Some new fixed point results in partial ordered metric spaces via admissible mappings and two new functions
-
1431
Downloads
-
2880
Views
Authors
Xiao-lan Liu
- School of Science, Sichuan University of Science and Engineering, Zigong, Sichuan 643000, China.
- Key Laboratory of Bridge Non-destruction Detecting and Engineering Computing, Sichuan Province University, 643000, China.
Arslan Hojat Ansari
- Department of Mathematics, Payame Noor University, P. O. Box 19395-3697, Tehran, Iran.
- Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran.
Sumit Chandok
- Department of Applied Science, Khalsa College of Engineering and Technology, Punjab Technical University, Armitsar 143-001, India.
Choonkil Park
- Research Institute for Natural Sciences, Hanyang University, Seoul 04763, Republic of Korea.
Abstract
The purpose of this paper is to discuss the existence of fixed points for new classes of mappings defined
on an ordered metric space. The obtained results generalize and improve some fixed point results in the
literature. Some examples show the usefulness of our results.
Share and Cite
ISRP Style
Xiao-lan Liu, Arslan Hojat Ansari, Sumit Chandok, Choonkil Park, Some new fixed point results in partial ordered metric spaces via admissible mappings and two new functions, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 4, 1564--1580
AMA Style
Liu Xiao-lan, Ansari Arslan Hojat, Chandok Sumit, Park Choonkil, Some new fixed point results in partial ordered metric spaces via admissible mappings and two new functions. J. Nonlinear Sci. Appl. (2016); 9(4):1564--1580
Chicago/Turabian Style
Liu, Xiao-lan, Ansari, Arslan Hojat, Chandok, Sumit, Park, Choonkil. "Some new fixed point results in partial ordered metric spaces via admissible mappings and two new functions." Journal of Nonlinear Sciences and Applications, 9, no. 4 (2016): 1564--1580
Keywords
- Common fixed point
- generalized weakly contraction
- generalized metric spaces
- upper class
- C-class function.
MSC
References
-
[1]
M. Abbas, D. Dorić , Common fixed point theorem for four mappings satisfying generalized weak contractive condition, Filomat, 24 (2010), 1-10.
-
[2]
H. Alikhani, S. Rezapour, N. Shahzad, Fixed points of a new type of contractive mappings and multifunctions, Filomat, 27 (2013), 1315-1319.
-
[3]
A. H. Ansari , Note on ''\(\varphi,\psi\)-contractive type mappings and related fixed point'', The 2nd Regional Conference on Mathematics and Applications, Payame Noor University, (2014), 377-380.
-
[4]
A. H. Ansari , Note on ''\(\alpha\)-admissible mappings and related fixed point theorems'', The 2nd Regional Conference on Mathematics and Applications, Payame Noor University, (2014), 373-376.
-
[5]
A. H. Ansari, S. Chandok, C. Ionescu, Fixed point theorems on b-metric spaces for weak contractions with auxiliary functions, J. Inequal. Appl., 2014 (2014), 17 pages.
-
[6]
A. H. Ansari, S. Shukla, Some fixed point theorems for ordered F-(F; h)-contraction and subcontractions in 0-f- orbitally complete partial metric spaces, J. Adv. Math. Stud., 9 (2016), 37-53.
-
[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]
H. Aydi, E. Karapinar, B. Samet , Remarks on some recent fixed point theorems, Fixed Point Theory Appl., 2012 (2012), 6 pages.
-
[9]
G. V. R. Babu, P. D. Sailaja , A fixed point theorem of generalized weakly contractive maps in orbitally complete metric spaces, Thai J. Math., 9 (2011), 1-10.
-
[10]
S. Banach , Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math., 3 (1922), 133-181.
-
[11]
V. Berinde, F. Vetro, Common fixed points of mappings satisfying implicit contractive conditions, Fixed Point Theory Appl., 2012 (2012), 8 pages.
-
[12]
S. K. Chatterjea , Fixed point theorem , C. R. Acad. Bulgare Sci., 25 (1972), 727-730.
-
[13]
B. S. Choudhury, A. Kundu, (\(\psi,\alpha,\beta\))-weak contractions in partially ordered metric spaces, Appl. Math. Lett., 25 (2012), 6-10.
-
[14]
L. B. Ćirić, A generalization of Banach's contraction principle, Proc. Amer. Math. Soc., 45 (1974), 267-273.
-
[15]
B. Damjanović, B. Samet, C. Vetro , Common fixed point theorems for multi-valued maps, Acta Math. Sci. Ser. B, Engl. Ed., 32 (2012), 818-824.
-
[16]
D. Dorić, Common fixed point for generalized (\(\psi,\phi\))-weak contractions, Appl. Math. Lett., 22 (2009), 1896-1900.
-
[17]
P. N. Dutta, B. S. Choudhury, A generalization of contraction principle in metric spaces, Fixed Point Theory Appl., 2008 (2008), 8 pages.
