PPF dependent fixed point in modified Razumikhin class with applications
-
1512
Downloads
-
2699
Views
Authors
M. Paknazar
- Department of Mathematics, Farhangian University, Iran.
M. A. Kutbi
- Department of Mathematics, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia.
M. Demma
- Università degli Studi di Palermo, Italy.
P. Salimi
- Young Researchers and Elite Club, Islamic Azad University--Rasht Branch, Rasht, Iran.
Abstract
In this paper we introduce the concepts of \(c-C_{\alpha\beta}-\)admissible mapping, \((\alpha\beta)_c-\Theta-\)contraction, weak
\((\alpha\beta)_c-\Theta-\)contraction, generalized \((\alpha\beta)_c-\Theta-\)contraction and establish the existence of PPF dependent fixed
point theorems for such classes of contractive nonself-mappings in the Razumikhin class. We give, also, a
result of existence of a PPF dependent fixed point by a condition of Suzuki type. As applications of our
theorems, we deduce some PPF dependent fixed point theorems for nonself-mappings valued in a Banach
space endowed with a graph or a partial order, and furnish an illustrative example to support our main
theorem.
Share and Cite
ISRP Style
M. Paknazar, M. A. Kutbi, M. Demma, P. Salimi, PPF dependent fixed point in modified Razumikhin class with applications, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 1, 270--286
AMA Style
Paknazar M., Kutbi M. A., Demma M., Salimi P., PPF dependent fixed point in modified Razumikhin class with applications. J. Nonlinear Sci. Appl. (2016); 9(1):270--286
Chicago/Turabian Style
Paknazar, M., Kutbi, M. A., Demma, M., Salimi, P.. "PPF dependent fixed point in modified Razumikhin class with applications." Journal of Nonlinear Sciences and Applications, 9, no. 1 (2016): 270--286
Keywords
- Razumikhin class
- PPF dependent fixed point
- \((\alpha\beta)_c-\Theta-\)contraction
- generalized \((\alpha\beta)_c-\Theta-\)contraction.
MSC
References
-
[1]
M. Abbas, T. Nazir , Common fixed point of a power graphic contraction pair in partial metric spaces endowed with a graph, Fixed Point Theoery Appl., 2013 (2013), 8 pages.
-
[2]
R. P. Agarwal, N. Hussain, M. A. Taoudi , Fixed point theorems in ordered Banach spaces and applications to nonlinear integral equations , Abstr. Appl. Anal., 2012 (2012), 15 pages.
-
[3]
R. P. Agarwal, P. Kumam, W. Sintunavarat , PPF dependent fixed point theorems for an \(\alpha_c\)-admissible non-self mapping in the Razumikhin class, Fixed Point Theory Appl., 2013 (2013), 14 pages.
-
[4]
A. G. B. Ahmad, Z. Fadail, H. K. Nashine, Z. Kadelburg, S. Radenović, Some new common fixed point results through generalized altering distances on partial metric spaces, Fixed Point Theory Appl., 2012 (2012), 15 pages.
-
[5]
S. R. Bernfeld, V. Lakshmikatham, Y. M. Reddy, Fixed point theorems of operators with PPF dependence in Banach spaces, Appl. Anal., 6 (1977), 271-280.
-
[6]
F. Bojor , Fixed point theorems for Reich type contraction on metric spaces with a graph, Nonlinear Anal., 75 (2012), 3895-3901.
-
[7]
L. B. Ćirić, M. Abbas, R. Saadati, N. Hussain , Common fixed points of almost generalized contractive mappings in ordered metric spaces, Appl. Math. Comput., 217 (2011), 5784-5789.
-
[8]
L. B. Ćirić, S. M. Alsulami, P. Salimi, P. Vetro, PPF dependent fixed point results for triangular \(\alpha_c\)-admissible mappings, The Sci. World J., 2014 (2014), 10 pages.
-
[9]
Y. J. Cho, Th. M. Rassias, P. Salimi, M. Turinici, Some PPF dependent fixed point theorems for new contractions in Banach spaces, Preprint, (2014)
-
[10]
M. Cosentino, P. Salimi, P. Vetro, Fixed point results on metric-type spaces , Acta Math. Sci. Ser. B Engl. Ed., 34 (2014), 1237-1253.
-
[11]
B. C. Dhage, Some basic random fixed point theorems with PPF dependence and functional random differential equations, Differ. Equat. Appl., 4 (2012), 181-195.
-
[12]
N. Hussain, S. Al-Mezel, P. Salimi, Fixed points for \(\psi\)-graphic contractions with application to integral equations, Abstr. Appl. Anal., 2013 (2013), 11 pages.
-
[13]
N. Hussain, S. Khaleghizadeh, P. Salimi, F. Akbar, New fixed point results with PPF dependence in Banach spaces endowed with a graph, Abstr. Appl. Anal., 2013 (2013), 9 pages.
-
[14]
N. Hussain, A. R. Khan, R. P. Agarwal, Krasnosel'skii and Ky Fan type fixed point theorems in ordered Banach spaces, J. Nonlinear Convex Anal., 11 (2010), 475-489.
-
[15]
J. Jachymski, The contraction principle for mappings on a metric space with a graph, Proc. Amer. Math. Soc., 136 (2008), 1359-1373.
-
[16]
R. Johnsonbaugh, Discrete Mathematics , Prentice-Hall, Inc., New Jersey (1997)
-
[17]
A. Kaewcharoen, PPF dependent common fixed point theorems for mappings in Bnach spaces, J. Inequal. Appl., 2013 (2013), 14 pages.
-
[18]
F. Khojasteh, E. Karapinar, S. Radenović , \(\theta\)-metric spaces: A generalization, Math. Probl. Eng., 2013 (2013), 7 pages.
-
[19]
M. Jleli, B Samet, A new generalization of the Banach contraction principle, J. Inequal. Appl., 2014 (2014), 8 pages.
-
[20]
A. C. M. Ran, M. C. B. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc., 132 (2003), 1435-1443.
-
[21]
P. Salimi, A. Latif, N. Hussain, Modified \(\alpha-\psi\)-contractive mappings with applications, Fixed Point Theory Appl., 2013 (2013), 19 pages.
-
[22]
P. Salimi, C. Vetro, P. Vetro, Fixed point theorems for twisted \((\alpha,\beta)-\psi\)-contractive type mappings and applications, Filomat, 27 (2013), 605-615.
-
[23]
B. Samet, C. Vetro, P. Vetro, Fixed point theorem for \(\alpha-\psi\) contractive type mappings, Nonlinear Anal., 75 (2012), 2154-2165.
-
[24]
M. Samreen, T. Kamran, Fixed point theorems for integral G-contraction, Fixed Point Theoery Appl., 2013 (2013), 11 pages.
-
[25]
T. Suzuki, A new type of fixed point theorem in metric spaces, Nonlinear Anal., 71 (2009), 5313-5317.