FIXED POINT THEOREMS FOR GENERALIZED WEAKLY S-CONTRACTIVE MAPPINGS IN PARTIAL METRIC SPACES

Lakshmi Narayan Mishra; Shiv Kant Tiwari; Vishnu Narayan Mishra

doi:10.11948/2015047

2015 Volume 5 Issue 4

Article Contents

Article navigation > Journal of Applied Analysis & Computation > 2015 > 5(4): 600-612

Next Article Previous Article

Lakshmi Narayan Mishra, Shiv Kant Tiwari, Vishnu Narayan Mishra. FIXED POINT THEOREMS FOR GENERALIZED WEAKLY S-CONTRACTIVE MAPPINGS IN PARTIAL METRIC SPACES[J]. Journal of Applied Analysis & Computation, 2015, 5(4): 600-612. doi: 10.11948/2015047

Citation:

Lakshmi Narayan Mishra, Shiv Kant Tiwari, Vishnu Narayan Mishra. FIXED POINT THEOREMS FOR GENERALIZED WEAKLY S-CONTRACTIVE MAPPINGS IN PARTIAL METRIC SPACES[J]. Journal of Applied Analysis & Computation, 2015, 5(4): 600-612. doi: 10.11948/2015047

FIXED POINT THEOREMS FOR GENERALIZED WEAKLY S-CONTRACTIVE MAPPINGS IN PARTIAL METRIC SPACES

1 Department of Mathematics, National Institute of Technology, Silchar-788 010, District-Cachar(Assam), India;
2 L. 1627 Awadh Puri Colony Beniganj, Phase Ⅲ, Opposite Industrial Training Institute(I. T. I.), Ayodhya Main Road, Faizabad-224 001(Uttar Pradesh), India;
3 Department of Applied Mathematics, University Institute of Technology, Rajiv Gandhi Technical University, Bhopal-462 033(M. P.) India;
4 Department of Applied Mathematics and Humanities, Sardar Vallabhbhai National Institute of Technology, Ichchhanath Mahadev Dumas Road, Surat-395 007(Gujarat), India

Abstract

Abstract

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.
- Fixed point /
- complete partial metric space /
- weakly S-contractive mapping /
- decreasing mapping /
- weakly increasing mappings
MSC: 47H10;54H25;54E50

FullText(HTML)

References

[1]	T. Abdeljawad, Fixed points for generalized weakly contractive mappings in partial metric spaces, Math. Comput. Modelling, 54(2011), 2923-2927. Google Scholar
[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. Google Scholar
[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. Google Scholar
[4]	I. Altun, F. Sola and H. Simsek, Generalized contraction on partial metric spaces, Topology Appl., 157(18)(2010), 2778-2785. Google Scholar
[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. Google Scholar
[6]	S.K. Chatterjee, Fixed point theorems, C.R. Acad. Bulgare Sci., 25(1975), 727-730. Google Scholar
[7]	C. Chen and C. Zhu, Fixed point theorems for weakly C-contractive mappings in partial metric spaces, Fixed Point Theory Appl., (2013) doi:10.1186/1687-1812-2013-107. Google Scholar
[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. Google Scholar
[9]	B.S. Choudhury, Unique fixed point theorem for weak C-contractive mappings, Kathmandu Univ. J. Sci. Eng. Tech., 5(1)(2009), 6-13. Google Scholar
[10]	Deepmala, A Study of Fixe Point Theorems for Nonlinear Contractions and Its Applications[Ph.D. thesis], Pt. Ravishankar Shukla University, Raipur, India, 2014. Google Scholar
[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. Google Scholar
[12]	Deepmala and H.K. Pathak, A study on some problems on existence of solutions for nonlinear functional-integral equations, ActaMathematica Scientia, Series BEnglish Edition, 33(5)(2013), 1305-1313. Google Scholar
[13]	M. Frechet, Sur quelques point du calcul fonctionnel, Rendiconti del circolo Matematio di palermo, 22(1906), 1-74. Google Scholar
[14]	E. Karapinar and I.M. Erhan, Fixed point theorems for operators on partial metric spaces, Appl. Math. Lett., 24(2011), 1894-1899. Google Scholar
[15]	E. Karapinar and I.S. Yuce, Fixed point theory for cyclic generalized weak ϕ-contraction on partial metric spaces, Abstr. Appl. Anal., (2012) Article ID 491542 doi:10.1155/2012. Google Scholar
[16]	S.C. Malik and S. Arora, Mathematical analysis, fourth edition, New age Int. Publ., (2010), page-87. Google Scholar
[17]	S.G. Matthews, Partial Metric Topology, in proceeding of 8^th summer conference on General Topology and Applications, at Queens College (1922) in:Annals of the New York Academy of Sciences, 728(1994), 183-197. Google Scholar
[18]	S.G. Matthews, Partial Metric Topology, Research Report 212, Dept. of Comput. Sci., University of Warwick, 1992. Google Scholar
[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. Google Scholar
[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. Google Scholar
[21]	V.N. Mishra, Some Problems on Approximations of Functions in Banach spaces[Ph.D. thesis], Indian Institute of Technology, Uttarakhand, India, 2007. Google Scholar
[22]	V.N. Mishra and L.N. Mishra, Trigonometric approximation in L_p(p ≥ 1)-spaces, International Journal of Contemporary Mathematical Sciences, 7(2012), 909-918. Google Scholar
[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. Google Scholar
[24]	W. Shatanawi, Fixed point theorems for nonlinear weakly C-contractive mappings in metric spaces, Math. Comput. Modelling, 54(2011), 2816-2826. Google Scholar
[25]	D.P. Shukla and S.K. Tiwari, Unique fixed point theorem for weakly Scontractive mappings, Gen. Math. Notes, 4(1)(2011), 28-34. Google Scholar
[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. Google Scholar
[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. Google Scholar
[28]	S. Wang, Multidimenstional fixed point theorems for isotone mappings in partially ordered metric spaces, Fixed Point Theory Appl., 54(2014), 2014-137. Google Scholar