Fixed point results for multivalued mappings on a sequence in a closed ball with applications
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Authors
Abdullah Shoaib
- Department of Mathematics and Statistics, Riphah International University, Islamabad - 44000, Pakistan.
Akbar Azam
- Department of Mathematics, COMSATS Institute of Information Technology, Chack Shahzad, Islamabad - 44000, Pakistan.
Muhammad Arshad
- Department of Mathematics, International Islamic University, H-10, Islamabad - 44000, Pakistan.
Eskandar Ameer
- Department of Mathematics, International Islamic University, H-10, Islamabad - 44000, Pakistan.
Abstract
In this paper, we establish fixed point results for semi \(\alpha_*\)-admissible multivalued mappings satisfying a contractive condition
of Reich type only for the elements in a sequence contained in closed ball in a complete dislocated metric space. As an
application, we derive some new fixed point theorems for ordered metric space and metric space endowed with a graph. An
example has been constructed to demonstrate the novelty of our results. Our results unify, extend, and generalize several
comparable results in the existing literature.
Share and Cite
ISRP Style
Abdullah Shoaib, Akbar Azam, Muhammad Arshad, Eskandar Ameer, Fixed point results for multivalued mappings on a sequence in a closed ball with applications, Journal of Mathematics and Computer Science, 17 (2017), no. 2, 308-316
AMA Style
Shoaib Abdullah, Azam Akbar, Arshad Muhammad, Ameer Eskandar, Fixed point results for multivalued mappings on a sequence in a closed ball with applications. J Math Comput SCI-JM. (2017); 17(2):308-316
Chicago/Turabian Style
Shoaib, Abdullah, Azam, Akbar, Arshad, Muhammad, Ameer, Eskandar. "Fixed point results for multivalued mappings on a sequence in a closed ball with applications." Journal of Mathematics and Computer Science, 17, no. 2 (2017): 308-316
Keywords
- Fixed point
- complete dislocated metric space
- closed ball
- \(\alpha_*\)- admissible.
MSC
References
-
[1]
M. U. Ali, T. Kamran, On (\(\alpha^*,\psi\))-contractive multi-valued mappings , Fixed Point Theory Appl., 2013 (2013 ), 7 pages.
-
[2]
A. Amini-Harandi, Metric-like spaces, partial metric spaces and fixed points, Fixed Point Theory Appl., 2012 (2012 ), 10 pages.
-
[3]
M. Arshad, A. Azam, M. Abbas, A. Shoaib, Fixed points results of dominated mappings on a closed ball in ordered partial metric spaces without continuity, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys., 76 (2014), 123–134.
-
[4]
M. Arshad, A. Shoaib, M. Abbas, A. Azam, Fixed points of a pair of Kannan type mappings on a closed ball in ordered partial metric spaces, Miskolc Math. Notes, 14 (2013), 769–784.
-
[5]
M. Arshad, A. Shoaib, I. Beg, Fixed point of a pair of contractive dominated mappings on a closed ball in an ordered dislocated metric space, Fixed Point Theory Appl., 2013 (2013 ), 15 pages.
-
[6]
M. Arshad, A. Shoaib, P. Vetro, Common fixed points of a pair of Hardy Rogers type mappings on a closed ball in ordered dislocated metric spaces, J. Funct. Spaces Appl., 2013 (2013 ), 9 pages.
-
[7]
J. H. Asl, S. Rezapour, N. Shahzad, On fixed points of \(\alpha-\psi\)-contractive multifunctions, Fixed Point Theory Appl. , 2012 (2012 ), 6 pages.
-
[8]
A. Azam, M. Arshad , Fixed points of a sequence of locally contractive multivalued maps , Comput. Math. Appl., 57 (2009), 96–100.
-
[9]
A. Azam, N. Mehmood, J. Ahmad, S. Radenović, Multivalued fixed point theorems in cone b-metric spaces , J. Inequal. Appl., 2013 (2013 ), 9 pages.
-
[10]
F. Bojor, Fixed point theorems for Reich type contractions on metric spaces with a graph , Nonlinear Anal., 75 (2012), 3895–3901.
