On random coincidence points and random best approximation in p-normed spaces

In this paper random coincidence point results are proved for pair of commuting mapping defined on weakly compact separable subset of complete p-normed space. And then , use them to study the random best approximation in p-normed space with separablity condition.Keywords : p-normed space ,random coincidence point ,random best approximation

Metrics and spectral triples for Dirichlet and resistance forms

The article deals with intrinsic metrics, Dirac operators and spectral triples induced by regular Dirichlet and resistance forms. We show, in particular, that if a local resistance form is given and the space is compact in resistance metric, then the intrinsic metric yields a geodesic space. Given a regular Dirichlet form, we consider Dirac operators within the framework of differential 1-forms proposed by Cipriani and Sauvageot, and comment on its spectral properties. If the Dirichlet form admits a carr\'e operator and the generator has discrete spectrum, then we can construct a related spectral triple, and in the compact and strongly local case the associated Connes distance coincides with the intrinsic metric. We finally give a description of the intrinsic metric in terms of vector fields

Some Coincidence and Fixed Point Results for Hybrid Contraction

Fixed point theory for multi-valued mappings has many useful applications in applied sciences, in particular in Game theory and Mathematical Economics. Thus it is natural to try of extending the known fixed point results for single-valued mappings to the setting of multi-valued mappings. Some theorems of existence of fixed points of single-valued mappings have been extended to the multi-valued case. For example, in 1969 Nadler extended the Banach contraction principle to multi-valued contractive mappings in complete metric space. However, many other questions remain open. Moreover, the study of existence of coincidence and fixed points for hybrid contraction that is a pair of single-valued and multi-valued maps became more interesting due to the recent investigation of Corley in 1986. He gave a good relationship between hybrid fixed points and optimization problems. Here we present the main known results and current research direction in this subject .This talk can be considered as a survey, but some new results are also included. Mathematics Subject Classifications: 47H10, 54H25