Browse > Article
http://dx.doi.org/10.5831/HMJ.2016.38.3.553

SOME EXISTENCE AND UNIQUENESS THEOREMS ON ORDERED METRIC SPACES VIA GENERALIZED DISTANCES UNDER NEW CONTROL FUNCTIONS  

Sharma, Anupam (Department of Mathematics & Statistics, Indian Institute of Technology)
Ansari, Arslan Hojat (Department of Mathematics, College of Basic Sciences, Karaj Branch, Islamic Azad University)
Publication Information
Honam Mathematical Journal / v.38, no.3, 2016 , pp. 553-581 More about this Journal
Abstract
The purpose of this paper is to prove some fixed point theorems in a complete metric space equipped with a partial ordering using w-distances together with the aid of an altering functions and new functions of admissible type.
Keywords
Partially ordered set; fixed point; altering functions; w-distance; orbitally continuous; orbitally U-continuous;
Citations & Related Records
연도 인용수 순위
  • Reference
1 A. H. Ansari, Note on "$\alpha$-admissible mappings and related fixed point theorems", The 2nd Regional Conference on Mathematics And Applications, PNU, September 2014, 373-376.
2 A. Branciari, A fixed point theorem for mapping satisfying a general contractive condition of integral type, International Journal of Mathematics and Mathematical Sciences, 10 (2002), 531-536.
3 J. Caristi, Fixed point theorems for mapping satisfying inwardness conditions, Trans. Amer. Math. Soc., 215 (1976), 241-251.   DOI
4 S. Cho, J. Bae and E. Karapinar, Fixed point theorems for $\alpha$-Geraghty contraction type maps in metric spaces, Fixed Point Theory and Applications 2013, 2013:329.   DOI
5 I. Ekeland, Nonconvex minimization problem, Bull. Amer. Math. Soc. 1 (1979), 443-474. MR 80h:49007.
6 E. Karapinar, P. Kumam, P. Salimi, On ${\alpha}-{\psi}$-Meir-Keeler contractive mappings, Fixed Point Theory and Applications 2013, 2013:94.   DOI
7 N. Hussain, P. Salimi, A. Latif, A Fixed point results for single and set-valued ${\alpha}-{\eta}-{\psi}$-contractive mappings, Fixed Point Theory and Applications 2013, 2013:212.   DOI
8 T. L. Hicks and B. E. Rhoades, A Banach type fixed-point theorem, Mathematica Japonica, 24 (3), 327-330, (1979)/80.
9 L. Hossein, and L. Ing-Jer, The Existence of Fixed Points for Nonlinear Contractive Maps in Metric Spaces with w-Distances, Journal of Applied Mathematics Volume , Article ID 161470, 11 pages (2012).
10 N. Hussain, P. Salimi and A. Lat, Fixed point results for single and set-valued ${\alpha}-{\eta}-{\psi}$-contractive mappings, Fixed Point Theory and Applications, 2013, 2013:212.   DOI
11 N. Hussain, M. Arshad, A. Shoaib and Fahimuddin, Common fixed point results $for{\alpha}-{\psi}$-contractions on a metric space endowedwith graph, Journal of inequalities and applications, 2014, 2014:136.
12 J. Jachymski, Remarks on contractive conditions of integral type, Nonlinear Anal.(TMA) 71 (2009), 1073-1081.   DOI
13 O. Kada, T. Suzuki and W. Takahashi, Nonconvex minimization theorems and fixed point theorems in complete metric spaces, Math. Japonica, 44 (1996), 381-391. MR 97J:49011.
14 M. S. Khan, M. Swaleh and S. Sessa, Fixed point theorems by altering distances between the points, Bull. Aust. Math. Soc., 30 (1984), 1-9.   DOI
15 S. Kumar, R. Chugh, R. Kumar, Fixed point theorem for compatible mapping satisfying a contractive condition of integral type, Soochow J. Math. 33(2) (2007), 181-185.
16 J.J. Nieto, R. Rodriguez-Lopez, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order 22(2005), 223-239.   DOI
17 V. Popa, M. Mocanu, A new view point in the study of fixed points for mappings satisfying a contractive condition of integral type, Bull. Inst. Politeh. Tasi, Ser. Mat. Mat. Teor. Fiz. 53(55) (2007), 269-280.
18 V. L. Rosa and P. Vetro, Common fixed points for ${\phi}-{\psi}$-contractions in generalized metric spaces, Nonlinear Analysis: Modelling and Control, 2014, 19 (1), 43-54.   DOI
19 A.C.M. Ran and M.C.B. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Am. Math. Soc. 132 (2004), 1435-1443.   DOI
20 A. Razani, Z. Mazlumi Nezhad, and M. Boujary, A fixed point theorem for w-distance, Applied Sciences, 11 (2009) 114-117.
21 F. Rouzkard, M. Imdad and D. Gopal, Some existence and uniqueness theorems on ordered metric spaces via generalized distances, Fixed Point Theory and Applications, 2013, 2013:45.   DOI
22 B. Samet, C. Vetro and P. Vetro, Fixed point theorems for ${\alpha}-{\psi}$-contractive type mappings, Nonlinear Analysis 75 (2012) 2154-2165.   DOI
23 T. Suzuki, Meir-Keeler contractions of integral type are still Meir-Keeler cotractions, Intern. J. Math. Math. Sci. Volume (2007), Article ID 39281, 6 pages.
24 T. Suzuki, Several fixed point theorem in complete metric space, J. Yokohama Math. 44 (1997) 61-72.
25 W. Takahashi, Existence theorems generalizing fixed point theorems for multi-valued mappings, Fixed Point Theory and Application (M. A. Thera and J. B. Baillon Ends.), Pitman Research Notes in Mathematics Series 252, 397-406, John Wiley Sons, New York, (1991). MR92m:54078
26 W. Takahashi, Nonlinear function analysis, Yokohama Publishers, (2000).
27 P. Vijayaraju, B.E. Rhoades and R. Mohanraj, A fixed point theorem for pair of maps satisfying a general contractive condition of integral type, International Journal of Mathematics and Mathematical Sciences 15 (2005), 2359-2364.