0000000000635853
AUTHOR
Hk Nashine
showing 3 related works from this author
Common best proximity points and global optimal approximate solutions for new types of proximal contractions
2015
Let $(\mathcal{X},d)$ be a metric space, $\mathcal{A}$ and $\mathcal{B}$ be two non-empty subsets of $\mathcal{X}$ and $\mathcal{S},\mathcal{T}: \mathcal{A} \to \mathcal{B}$ be two non-self mappings. In view of the fact that, given any point $x \in \mathcal{A}$, the distances between $x$ and $\mathcal{S}x$ and between $x$ and $\mathcal{T}x$ are at least $d(\mathcal{A}, \mathcal{B}),$ which is the absolute infimum of $d(x, \mathcal{S} x)$ and $d(x, \mathcal{T} x)$, a common best proximity point theorem affirms the global minimum of both the functions $x \to d(x, \mathcal{S}x)$ and $x \to d(x, \mathcal{T}x)$ by imposing the common approximate solution of the equations $\mathcal{S}x = x$ and $…
A fixed point theorem for (varphi,L)-weak contraction mappings on a partial metric space
2014
In this paper, we explore (varphi,L)-weak contractions of Berinde by obtaining Suzuki-type fixed point results. Thus, we obtain generalized fixed point results for Kannan's, Chatterjea's and Zamfirescu's mappings on a 0-complete partial metric space. In this way we obtain very general fixed point theorems that extend and generalize several related results from the literature.
Recent Developments on Fixed Point Theory in Function Spaces and Applications to Control and Optimization Problems
2015
Nonlinear and Convex Analysis have as one of their goals solving equilibrium problems arising in applied sciences. In fact, a lot of these problems can be modelled in an abstract form of an equation (algebraic, functional, differential, integral, etc.), and this can be further transferred into a form of a fixed point problem of a certain operator. In this context, finding solutions of fixed point problems, or at least proving that such solutions exist and can be approximately computed, is a very interesting area of research. The Banach Contraction Principle is one of the cornerstones in the development of Nonlinear Analysis, in general, and metric fixed point theory, in particular. This pri…