Some applications of uniformly $ p $-convergent sets

Abstract: In this paper, we introduce a new class of subsets of bounded linear operators between Banach spaces which is p-version of the uniformly completely continuous sets. Then, we study the relationship between these sets with the equicompact sets. Moreover, we introduce the concept of weakly p-sequentially continuous differentiable mappings and obtain some characterizations of these mappings. Finally, we give a factorization result for differentiable mappings through p-convergent operators.