We consider valued fields with a distinguished contractive map as valued modules over the Ore ring of difference operators. We prove quantifier elimination for separably closed valued fields with the Frobenius map, in the pure module language augmented with functions yielding components for a p-basis and a chain of subgroups indexed by the valuation group.

In this paper, a generalization of Nadler’s fixed point theorem is presented for H-type k-multivalued weak contractive mappings. We consider a nonconvex Hammerstein type integral inclusion and prove an existence theorem by using an H-type multi-valued weak contractive mapping.

Polynomial generalizations of all 130 of the identities in Slater’s list of identities of the Rogers-Ramanujan type are presented. Furthermore, duality relationships among many of the identities are derived. Some of the these polynomial identities were previously known but many are new. The author has implemented much of the finitization process in a Maple package which is available for free do...

‎recently‎, ‎hussain et al.‎, ‎discussed the concept of $wt$-distance on a‎ ‎metric type space‎. ‎in this paper‎, ‎we prove some fixed‎ ‎point theorems for classes of contractive type multi-valued operators‎, ‎by using $wt$-distances in the setting of a complete metric type space‎. ‎these results generalize a result of feng and liu on multi-valued operators.

Many fixed point theorems for mapping satisfies a generalized weak contractive condition is already established. In this paper we also give a result on fixed point for mapping satisfying a weakly contractive condition of integral type.

We give formulas for the image Milnor number of a weighted-homogeneous map-germ $$({\mathbb {C}}^n,0)\rightarrow ({\mathbb {C}}^{n+1},0)$$ , $$n=4$$ and 5, in terms weights degrees. Our expressions are obtained by purely interpolative method, applied to result Ohmoto. use our approach recover $$n=2$$ 3 due Mond Ohmoto, respectively. For $$n\ge 6$$ method is valid as long certain multi-singulari...