Given a Poisson structure (or, equivalently, a Hamiltonian operator) P , we show that its Lie derivative Lτ (P ) along a vector field τ defines another Poisson structure, which is automatically compatible with P , if and only if [L τ (P ), P ] = 0, where [·, ·] is the Schouten bracket. This result yields a new local description for the set of all Poisson structures compatible with a given Poiss...

The focus of this paper is to acquaint with generalized condition (B) in a quasi-partial b-metric space and establish coincidence common fixed point theorems for weakly compatible pairs mapping. Additionally, the background space, outcomes obtained are exemplified prove existence uniqueness point.

In the present work, the integrable bi-Hamiltonian hierarchies related to compatible nonlocal Poisson brackets of hydrodynamic type are effectively constructed. For achieving this aim, first of all, the problem on the canonical form of a special type for compatible nonlocal Poisson brackets of hydrodynamic type is solved. The compatible pairs of nonlocal Poisson brackets of hydrodynamic type ha...

Despite decades of research, empirical support for the “compatible genes” and “good genes” hypotheses as explanations for adaptive female extra-pair mating remains discordant. One largely un-tested theoretical prediction that could explain equivocal findings is that mating for compatible genes benefits should reduce selection for good genes. However, this prediction does not consider demographi...

In this paper, we establish a common coupled fixed point theorem for three pairs of w-compatible maps in G-metric space which improve and generalize the results of Ding and Karapnar [5]. Example are presented to support our result.

We establish a common fixed point theorem for two pairs of compatible mappings under a new contractive condition, which is independent of the known contractive definitions. This theorem improves various known results.

The aim of this paper is to obtain some common fixed point theorems for hybrid pairs of single and multi-valued occasionally weakly compatible mappings using a symmetric derived from an ordinary symmetric d in b-metric space.

The objective of this paper is to obtain some common fixed point theorems for hybrid pairs of single and multi-valued occasionally weakly compatible mappings in b-metric space.