

Ben Amar, A., Tlili, A. Critical fixed point theorems in Banach algebras under weak topology features. Bulletin of the Iranian Mathematical Society, 2017; 43(5): 995-1015.

Critical fixed point theorems in Banach algebras under weak topology features

^{}Department of Mathematics, Sfax University, Faculty of Sciences, Sfax, LA 1171, 3000, Tunisia.

Receive Date: 28 October 2014,
Revise Date: 02 December 2015,
Accept Date: 25 February 2016

Abstract

In this paper, we establish some new critical fixed point theorems for the sum $AB+C$ in a Banach algebra relative to the weak topology, where $\frac{I-C}{A}$ allows to be noninvertible. In addition, a special class of Banach algebras will be considered.

A.A. Ali and A. Ben Amar, Fixed point theorems for multivalued mappings in Banach algebras and an application for fractional integral inclusion, (Submitted).

J. Banas and M.-A. Taoudi, Fixed points and solutions of operators equations for the weak topology in Banach algebras, Taiwanese J. Math. 18 (2014), no. 3, 871--893.

A. Ben Amar, S. Chouayekh and A. Jeribi, New fixed point theorems in Banach algebras under weak topology features and applications to nonlinear integral equations, J. Funct. Anal. 259 (2010), no. 9, 2215--2237.

A. Ben Amar, S. Chouayekh and A. Jeribi, Fixed point theory in a new class of Banach algebras and application, Afr. Mat. 24 (2013), no. 4, 725--724.

A. Ben Amar, I. Feki and A. Jeribi, Critical Krasnoselskii-Schaefer type fixed point theorems for weakly sequentially continuous mappings and application to a nonlinear integral equation, Fixed Point Theory 17 (2016), no. 1, 3--20.

A. Ben Amar, A. Jeribi and M. Mnif, Some fixed point theorems and application to biological model, Numer. Funct. Anal. Optim. 29 (2008), no. 1-2, 1--23.

A. Ben Amar, A. Jeribi and R. Moalla, Leray-Schauder alternatives in Banach algebras involving three operators with application, Fixed Point Theory 15 (2014), no. 2, 359--372.

A. Ben Amar and D. O'Regan, Measures of weak noncompactness and new fixed point theory in Banach algebras satisfying condition (P), (to appear in Fixed Point Theory).

A. Ben Amar and A. Sikorska-Nowak, On some fixed point theorems for 1-set weakly contractive multi-valued mappings with weakly sequentially closed graph, Advanced in Pure Mathematics 1 (2011), 163--169.

D. W. Boyd and J.S.W. Wong, On nonlinear contractions, Proc. Amer. Math. Soc. 20 (1969) 458--464.

F.S. De Blasi, On a property of the unit sphere in a Banach space, Bull. Math. Soc. Sci.

Math. R. S. Roumanie (N.S) 21 (1997), no. 3-4, 259--262.

B.C. Dhage, A fixed theorem in Banach algebras involving three operators with applications, Kyungpook Math. J. 44 (2004), no. 1, 145--155.

B.C. Dhage, On some nonlinear alternatives of Leray-Schauder type and functional integral equations, Arch. Math. (Brno) 42 (2006), no. 1, 11--23.

B.C. Dhage and D. O'Regan, A fixed point theorem in Banach algebras with applications to functional integral equations, Funct. Differ. Equ. 7 (2000) no. 3-4, 259--267.

J. Diestel, A survey of results related to Dunford-Pettis property, in: Proceedings of the Conference on Integration, Topology, and Geometry in Linear Spaces (Univ. North Carolina, Chapel Hill, N.C. 1979), pp. 15--60, Contemp. Math. 2, Amer. Math. Soc. Providence, RI, 1980.

I. Dobrakov, On representation of linear operators on C0(T;X); Czechoslovak Math. J. 21 (1971) 13--30.

N. Dunford and B. J. Pettis, Linear operations on summable functions, Trans. Amer. Math. Soc. 47 (1940) 323--392 .

R. E. Edwards, Functional Analysis, Theory and Applications, Holt, Rinehart and Winston, New York, 1965.

A. Grothendieck, Sur les applications lineaires faiblement compactes d'espaces du type C(K), Canad. J. Math. 5 (1953) 129--173.

A. Jeribi, N. Kaddachi and B. Krichen, Fixed point theorems of block operator matrices on Banach algebras and an application to functional integral equations, Math. Methods Appl. Sci. 36 (2013), no. 6, 659--673.

A. Jeribi and R. Moalla, Nonlinear alternatives of Leray-Schauder type in Banach algebra involving four operators with application, Numer. Funct. Anal. Optim. 34 (2013), no. 10, 1097--1114.

H. Schaefer, Uber die Methode der a priori-Schranken, Math. Ann. 129 (1955) 415--416. I.I. Vrabie, A.I. Cuza and O. Mayer, C0-Semigroups and Applications, Elsevier, New York, 2003.

E. Zeidler, Nonlinear Functional Analysis and Applications, Springer-Verlag, New York, 1986.