Research Communication | Open Access
Volume 2019 | Communication ID 173
Volume 2019 | Communication ID 173
| Noncyclic mappings and best proximity pair in modular spaces |
Nour-Eddine Elharmouchi, El Miloudi Marhrani, Karim Chaira
Received |
Accepted |
Published |
Jan 30, 2019 |
Feb 26, 2019 |
Mar 01, 2019 |
Abstract: The notion of modular space, as a generalization of Banach spaces, was introduced by H. Nakano [6] in 1950. After that, many authors studied and developed Nakano’s results. Let A and B two nonempty subsets of a modular space. A mapping T∶A∪B→A∪B is said noncyclic if T(A)⊂A and T(B)⊂B. If A and B are disjoint, then the fixed point equation T(x)=x does not have a solution. Hence, it is interesting to ask even if possible to find a pair (p,q)∈A×B such that p=T(p), q=T(q) and ρ(p-q)=dist_ρ (A,B)=inf {ρ (x - y)∶ x ∈ A,y ∈ B} The pair (p,q) is called best ...