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...

The purpose of this paper is to present a common fixed point theorem for pair R-weakly commuting mappings defined on b-fuzzy metric spaces satisfying nonlinear contractive conditions Boyd-Wong type, obtained in D. W. Boyd, J. S. Wong: On contractions, Proc. Amer. Math. Soc. 20 (1969), 458-464.

Given non-empty subsets A and B of a metric space, let S : A → B and T : A → B be non-self mappings. Taking into account the fact that, given any element x in A, the distance between x and Sx, and the distance between x and Tx are at least d(A,B), a common best proximity point theorem affirms global minimum of both functions x → d(x, Sx) and x → d(x, Tx) by imposing a common approximate solutio...

Banach contraction principle is a fundamental result in fixed point theory and has been applied and extended in many different directions. In 2002, Branciari [3] obtained a fixed point theorem for a single mapping satisfying an analogue of Banach’s contraction principle for an integral type inequality. Aliouche [2] established a common fixed point theorem for weakly compatible mappings in symme...