Fixed point results for \(GP_{(\Lambda,\Theta)}\)-contractive mappings
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Authors
Vahid Parvaneh
- Department of Mathematics, College of Science, Gilan-E-Gharb Branch, Islamic Azad University, Gilan-E-Gharb, Iran.
Peyman Salimi
- Young Researchers and Elite Club, Rasht Branch, Islamic Azad University, Rasht, Iran.
Pasquale Vetro
- Dipartimento di Matematica e Informatica, Universita degli Studi di Palermo, via Archira 34, 90123 Palermo, Italy.
Akbar Dehghan Nezhad
- Department of Mathematics, Yazd University, Yazd, Iran.
Stojan Radenović
- Faculty of Mathematics, University of Belgrade, Studentski trg 16, 11000 Beograd, Serbia.
Abstract
In this paper, we introduce new notions of \(GP\)-metric space and \(GP_{(\Lambda,\Theta)}\)-contractive mapping and then
prove some fixed point theorems for this class of mappings. Our results extend and generalized Banach
contraction principle to \(GP\)-metric spaces. An example shows the usefulness of our results.
Share and Cite
ISRP Style
Vahid Parvaneh, Peyman Salimi, Pasquale Vetro, Akbar Dehghan Nezhad, Stojan Radenović, Fixed point results for \(GP_{(\Lambda,\Theta)}\)-contractive mappings, Journal of Nonlinear Sciences and Applications, 7 (2014), no. 3, 150--159
AMA Style
Parvaneh Vahid, Salimi Peyman, Vetro Pasquale, Nezhad Akbar Dehghan, Radenović Stojan, Fixed point results for \(GP_{(\Lambda,\Theta)}\)-contractive mappings. J. Nonlinear Sci. Appl. (2014); 7(3):150--159
Chicago/Turabian Style
Parvaneh, Vahid, Salimi, Peyman, Vetro, Pasquale, Nezhad, Akbar Dehghan, Radenović, Stojan. "Fixed point results for \(GP_{(\Lambda,\Theta)}\)-contractive mappings." Journal of Nonlinear Sciences and Applications, 7, no. 3 (2014): 150--159
Keywords
- \(GP\)-metric spaces
- \(GP_(\Lambda
- \Theta)\)-contractive mappings
- \(O-GP\)-continuous.
MSC
References
-
[1]
M. Abbas, T. Nazir, P. Vetro, Common fixed point results for three maps in G-metric spaces, Filomat, 25:4 (2011), 1-17.
-
[2]
H. Aydi, M. Abbas, C. Vetro, Partial Hausdorff metric and Nadler's fixed point theorem on partial metric spaces, Topology Appl., 159 (2012), 3234-3242.
-
[3]
H. Aydi, E. Karapinar, P. Salimi , Some fixed point results in GP-metric spaces, J. Appl. Math., Article ID 891713. (2012)
-
[4]
H. Aydi, W. Shatanawi, C. Vetro , On generalized weak G-contraction mapping in G-metric spaces, Comput. Math. Appl., 62 (2011), 4223-4229.
-
[5]
H. Aydi, C. Vetro, W. Sintunavarat, P. Kumam , Coincidence and fixed points for contractions and cyclical contractions in partial metric spaces, Fixed Point Theory Appl., 2012: 124 (2012)
-
[6]
S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales , Fund. Math., 3 (1922), 133-181.
-
[7]
V. Berinde, F. Vetro, Common fixed points of mappings satisfying implicit contractive conditions, Fixed Point Theory Appl., 2012:105 (2012)
-
[8]
S. K. Chatterjea, Fixed point theorem, Comte Rend. Acad. Bulgare Sc., 25 (1972), 727-730.
-
[9]
S. Chauhan, B. D. Pant , Fixed point theorems for compatible and subsequentially continuous mappings in Menger spaces, J. Nonlinear Sci. Appl., 7 (2) (2014), 78-89.
-
[10]
Lj. B. Ćirić , A Generalization of Banach's contraction principle, Proc. Amer. Math. Soc., 45 (1974), 267-273.
-
[11]
Lj. B. Ćirić, B. Samet, H. Aydi, C. Vetro , Common fixed points of generalized contractions on partial metric spaces and an application, Appl. Math. Comput., 218 (2011), 2398-2406.
