ON MULTIVALUED theta-CONTRACTIONS OF BERINDE TYPE WITH AN APPLICATION TO FRACTIONAL DIFFERENTIAL INCLUSIONS
Abstract
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.
Keywords
Full Text:
PDFReferences
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),
-566.
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),
-410.
DOI: https://doi.org/10.22190/FUMI210411076M
Refbacks
- There are currently no refbacks.
ISSN 0352-9665 (Print)