scholarly journals Results in Strongly Minihedral Cone and Scalar Weighted Cone Metric Spaces and Applications

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Anita Tomar ◽  
Meena Joshi
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Spaces ◽  
Negative Answer ◽  
Contractive Condition ◽  
Natural Question ◽  
Cone Metric Spaces ◽  
Convergence Of Sequences ◽  
Cone Metric

Abstract The convergence of sequences and non-unique fixed points are established in ℳ-orbitally complete cone metric spaces over the strongly mini-hedral cone, and scalar weighted cone assuming the cone to be strongly mini-hedral. Appropriate examples and applications validate the established theory. Further, we provide one more answer to the question of the existence of the contractive condition in Cone metric spaces so that the fixed point is at the point of discontinuity of a map. Also, we provide a negative answer to a natural question of whether the contractive conditions in the obtained results can be replaced by its metric versions.

scholarly journals Common Fixed Points for Nonlinear Quasi-Contractions of Ćirić Type

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Fei He
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Metric Spaces ◽  
Common Fixed Points ◽  
Positive Answer ◽  
Contractive Condition ◽  
Cone Metric Spaces ◽  
Scalarization Method ◽  
Cone Metric

We establish common fixed points theorems for two self-mappings satisfying a nonlinear contractive condition of Ćirić type with aQ-function. Furthermore, using the scalarization method, we deduce some results of common fixed point in tvs-cone metric spaces with ac-distance. As application, we give a positive answer to the question of Ćirić et al. posed in 2012. Our results extend and generalize many recent results.

scholarly journals Common Fixed Point Theorems in Intuitionistic Generalized Fuzzy Cone Metric Spaces

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1212
Author(s):  
Mathuraiveeran Jeyaraman ◽  
Mookiah Suganthi ◽  
Wasfi Shatanawi
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Cone Metric Space ◽  
Contractive Condition ◽  
Cone Metric Spaces ◽  
Common Fixed Point Theorems ◽  
Cone Metric

In the present work, we study many fixed point results in intuitionistic generalized fuzzy cone metric space. Precisely, we prove new common fixed point theorems for three self mappings that do not require any commutativity or continuity but a generalized contractive condition. Our results are generalizations for many results in the literature. Some examples are given to support these results.

scholarly journals On Fixed Point Theory of Monotone Mappings with Respect to a Partial Order Introduced by a Vector Functional in Cone Metric Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Zhilong Li ◽  
Shujun Jiang
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Partial Order ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Monotone Mappings ◽  
Cone Metric Spaces ◽  
Cone Metric ◽  
Minimal Fixed Point

We presented some maximal and minimal fixed point theorems of set-valued monotone mappings with respect to a partial order introduced by a vector functional in cone metric spaces. In addition, we proved not only the existence of maximal and minimal fixed points but also the existence of the largest and the least fixed points of single-valued increasing mappings. It is worth mentioning that the results on single-valued mappings in this paper are still new even in the case of metric spaces and hence they indeed improve the recent results.

scholarly journals Fixed point Theorems for Non-self mappings with nonlinear contractive condition in strictly convex FCM-spaces

2020 ◽  
Vol 26 (1) ◽  
pp. 1-21
Author(s):  
Mohammad H.M. Rashid
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Cone Metric Spaces ◽  
Strictly Convex ◽  
Convex Structure ◽  
Cone Metric

In this paper we define convex, strict convex and normal structures for sets in fuzzy cone metric spaces. Also, existence and uniqueness of a fixed point for non-self mappings with nonlinear contractive condition will be proved, using the notion of strictly convex structure. Moreover, we give some examples illustrate our results.

Common Fixed Points for Maps on Topological Vector Space Valued Cone Metric Spaces

2009 ◽  
Vol 2009 ◽  
pp. 1-8 ◽  
Author(s):  
Ismat Beg ◽  
Akbar Azam ◽  
Muhammad Arshad
Keyword(s):  
Fixed Point ◽  
Vector Space ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Topological Vector Space ◽  
Metric Space ◽  
Metric Spaces ◽  
Common Fixed Points ◽  
Cone Metric Spaces ◽  
Cone Metric

We introduced a notion of topological vector space valued cone metric space and obtained some common fixed point results. Our results generalize some recent results in the literature.

scholarly journals Fixed points of nodal contractions in cone metric spaces

2011 ◽  
Vol 42 (1) ◽  
pp. 39-51
Author(s):  
G. V. R. Babu ◽  
G. N. Alemayehu
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Local Power ◽  
Cone Metric Spaces ◽  
Contractive Mappings ◽  
Cone Metric

We introduce local power contractions and nodal contractions in cone metric spaces and prove the existence of fixed points of such contractions in cone metric spaces. Our theorems generalize the results of Haung and Zhang [L-G. Haung, X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 332 (2007) 1468-1476].

scholarly journals Fixed Point Theorems of Quasicontractions on Cone Metric Spaces with Banach Algebras

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Hao Liu ◽  
Shaoyuan Xu
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Banach Algebras ◽  
New Method ◽  
Cone Metric Spaces ◽  
Cone Metric

We introduce the concept of quasicontractions on cone metric spaces with Banach algebras, and by a new method of proof, we will prove the existence and uniqueness of fixed points of such mappings. The main result generalizes the well-known theorem of Ćirić (Ćirić 1974).

scholarly journals Fixed Point Results for F-Contractions in Cone Metric Spaces over Topological Modules and Applications to Integral Equations

2021 ◽  
Vol 6 (1) ◽  
pp. 16
Author(s):  
Adrian Nicolae Branga
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Fractional Integral ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Cone Metric Spaces ◽  
Fractional Integral Equation ◽  
Topological Modules ◽  
Cone Metric

In this paper, the concept of F-contraction was generalized for cone metric spaces over topological left modules and some fixed point results were obtained for self-mappings satisfying a contractive condition of this type. Some applications of the main result to the study of the existence and uniqueness of the solutions for certain types of integral equations were presented in the last part of the article, one of them being a fractional integral equation.

scholarly journals Common fixed point under contractive condition of Ciric's type in cone metric spaces

2011 ◽  
Vol 5 (1) ◽  
pp. 159-164 ◽  
Author(s):  
Bessem Samet
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Metric Spaces ◽  
Common Fixed Points ◽  
Contractive Condition ◽  
Uniform Spaces ◽  
Cone Metric Spaces ◽  
Common Fixed Point Theorem ◽  
Cone Metric

A common fixed point theorem is established for a pair of self-mappings of a complete cone metric space. The obtained result is an extension of Ljubomir Ciric?s theorem [Lj. Ciric: On common fixed points in uniform spaces, Publ. Inst. Math. 24 (38) (1978), 39[43].

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