-
[11]
R. Espínola, W. A. Kirk, Fixed point theorems in R-trees with applications to graph theory, Topology Appl., 153 (2006), 1046–1055.
-
[12]
P. Hitzler, A. K. Seda, Dislocated topologies, J. Electr. Eng., 51 (2000), 3–7.
-
[13]
N. Hussain, J. Ahmad, A. Azam, Generalized fixed point theorems for multi-valued \(\alpha-\psi\)-contractive mappings, J. Inequal. Appl., 2014 (2014 ), 15 pages.
-
[14]
N. Hussain, M. Arshad, A. Shoaib, Fahimuddin, Common fixed point results for \(\alpha-\psi\)-contractions on a metric space endowed with graph, J. Inequal. Appl., 2014 (2014 ), 14 pages.
-
[15]
N. Hussain, P. Salimi, A. Latif, Fixed point results for single and set-valued \(\alpha-\eta-\psi\)-contractive mappings , Fixed Point Theory Appl., 2013 (2013 ), 23 pages.
-
[16]
J. Jachymski, The contraction principle for mappings on a metric space with a graph , Proc. Amer. Math. Soc., 136 (2008), 1359–1373.
-
[17]
E. Karapınar, P. Salimi, Dislocated metric space to metric spaces with some fixed point theorems, Fixed Point Theory Appl., 2013 (2013 ), 19 pages.
-
[18]
M. A. Kutbi, M. Arshad, A. Hussain, On modified (\(\alpha-\eta\))-contractive mappings, Abstr. Appl. Anal., 2014 (2014 ), 7 pages.
-
[19]
S. G. Matthews, Partial metric topology, Papers on general topology and applications, Flushing, NY, (1992), Ann. New York Acad. Sci., New York Acad. Sci., New York, 728 (1994), 183–197.
-
[20]
S. B. Nadler, Jr., Multi-valued contraction mappings, Pacific J. Math., 30 (1969), 475–488.
-
[21]
M. Nazam, M. Arshad, On a fixed point theorem with application to integral equations, Int. J. Anal. , 2016 (2016 ), 7 pages.
-
[22]
M. Nazam, M. Arshad, M. Abbas, Some fixed point results for dualistic rational contractions, Appl. Gen. Topol., 17 (2016), 199–209.
-
[23]
M. Nazam, M. Arshad, C. Park, Fixed point theorems for improved \(\alpha\)-Geraghty contractions in partial metric spaces, J. Nonlinear Sci. Appl., 9 (2016), 4436–4449.
-
[24]
S. Reich, Some remarks concerning contraction mappings, Canad. Math. Bull., 14 (1971), 121–124.
-
[25]
Y.-J. Ren, J.-L. Li, Y.-R. Yu, Common fixed point theorems for nonlinear contractive mappings in dislocated metric spaces, Abstr. Appl. Anal., 2013 (2013 ), 5 pages.
-
[26]
B. Samet, M. Rajović, R. Lazović, R. Stojiljković, Common fixed-point results for nonlinear contractions in ordered partial metric spaces, Fixed Point Theory Appl., 2011 (2011 ), 14 pages.
-
[27]
B. Samet, C. Vetro, P. Vetro, Fixed point theorems for \(\alpha\psi\)-contractive type mappings , Nonlinear Anal., 75 (2012), 2154–2165.
-
[28]
A. Shoaib, M. Arshad, J. Ahmad, Fixed point results of locally contractive mappings in ordered quasi-partial metric spaces, Scientific World J., 2013 (2013 ), 8 pages.
-
[29]
A. Shoaib, M. Arshad, A. Azam, Fixed points of a pair of locally contractive mappings in ordered partial metric spaces, Mat. Vesnik, 67 (2015), 26–38.
-
[30]
A. Shoaib, M. Arshad, M. A. Kutbi, Common fixed points of a pair of Hardy Rogers type mappings on a closed ball in ordered partial metric spaces, J. Comput. Anal. Appl., 17 (2014), 255–264.
-
[31]
J. Tiammee, S. Suantai, Coincidence point theorems for graph-preserving multi-valued mappings, Fixed Point Theory Appl., 2014 (2014 ), 11 pages.