-
[18]
M. Eslamian, A. Abkar , A fixed point theorem for generalized weakly contractive mappings in complete metric space, Ital. J. Pure Appl. Math., (in press),
-
[19]
Z. M. Fadail, A. G. B. Ahmad, A. H. Ansari, S. Radenović, M. Rajović, Some common fixed point results of mappings in 0-complete metric-like spaces via new function, Appl. Math. Sci., 9 (2015), 4109-4127.
-
[20]
M. Geraghty , On contractive mappings, Proc. Amer. Math. Soc., 40 (1973), 604-608.
-
[21]
O. Hadžić, E. Pap, Fixed Point Theory in Probabilistic Metric Spaces, Kluwer Academic Publishers, Dordrecht (2001)
-
[22]
J. Harjani, K. Sadarangani , Generalized contractions in partially ordered metric spaces and applications to ordinarydifferential equations, Nonlinear Anal., 72 (2010), 1188-1197.
-
[23]
E. Hoxha, A. H. Ansari, K. Zoto, Some common fixed point results through generalized altering distances on dislocated metric spaces, Proceedings in EIIC-The 3rd Electronic International Interdisciplinary Conference, (2014), 403-409.
-
[24]
N. Hussain, E. Karapinar, P. Salimi, F. Akbar, \(\alpha\)-admissible mappings and related fixed point theorems, J. Inequal. Appl., 2013 (2013), 11 pages.
-
[25]
N. Hussain, E. Karapinar, P. Salimi, P. Vetro, Fixed point results for \(G^m\)-Meir-Keeler contractive and \(G-\alpha-\psi\)-Meir-Keeler contractive mappings, Fixed Point Theory Appl., 2013 (2013), 14 pages.
-
[26]
N. Hussain, M. A. Kutbi, P. Salimi, Best proximity point results for modified \(\alpha-\psi\)-proximal rational contractions, Abstr. Appl. Anal., 2013 (2013), 14 pages.
-
[27]
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.
-
[28]
R. Kannan, Some results on fixed points, Bull. Calcutta Math. Soc., 60 (1968), 71-76.
-
[29]
R. Kannan , Some results on fixed points-II, Amer. Math. Monthly, 76 (1969), 405-408.
-
[30]
E. Karapinar, P. Kumam, P. Salimi, On \(\alpha-\psi\)-Meir-Keeler contractive mappings, Fixed Point Theory Appl., 2013 (2013), 12 pages.
-
[31]
E. Karapinar, P. Salimi, Fixed point theorems via auxiliary functions, J. Appl. Math., 2012 (2012), 9 pages.
-
[32]
A. Latif, H. Isikb, A. H. Ansari, Fixed points and functional equation problems via cyclic admissible generalized contractive type mappings, J. Nonlinear Sci. Appl., 9 (2016), 1129-1142.
-
[33]
W. Long, S. Khaleghizadeh, P. Salimi, S. Radenović, S. Shukla , Some new fixed point results in partial ordered metric spaces via admissible mappings, Fixed Point Theory Appl., 2014 (2014), 18 pages.
-
[34]
S. G. Matthews, Partial metric topology, Papers on general topology and applications, New York Acad. Sci., New York, (1994), 183-197.
-
[35]
B. Mohammadi, S. Rezapour, N. Shahzad, Some results on fixed points of \(\alpha-\psi\)- Ćirić generalized multifunctions, Fixed Point Theory Appl., 2013 (2013), 10 pages.
-
[36]
Z. Mustafa, B. Sims, A new approach to generalized metric spaces, J. Nonlinear Convex Anal., 7 (2006), 289-297.
-
[37]
S. B. Jr. Nadler , Multi-valued contraction mappings, Pacific J. Math., 30 (1969), 475-488.
-
[38]
A. C. M. Ran, M. C. B. Reurings, A fixed point theorem in partially ordered sets and some application to matrix equations, Proc. Amer. Math. Soc., 132 (2004), 1435-1443.
-
[39]
S. Reich, Kannan's fixed point theorem, Boll. Un. Mat. Ital., 4 (1971), 1-11.
-
[40]
P. Salimi, A. Latif, N. Hussain, Modified \(\alpha-\psi\)-contractive mappings with applications, Fixed Point Theory Appl., 2013 (2013), 19 pages.
-
[41]
P. Salimi, C. Vetro, P. Vetro, Fixed point theorems for twisted \((\alpha,\beta)-\psi\)-contractive type mappings and applications, Filomat, 27 (2013), 605-615.
-
[42]
P. Salimi, C. Vetro, P. Vetro, Some new fixed point results in non-Archimedean fuzzy metric spaces, Nonlinear Anal. Model. Control., 18 (2013), 344-358.
-
[43]
B. Samet, C. Vetro, P. Vetro, Fixed point theorems for \(\alpha-\psi\)-contractive type mappings, Nonlinear Anal., 75 (2012), 2154-2165.
-
[44]
T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc., 136 (2008), 1861-1869.
-
[45]
F. Vetro, On approximating curves associated with nonexpansive mappings, Carpathian J. Math., 27 (2011), 142-147.