“…Our results generalize, extend and improve some recent fixed point results in K-metric spaces including the results of Abbas and Jungck [1], Olaleru [28], Huang and Zhang [14] and Rezapour and Hamlbarani [33]. It is worth mentioning that our results do not require the assumption that the cone is normal.…”
Section: Introductionsupporting
confidence: 88%
“…Fixed point theory in K-metric and K-normed spaces was developed by Perov et al [18,28,29], Mukhamadijev and Stetsenko [19], and Vandergraft [41]. For more details on this subject, we refer to Zabrejko [42].…”
Using the setting of TVS-valued ordered cone metric spaces ( order is induced by a non normal cone), common fixed point results for four mappings satisfying implicit contractive conditions are obtained. These results extend, unify and generalize several well known comparable results in the literature.
“…Our results generalize, extend and improve some recent fixed point results in K-metric spaces including the results of Abbas and Jungck [1], Olaleru [28], Huang and Zhang [14] and Rezapour and Hamlbarani [33]. It is worth mentioning that our results do not require the assumption that the cone is normal.…”
Section: Introductionsupporting
confidence: 88%
“…Fixed point theory in K-metric and K-normed spaces was developed by Perov et al [18,28,29], Mukhamadijev and Stetsenko [19], and Vandergraft [41]. For more details on this subject, we refer to Zabrejko [42].…”
Using the setting of TVS-valued ordered cone metric spaces ( order is induced by a non normal cone), common fixed point results for four mappings satisfying implicit contractive conditions are obtained. These results extend, unify and generalize several well known comparable results in the literature.
“…We establish b-coupled coincidence and b-common coupled fixed point theorems in such spaces. The presented theorems generalize and extend several well-known comparable results in the literature, in particular the recent results of Abbas et al [8] and the result of Olaleru [13]. Some examples and an application to non-linear integral equations are also considered.…”
Section: Introductionsupporting
confidence: 84%
“…Huang and Zhang [7] re-introduced such spaces under the name of cone metric spaces, and went further, defining convergent and Cauchy sequences in the terms of interior points of the underlying cone. Afterwards, many papers about fixed point theory in cone metric spaces were appeared (see, for example, [8][9][10][11][12][13][14][15]). …”
In this paper, we introduce the concepts of w -compatible mappings, b-coupled coincidence point and b-common coupled fixed point for mappings F, G : X × X X, where (X, d) is a cone metric space. We establish b-coupled coincidence and bcommon coupled fixed point theorems in such spaces. The presented theorems generalize and extend several well-known comparable results in the literature, in particular the recent results of Abbas et al. [Appl. Math. Comput. 217, 195-202 (2010)]. Some examples are given to illustrate our obtained results. An application to the study of existence of solutions for a system of non-linear integral equations is also considered.
“…Expanding mappings have enjoyed a relatively lower popularity with the results of Wang et al [26], Daffer and Kaneko [7], Kumar and Garg [13] among others. However, with the generalization of metric spaces to b-metric spaces [3], cone metric spaces [10,15,16,20] and recently, cone b-metric spaces [11], fixed point theorems for expanding mappings have been proved in cone metric spaces (e.g. [1,23,25] The most recent and perhaps most general theorems on expanding mappings in cone metric spaces were initially proposed by Han and Xu [8] who considered a pair of surjective expansion mappings.…”
In this research work, we generalize classical results on the existence of common fixed points of generalized expanding mappings by removing the constraint on the signs of the underlining coefficients in the inequality considered. The hybrid class obtained surprisingly regroups both classes of generalized contractive maps and classes of generalized expansive maps. The research work also provides a clear understanding of the boundary between contractive and expansive mappings in literature and is applied to product metric-type spaces.
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