We study the solvability of special partial differential relations of the form Du(x) ∈ K for u ∈ W (Ω;R), where Ω ⊂ R is a bounded domain, Du(x) is the Jacobi matrix of u, and K is a given set of m × n matrices. In this note, we present some results obtained in the paper [16] on the W -reduction principles and a general existence theorem that generalize the similar reduction principles for Lips...

The Banach contraction principle is one of the pivotal results in the metric fixed-point theory. It is a popular tool for the solution of existence problems in various fields of mathematics. There are several generalizations of the Banach contraction principle in the related literature on the metric fixed-point theory. Ran and Reurings [15] extended the Banach contraction principle in partially...

The Bäcklund transformation (BT) of Adler’s lattice equation is inherent in the equation itself by virtue of its multidimensional consistency. We refer to a solution of the equation that is related to itself by the composition of two BTs (with different Bäcklund parameters) as a 2-cycle of the BT. In this article we will show that such solutions are associated with a commuting one-parameter fam...

In this paper first, we introduce the notions of subcompatible mappings and occasionally weakly compatible mappings in multiplicative metric spaces analogue to these notions introduced in metric spaces. Also, we prove common fixed point theorems for these mappings. Mathematics Subject Classification: 47H10, 54H25