Abstract
Abstract In the present paper, existence theorems of coincidence points of a crisp mapping and a sequence of L-fuzzy mappings have been established in a complete metric space under contractive type conditions in connection with newly defined notions of D α L and d L ∞ distances on the class of L-fuzzy sets. Furthermore, we obtain some fixed point theorems for L-fuzzy set-valued mappings to extend a variety of recent results on fixed points for fuzzy mappings and multivalued mappings in the literature. As applications, first we obtain coincidence points of a sequence of multivalued mappings with a self mapping and next established an existence and uniqueness theorem of the solution for a generalized class of nonlinear integral equations. MSC:46S40, 47H10, 54H25.
Highlights
Since his creation, man has always been making sincere efforts in understanding nature intelligently and developing a powerful connection between life and its requirements
By introducing a contraction condition for fuzzy mappings Heilpern [ ] generalized the Banach principle and established a fixed point theorem for fuzzy mappings in complete metric linear spaces
Rashid et al [ ] introduced the concept of L-fuzzy mappings and proved a common fixed point theorem via βFL -admissible pair of L-fuzzy mappings
Summary
Man has always been making sincere efforts in understanding nature intelligently and developing a powerful connection between life and its requirements. Let ε ∈ ( , ∞], (X, d) a complete ε-chainable metric space and {Tq}∞ q= a sequence of L-fuzzy mappings from X into FL(X) such that for each u ∈ X and q ∈ N, [Tq(u)]αL ∈ CB(X), for some αL ∈ L\{ L}.
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