A Sard theorem for tame set-valued mappings

A Sard Theorem for Set-Valued Mappings∗†

If F is a set-valued mapping from IRn into IRm with closed graph, then y ∈ IRm is a critical value of F if for some x with y ∈ F (x), F is not metrically regular at (x, y). We prove that the set of critical values of a set-valued mapping whose graph is a definable (tame) set in an o-minimal structure containing additions and multiplications is a set of dimension not greater than m − 1 (resp. a ...

2 7 Ju l 2 00 6 A Sard Theorem for Tame Set - Valued Mappings ∗ †

If F is a set-valued mapping from IR n into IR m with closed graph, then y ∈ IR m is a critical value of F if for some x with y ∈ F (x), F is not metrically regular at (x, y). We prove that the set of critical values of a set-valued mapping whose graph is a definable (tame) set in an o-minimal structure containing additions and multiplications is a set of dimension not greater than m − 1 (resp....

Common fixed point theorem for nonexpansive type single valued mappings

The aim of this paper is to prove a common fixed point theorem for nonexpansive type single valued mappings which include both continuous and discontinuous mappings by relaxing the condition of continuity by weak reciprocally continuous mapping. Our result is generalize and extends the corresponding result of Jhade et al. [P.K. Jhade, A.S. Saluja and R. Kushwah, Coincidence and fixed points of ...

common fixed point theorem for nonexpansive type single valued mappings

the aim of this paper is to prove a common fixed point theorem for nonexpansive type single valued mappings which include both continuous and discontinuous mappings by relaxing the condition of continuity by weak reciprocally continuous mapping. our result is generalize and extends the corresponding result of jhade et al. [p.k. jhade, a.s. saluja and r. kushwah, coincidence and fixed points of ...

Fixed Point Theorems for Set-valued Mappings