-
[12]
L. W. Cohen, C. Goffman, The topology of ordered Abelian groups, Trans. Amer. Math. Soc., 67 (1949), 310-319.
-
[13]
B. Damjanovic, B. Samet, C. Vetro, Common fixed point theorems for multi-valued maps, Acta Math. Sci. Ser. B Engl. Ed., 32 (2012), 818-824.
-
[14]
C. Di Bari, P. Vetro, Fixed points for weak \(\phi\)-contractions on partial metric spaces, Int. J. of Engineering, Contemporary Mathematics and Sciences, 1 (2011), 5-13.
-
[15]
C. Di Bari, M. Milojević, S, Radenović, P. Vetro , Common fixed points for self-mappings on partial metric spaces, Fixed Point Theory Appl., 2012:140 (2012)
-
[16]
C. Di Bari, Z. Kadelburg, H. Nashine, S. Radenović, Common fixed points of g-quasicontractions and related mappings in 0-complete partial metric spaces, Fixed Point Theory Appl., 2012:113 (2012)
-
[17]
R. Kannan, Some results on fixed points, Bull. Cal. Math. Soc., 60 (1968), 71-76.
-
[18]
V. La Rosa, P. Vetro, Fixed points for Geraghty-contractions in partial metric spaces, J. Nonlinear Sci. Appl., 7 (1) (2014), 1-10.
-
[19]
S. G. Matthews, Partial metric topology , in: Proc. 8th Summer Conference on General Topology and Applications, Ann. New York Acad. Sci., 728 (1994), 183-197.
-
[20]
D. Miheţ , Common coupled fixed point theorems for contractive mappings in fuzzy metric spaces , J. Nonlinear Sci. Appl., 6 (1) (2013), 35-40.
-
[21]
Z. Mustafa, B. Sims, A new approach to generalized metric spaces, J. Nonlinear Convex Anal., 7 (2) (2006), 289-297.
-
[22]
Z. Mustafa, H. Obiedat, A fixed point theorem of Reich in G-metric spaces, CUBO, 12 (1) (2010), 83-93.
-
[23]
Z. Mustafa, W. Shatanawi, M. Bataineh, Existence of fixed point results in G-metric spaces, Int. J. Math. Math. Sci., Article ID 283028, 2009 (2009), 10 pages.
-
[24]
Z. Mustafa, B. Sims, Fixed point theorems for contractive mappings in complete G-metric spaces, Fixed Point Theory Appl., Article ID 917175, 2009 (2009), 10 pages.
-
[25]
D. Paesano, P. Vetro, Suzuki's type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces, Topology Appl., 159 (2012), 911-920.
-
[26]
S. Radenović, P. Salimi, S. Pantelic, J. Vujaković, A note on some tripled coincidence point results in G-metric spaces, Int. J. Math. Sci and Engg. Appls.(November 2012), 6 (2012), 23-38.
-
[27]
S. Reich, Kannan's fixed point theorem, Boll. Un. Mat. Ital., 4 (1971), 1-11.
-
[28]
I. A. Rus, Fixed point theory in partial metric spaces, Anal. Univ. de Vest, Timisoara, Seria Matematică-Informatică, 46 (2008), 141-160.
-
[29]
B. Samet, M. Rajović, R. Lazović, R. Stoiljković, Common fixed point results for nonlinear contractions in ordered partial metric spaces , Fixed Point Theory Appl., 2011:71 (2011)
-
[30]
B. Samet, C. Vetro, P. Vetro, Fixed point theorems for \(\alpha-\psi\)-contractive type mappings, Nonlinear Anal., 75 (2012), 2154-2165.
-
[31]
R. Saadati, S. M. Vaezpour, P. Vetro, B. E. Rhoades , Fixed point theorems in generalized partially ordered G-metric spaces , Mathematical and Computer Modelling., 52 (2010), 797-801.
-
[32]
T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc., 136 (2008), 1861-1869.
-
[33]
C. Vetro, F. Vetro, Common fixed points of mappings satisfying implicit relations in partial metric spaces, J. Nonlinear Sci. Appl. , 6 (3) (2013), 152-161.
-
[34]
F. Vetro, On approximating curves associated with nonexpansive mappings, Carpathian J. Math., 27 (2011), 142-147.
-
[35]
F. Vetro, S. Radenović, Nonlinear -quasi-contractions of Ćirić-type in partial metric spaces, Appl. Math. Comput., 219 (4) (2012), 1594-1600.
-
[36]
M. R. A. Zand, A. D. Nezhad , A generalization of partial metric spaces, Journal of Contemporary Applied Mathematics., 24 (2011), 86-93.