Results on n-tupled fixed points in complete ordered metric spaces.

The aim of this paper is to study  n-tupled coincidence and n-tupled fixed point results, a new notion propounded by M.Imdad et.al.[13] for compatible maps in partially ordered metric spaces. Our results generalize, extend and improve  the coupled fixed point results of Bhaskar and Lakshmikantham, Nonlinear Analysis: Theory, Methods and Applications, vol.65, no.7, 2006, pp. 1379-1393, V. Lakshmikantham and L. Ciric, Nonlinear Analysis, Theory, Method and Applications, vol. 70, no12, 2009, pp. 4341-4349, tripled fixed point theorems by Berinde and Borcut, Nonlinear Analysis, Volume 74, Issue 15, October 2011,  Pages 4889-4897, Quadruple fixed point theorems by E. Karapınar and V. Berinde, Banach Journal of Mathematical Analysis, vol. 6, no. 1, pp. 74 89, 2012 and multidimensional fixed point results by Muzeyyen Erturk and Vatan Karakaya, Journal of Inequalities and Applications 2013, 2013:196, pp. 1-19, M. Imdad, A. H. Soliman, B. S. Choudhary and P. Das, Journal of Operators, Volume 2013, Article ID 532867, pp. 1-8 and M. Paknazar, M. E. Gordji, M. D. L. Sen and S. M. Vaezpour, Fixed Point Theory and Applications 2013, 2013:11 etc

Some Remarks on Multidimensional Fixed Point Theorems in Partially Ordered Metric Spaces.

In this paper , we show that multidimensional ( coupled, tripled, quadrupled, n-tupled)  theorems can be  reduced to unidimensional fixed point theorems. . Our results generalize, extend and improve the coupled fixed point results of Bhaskar and Lakshmikantham, Nonlinear Analysis: Theory, Methods and Applications, vol.65, no.7, 2006, pp. 1379-1393, V. Lakshmikantham and L. Ciric, Nonlinear Analysis, Theory, Method and Applications, vol. 70, no12, 2009, pp. 4341-4349, tripled fixed point result by Berinde and Borcut, Nonlinear Analysis, Volume 74, Issue 15, October 2011, Pages 4889-4897, Quadruple fixed point theorems by E. Karapinar and V. Berinde, Banach Journal of Mathematical Analysis, vol. 6, no.1, pp. 74-89, 2012 and multidimensional fixed point results by Muzeyyen Erturk and Vatan Karakaya, Journal of Inequalities and Applications 2013, 2013:196, pp. 1-19, M. Imdad, A. H.Soliman, B. S. Choudhary and P. Das, Journal of Operators, Volume 2013, Article ID 532867, pp. 1-8 and M. Paknazar, M. E. Gordji, M. D. L. Sen and S. M. Vaezpour, Fixed Point Theory and Applications 2013, 2013:11 etc

Berinde-Borcut tripled fixed point theorem in partially ordered (intuitionistic) fuzzy normed spaces

In this paper, we prove some tripled fixed point theorems in fuzzy normed spaces. Our results improve and restate the proof lines of the main results given in the paper (Abbas et al. in Fixed Point Theory Appl. 2012:187, 2012).The first author was supported by the Higher Education Research Promotion and National Research University Project of Thailand, Office of the Higher Education Commission (Under NRU-CSEC Project No. NRU56000508). The last three authors have been partially supported by Junta de Andalucía, by projects FQM-268, FQM-178 and FQM-235 of the Andalusian CICYE

Higher dimensional fixed point results in complete ordered metric spaces.

The aim of this paper is to define the concept of compatible maps for n-tupled maps, a new notion propounded by M.Imdad et.al.[13] and prove n-tupled coincidence and n-tupled fixed point theorems in partially ordered metric spaces. Our results generalize, extend and improve the results of [3,7,8,12,13,19.25,26]

F-closed sets and coupled fixed point theorems without the mixed monotone property

In this paper we present the notion of F-closed set (which is weaker than the concept of F-invariant set introduced in Samet and Vetro (Ann. Funct. Anal. 1:46-56, 2010), and we prove some coupled fixed point theorems without the condition of mixed monotone property. Furthermore, we interpret the transitive property as a partial preorder and, then, some results in that paper and in Sintunavarat et al. (Fixed Point Theory Appl. 2012:170, 2012) can be reduced to the unidimensional case

Tripled coincidence points for weakly compatible and its variants in fuzzy metric spaces

In this paper, we will introduce the concept of weakly commuting and variants of weakly commuting mappings (R-weakly commuting, R-weakly commuting of type (Af), type (Ag), type (P) mappings) for triplet in fuzzy metric spaces. Secondly, we introduce the notion of weakly compatibility and its variants weakly f-compatible maps and weakly g-compatible maps. At the end, we prove common ï¬xed point theorems for a pair of weakly compatible map and their variants, which generalize the results of various authors present in ï¬xed point theory literature. Our result is validated with a suitable example

Some fixed point theorems for G-isotone mappings in partially ordered metric spaces

AbstractFixed point theorems for G-isotone mappings, which extend some recent results for mixed monotone and isotone mappings in partially ordered metric spaces are proved. Moreover, the equivalence between unidimensional and multidimensional fixed point theorems is investigated