×

Fixed point theorems for generalized weakly \(S\)-contractive mappings in partial metric spaces. (English) Zbl 1441.54035

Summary: In this paper, we establish some unique fixed point theorems for generalized weakly \(S\)-contractive with nondecreasing and weakly increasing mappings in complete partial metric space. Also, we give some examples for strengthens of our main results.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
47H10 Fixed-point theorems
54E50 Complete metric spaces
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] T. Abdeljawad,Fixed points for generalized weakly contractive mappings in partial metric spaces, Math. Comput. Modelling, 54(2011), 2923-2927. · Zbl 1237.54038
[2] I. Altun and A. Erduran,Fixed point theorems for monotone mappings on partial metric spaces, Fixed Point Theory Appl., (2011) Article ID 508730 doi: 10.1155/2011/508730. · Zbl 1207.54051
[3] I. Altun, B. Damjanovic and D. Djoric,Fixed point and common fixed point theorems on ordered cone metric spaces, Appl. Math. Lett., 23(2009), 310-316. · Zbl 1197.54052
[4] I. Altun, F. Sola and H. Simsek,Generalized contraction on partial metric spaces, Topology Appl., 157(18)(2010), 2778-2785. · Zbl 1207.54052
[5] H. Aydi, S. Hadj-Amor and E. Karapinar,Berinde-Type generalized contractions on partial metric spaces, Abstr. Appl. Anal., (2013) Article ID 312479 doi: 10.1155/2013. · Zbl 1266.54083
[6] S.K. Chatterjee,Fixed point theorems, C.R. Acad. Bulgare Sci., 25(1975), 727- 730. · Zbl 0274.54033
[7] C. Chen and C. Zhu,Fixed point theorems for weakly C-contractive mappings in partial metric spaces, Fixed Point Theory Appl., (2013) doi: 10.1186/16871812-2013-107. · Zbl 1423.54072
[8] K.P. Chi, E. Karapinar and T.D. Thanh,A generalized contraction principle in partial metric spaces, Math. Comput. Modelling, 55(2012), 71673-1681. · Zbl 1255.54020
[9] B.S. Choudhury,Unique fixed point theorem for weak C-contractive mappings, Kathmandu Univ. J. Sci. Eng. Tech., 5(1)(2009), 6-13.
[10] Deepmala,A Study of Fixe Point Theorems for Nonlinear Contractions and Its Applications[Ph.D. thesis], Pt. Ravishankar Shukla University, Raipur, India, 2014. · Zbl 1286.39018
[11] Deepmala,Existence theorems for solvability of a functional equation arising in dynamic programming, International Journal of Mathematics and Mathematical Sciences, 2014(2014), Article ID 706585, 9 pages. · Zbl 1286.39018
[12] Deepmala and H.K. Pathak,A study on some problems on existence of solutions for nonlinear functional-integral equations, ActaMathematica Scientia, Series · Zbl 1299.47108
[13] M. Frechet,Sur quelques point du calcul fonctionnel, Rendiconti del circolo Matematio di palermo, 22(1906), 1-74. · JFM 37.0348.02
[14] E. Karapinar and I.M. Erhan,Fixed point theorems for operators on partial metric spaces, Appl. Math. Lett., 24(2011), 1894-1899. · Zbl 1229.54056
[15] E. Karapinar and I.S. Yuce,Fixed point theory for cyclic generalized weakϕcontraction on partial metric spaces, Abstr. Appl. Anal., (2012) Article ID 491542 doi: 10.1155/2012. · Zbl 1246.54045
[16] S.C. Malik and S. Arora,Mathematical analysis, fourth edition, New age Int. Publ., (2010), page-87.
[17] S.G. Matthews,Partial Metric Topology, in proceeding of8thsummer conference on General Topology and Applications, at Queens College (1922) in: Annals of the New York Academy of Sciences, 728(1994), 183-197. · Zbl 0911.54025
[18] S.G. Matthews,Partial Metric Topology, Research Report 212, Dept. of Comput. Sci., University of Warwick, 1992.
[19] L.N. Mishra, S.K. Tiwari, V.N. Mishra and I.A. Khan,Unique fixed point theorems for generalized contractive mappings in partial metric spaces, J. Function Spaces, (2015) Manuscript Id 960827, in press. · Zbl 1330.54062
[20] V.N. Mishra, M.L. Mittal, and U. Singh,On best approximation in locally convex space, Varahmihir Journal of Mathematical Sciences India, 6(1)(2006), 43-48. · Zbl 1185.47058
[21] V.N. Mishra,Some Problems on Approximations of Functions in Banach spaces [Ph.D. thesis], Indian Institute of Technology, Uttarakhand, India, 2007.
[22] V.N. Mishra and L.N. Mishra,Trigonometric approximation inLp(p≥1)spaces, International Journal of Contemporary Mathematical Sciences, 7(2012), 909-918. · Zbl 1246.94015
[23] H.K. Nashine, Z. Kadelburg and S. Radenovic,Common fixed point theorems for weakly isotone increasing mappings in ordered partial metric spaces, Math. Comput. Modelling, 57(2013), 2355-2365. · Zbl 1286.54051
[24] W. Shatanawi,Fixed point theorems for nonlinear weakly C-contractive mappings in metric spaces, Math. Comput. Modelling, 54(2011), 2816-2826. · Zbl 1235.54054
[25] D.P. Shukla and S.K. Tiwari,Unique fixed point theorem for weakly Scontractive mappings, Gen. Math. Notes, 4(1)(2011), 28-34.
[26] D.P. Shukla, S.K. Tiwari and S.K. Shukla,Fixed point theorems for a pair of compatible mappings in integral type equation, Int. J. of Math. Sci. & Engg. Appls, 7(VI)(2013), 413-419.
[27] D.P. Shukla, S.K. Tiwari and S.K. Shukla,Unique common fixed point theorems for compatible mappings in complete metric space, Gen. Math. Notes, 18(1)(2013), 13-23.
[28] S. Wang,
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.