Fixed point results for admissible mappings with application to integral equations
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Authors
Huaping Huang
- School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing Normal University, Beijing, 100875, China.
Guantie Deng
- School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing Normal University, Beijing, 100875, China.
Stojan Radenović
- Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120, Beograd, Serbia.
Zhanmei Chen
- School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing Normal University, Beijing, 100875, China.
Abstract
This work is intended as an attempt to improve and simplify some recent fixed point theorems for (weak)
\(\alpha\)-admissible mappings and (\(\alpha,\beta\))-admissible mappings from several articles in the framework of \(b\)-metric
spaces. An application in proving the existence of solution for a class of nonlinear integral equations is given.
Share and Cite
ISRP Style
Huaping Huang, Guantie Deng, Stojan Radenović, Zhanmei Chen, Fixed point results for admissible mappings with application to integral equations, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 12, 6260--6273
AMA Style
Huang Huaping, Deng Guantie, Radenović Stojan, Chen Zhanmei, Fixed point results for admissible mappings with application to integral equations. J. Nonlinear Sci. Appl. (2016); 9(12):6260--6273
Chicago/Turabian Style
Huang, Huaping, Deng, Guantie, Radenović, Stojan, Chen, Zhanmei. "Fixed point results for admissible mappings with application to integral equations." Journal of Nonlinear Sciences and Applications, 9, no. 12 (2016): 6260--6273
Keywords
- \(\alpha\)-admissible mapping
- fixed point
- (\(\alpha،\beta\))-admissible mapping
- \(b\)-continuous
- integral equation.
MSC
References
-
[1]
A. Aghajani, M. Abbas, J. R. Roshan, Common fixed point of generalized weak contractive mappings in partially ordered b-metric spaces, Math. Slovaca, 64 (2014), 941--960
-
[2]
I. A. Bakhtin, The contraction mapping principle in almost metric space, (Russian) Functional analysis, Ulyanovsk. Gos. Ped. Inst., Ulyanovsk, 30 (1989), 26--37
-
[3]
S. Banach, Sur les opérations dans les ensembles abstraits et leurs applications aux équations intégrales, Fund. Math., 3 (1922), 133--181
-
[4]
S. Chandok, Some fixed point theorems for (\(\alpha,\beta\))-admissible Geraghty type contractive mappings and related results, Math. Sci. (Springer), 9 (2015), 127--135
-
[5]
S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostraviensis, 1 (1993), 5--11
-
[6]
H.-P. Huang, S. Radenović, J. Vujaković, On some recent coincidence and immediate consequences in partially ordered b-metric spaces, Fixed Point Theory and Appl., 2015 (2015), 18 pages
-
[7]
J. Jachymski, The contraction principle for mappings on a metric space with a graph, Proc. Amer. Math. Soc., 136 (2008), 1359--1373
-
[8]
M. Jovanović, Z. Kadelburg, S. Radenović, Common fixed point results in metric-type spaces, Fixed Point Theory and Appl., 2010 (2010), 15 pages
-
[9]
W. A. Kirk, P. S. Srinivasan, P. Veeramani, Fixed points for mappings satisfying cyclical contractive conditions, Fixed Point Theory, 4 (2003), 79--89
-
[10]
J. J. Nieto, R. Rodíguez-López, Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations, Acta Math. Sin. (Engl. Ser.), 23 (2007), 2205
-
[11]
R. Pant, R. Panicker, Geraghty and Ćirić type fixed point theorems in b-metric spaces, J. Nonlinear Sci. Appl., 9 (2016), 5741--5755
-
[12]
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 (2004), 1435--1443
-
[13]
J. R. Roshan, V. Parvaneh, S. Sedghi, N. Shobkolaei, W. Shatanawi, Common fixed points of almost generalized \((\psi,\varphi)_s\)-contractive mappings in ordered b-metric spaces, Fixed Point Theory and Appl., 2013 (2013), 23 pages
-
[14]
P. Salimi, N. Hussain, S. Shukla, Sh. Fathollahi, S. Radenović, Fixed point results for cyclic \(\alpha-\psi\varphi\)-contractions with application to integral equations, J. Comput. Appl. Math., 290 (2015), 445--458
-
[15]
B. Samet, C. Vetro, P. Vetro, Fixed point theorems for \(\alpha\psi\)-contractive type mappings, Nonlinear Anal., 75 (2012), 2154--2165
-
[16]
S. Sedghi, N. Shobkolaei, J. R. Roshan, W. Shatanawi, Coupled fixed point theorems in Gb-metric spaces, Mat. Vesnik, 66 (2014), 190--201
-
[17]
W. Shatanawi, Fixed and common fixed point for mapping satisfying some nonlinear contraction in b-metric spaces, J. Math. Anal., 7 (2016), 1--12
-
[18]
W. Shatanawi, A. Pitea, R. Lazović, Contraction conditions using comparison functions on b-metric spaces, Fixed Point Theory and Appl., 2014 (2014), 11 pages
-
[19]
W. Sintunavarat, Fixed point results in b-metric spaces approach to the existence of a solution for nonlinear integral equations, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Math. RACSAM, 110 (2016), 585--600
-
[20]
W. Sintunavarat, Nonlinear integral equations with new admissibility types in b-metric spaces, J. Fixed Point Theory Appl., 18 (2016), 397--416