FG-coupled fixed point theorems in cone metric spaces
Journal Title: Карпатські математичні публікації - Year 2017, Vol 9, Issue 2
Abstract
The concept of $FG$-coupled fixed point introduced recently is a generalization of coupled fixed point introduced by Guo and Lakshmikantham. A point $(x,y)\in X\times X$ is said to be a coupled fixed point of the mapping $F: X\times X \rightarrow X$ if $F(x,y)=x$ and $F(y,x)=y$, where $X$ is a non empty set. In this paper, we introduce $FG$-coupled fixed point in cone metric spaces for the mappings $F:X\times Y \rightarrow X$ and $G:Y\times X\rightarrow Y$ and establish some $FG$-coupled fixed point theorems for various mappings such as contraction type mappings, Kannan type mappings and Chatterjea type mappings. All the theorems assure the uniqueness of $FG$-coupled fixed point. Our results generalize several results in literature, mainly the coupled fixed point theorems established by Sabetghadam et al. for various contraction type mappings. An example is provided to substantiate the main theorem.
Authors and Affiliations
E. Prajisha, P. Shaini
Keywords
Related Articles
- EP ID EP325351
- DOI 10.15330/cmp.9.2.163-170
- Views 53
- Downloads 0
k-bitransitive and compound operators on Banach spaces
In this this paper, we introduce new classes of operators in complex Banach spaces, which we call k-bitransitive operators and compound operators to study the direct sum of diskcyclic operators. We create a set of suffic...
ON A COMPLETE TOPOLOGICAL INVERSE POLYCYCLIC MONOID
We give sufficient conditions when a topological inverse l-polycyclic monoid Pl is absolutely Hclosed in the class of topological inverse semigroups. For every infinite cardinal l we construct the coarsest semigroup inve...
Periodic words connected with the Fibonacci words
In this paper we introduce two families of periodic words (FLP-words of type 1 and FLP-words of type 2) that are connected with the Fibonacci words and investigated their properties.
Parabolic by Shilov systems with variable coefficients
Because of the parabolic instability of the Shilov systems to change their coefficients, the definition parabolicity of Shilov for systems with time-dependent $t$ coefficients, unlike the definition parabolicity of Petro...
Approximation of capacities with additive measures
For a space of non-additive regular measures on a~metric compactum with the~Prokhorov-style metric, it is shown that the~problem of approximation of arbitrary measure with an~additive measure on a~fixed finite subspace r...