We mainly study fixed point theorem for multivalued mappings withδ-distance using Wardowski’s technique on complete metric space. Let(X,d)be a metric space and letB(X)be a family of all nonempty bounded subsets ofX. Defineδ:B(X)×B(X)→Rbyδ(A,B)=supd(a,b):a∈A,b∈B.Consideringδ-distance, it is proved that if(X,d)is a complete metric space andT:X→B(X)is a multivalued certain contraction, thenThas a fixed point.
The concept of partial metric p on a nonempty set X was introduced by Matthews [13] and it was slightly modified by Heckmann [11] as weak partial metric. In [12], the authors studied fixed point result of new extension of Banach's contraction principle to partial metric space and give some generalized versions of the fixed point theorem of Matthews. In the present paper, we extend and generalize the previous results to weak partial metric spaces.
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