Common Fixed-Point Theorems and c-distance in Ordered Cone Metric Spaces

Abstract

We present a generalization of several fixed and common fixed point theorems on the c-distance in ordered cone metric spaces. In this way, we improve and generalize various results existing in the literature. Наведено узагальнення деяких теорем про нерухому точку та спiльну нерухому точку для c-вiдстанi в упорядкованих конiчних метричних просторах. Таким чином, покращено та узагальнено рiзноманiтнi результати, що наведенi в лiтературi.

w-b-Cone Distance and Its Related Results: A Survey

“…On the other hands, in 2011, Cho et al [21] and Wang and Guo [22] introduced a cone version of the w-distance which is named c-distance. Then, some fixed point results under w-distance in metric spaces and under c-distance in cone metric spaces and tvs-cone metric spaces were obtained in [23,24] and the references cited therein. In 2015, Bao et al [25] introduced a generalized c-distance in cone b-metric spaces and proved several fixed point theorems with respect to this generalized distance (also, see [26,27]).…”

Fixed point results for Hardy-Rogers type contractions with respect to a c-distance in graphical cone metric spaces

“…Conclusion. In this paper, we have considered the condition of orbitally -continuity of mappings instead of the condition of continuity of mappings and cone metric spaces endowed with graph instead of cone metric spaces; some theorems of existing literature, such as Kada et al [11], Cho et al [3], Fallahi et al [4], Fallahi and Soleimani Rad [5], Petrusel and Rus [13], Rahimi and Soleimani Rad [15], [16], and Wang and Guo [17] can be unified there. We finish this paper with some questions: Question 1.…”

“…In 2011, Cho et al [3] defined a cone version of the -distance (where it is called -distance) and obtained some fixed point theorems under a -distance in ordered cone metric spaces. For more results, see the papers [7] by Huang et al and [15], [16] by Rahimi and Soleimani Rad. Further, in 2008, Jachymski [9] equipped the underlying metric space with a directed graph and formulated the Banach contraction in the graph language.…”

New Conditions of The Existence of Fixed Point in Δ- Ordered Δ Banach Algebra

“…But Nashine and Altun (2012) [10] defined cone metric spaces and proved some fixed point theorems of contractive maps in such a space using the normality condition. Also, Rahimi & Soleimani (2014) [12] used the notion ordered cone metric space.…”