Maroua Meneceur, Said Beloul

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In this paper, we discuss the existence of fixed points for Berinde type
multivalued $\theta$- contractions. An example is provided to demonstrate our findings and, as an application, the existence of the solutions for a nonlinear fractional inclusions boundary value problem with integral boundary conditions is given to illustrate the utility of our results.


fixed point, $\theta$ contraction, $\alpha$-admissible, fractional differential inclusions.

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J. Ahmad, A. E. Al-Mazrooei, Y. J. Cho and Y.O. Yang, Fixed point results for generalized

theta-contractions, J. Nonlinear Sci. Appl., 10 (2017), 2350-2358.

H. Asl, J, Rezapour and S, Shahzad, On fixed points of ???? -contractive multifunctions,

Fixed Point Theory Appl. 2012, Article ID 212 (2012).

G. V. R. Babu, M. L. Sandhy and M. V. R. Kameshwari, A note on a fixed point theorem

of Berinde on weak contractions, Carpathian J. Math 24 (2008), 8-12.

S. Beloul, Common fixed point theorems for multi-valued contractions satisfying generalized

condition(B) on partial metric spaces, Facta Univ Nis Ser. Math. Inform., vol. 30 (5) (2015),


S. Beloul, A Common Fixed Point Theorem For Generalized Almost Contractions In

Metric-Like Spaces. Appl. Maths. E - Notes.18(2018), 27-139.

V. Berinde, Approximating f

fixed points of weak '-contractions using the Picard iteration,

Fixed Point Theory, (2003), 131-142.

V. Berinde, Iterative Approximation of Fixed Points, Springer-Verlag, Berlin Heidelberg,

V. Berinde and M. Berinde, On a general class of multi-valued weakly Picard mappings, J.

Math. Anal. Appl., 326 (2007), 772782.

V. Berinde, Some remarks on a xed point theorem for Ciric-type almost contractions,

Carpath. J. Math. 25 (2009), 157-162.

L. B. Ciric, Multi-valued nonlinear contraction mappings, Nonlinear Anal. (2009), 2716-

M. Cosentino and P. Vetro, Fixed point results for F-contractive mappings of Hardy-Rogers-

type, Filomat 28:4 (2014), 715-722.

G. Durmaz, Some theorems for a new type of multivalued contractive maps on metric space,

Turkish J. Math., 41 (2017), 1092-1100.

N.Hussain, P. Salimi and A. Latif, Fixed point results for single and set-valued ???? ???? -

contractive mappings, Fixed Point Theory Appl. 2013, Article ID 212 (2013).

I. Iqbal and N.Hussain, Fixed point results for generalized multivalued nonlinear F-

contractions, J. Nonlinear Sci. Appl. 9 (2016), 5870-5893.

H. Isik and C. Ionescu, New type of multivalued contractions with related results and

applications U.P.B. Sci. Bull., Series A, 80(2) (2018), 13-22.

H. Kaddouri, H. Isik and S. Beloul, On new extensions of F-contraction with an application

to integral inclusions, U.P.B. Sci. Bull., Series A, Vol.81(3) (2019), 31-42.

J. Jachymski, The contraction principle for mappings on a metric space with a graph,

Proc.Amer. Math. Soc., 136 (2008), 1359-1373.

M. Jleli and B. Samet, A new generalization of the Banach contraction principle, J. Inequal.

Appl., 2014:38,(2014), 8 pp.

M. A. Kutbi, W. Sintunavarat, On new xed point results for (; ; )-contractive multi-

valued mappings on -complete metric spaces and their consequences, Fixed Point Theory

Appl., 2015 (2015), 15 pages.

B. Mohammadi, S. Rezapour and N. Shahzad, Some results on xed points of ???? - Ciric

generalized multifunctions, Fixed Point Theory Appl., 2013, Art. No. 24 (2013).

S.B. Nadler, Multi-valued contraction mappings, Pacic J. Math. 30 (1969), 475-488.

J.J. Nieto, and R. Rodriguez-Lopez, Contractive mapping theorems in partially ordered

sets and applications to ordinary dierential equations, Order. 22(2005), 223-239 .

B. Samet, C. Vetro and P. Vetro, Fixed point theorems for ???? -contractive type mappings,

Nonlinear Analysis, vol. 75, no. 4(2012), 2154-2165.

C. Shiau, K.K. Tan and C.S. Wong, Quasi-nonexpansive multi-valued maps and selections,

Fund. Math. 87 (1975), 109-119.

M. Sgroi and C. Vetro, Multi-valued F-contractions and the solution of certain mappings

and integral equations, Filomat, 27:7, (2013), 1259-1268.

A. Tomar, S. Beloul, R. Sharma and Sh. Upadhyay, Common fixed point theorems via

generalized condition (B) in quasi-partial metric space and applications, Demonst.maths

journal 50 (2017),278-298.

M. Usman Ali and T. Kamran, Multivalued F-Contractions and Related Fixed Point Theorems with an Application, Filomat 30:14, (2016), 3779-3793.

F. Vetro, A generalization of Nadler fixed point theorem, Carpathian J. Math.31(3) (2015),


DOI: https://doi.org/10.22190/FUMI210411076M


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