One of the generalizations of the Banach Fixed Point Theorem is due to Matkowski, who replaced contractivity by a weaker but still effective property. The aim of this note is to extend the contraction principle in this spirit for such semimetric spaces that are equipped with a natural generalization of the standard triangle inequality. The stability of fixed points is also investigated in this ...

Abstract For studying the evolution of transverse deflection an extensible beam derived from connection mechanics, we investigate initial boundary value problem nonlinear equation with linear strong damping term, weak and source term. The key idea our analysis is to describe invariant manifold via Nehari manifold. To establish results global well-posedness solution, consider at three different ...

Objectives: In this paper, we have to establish a generalized common fixed point theorem in cone rectangular metric spaces. Methods: use the Banach contraction principle technique theorem. Findings: The paper presents unique for two weakly compatible self-maps satisfying expansive type mapping space without assuming normality condition of cone. Our result extends and supplements some well-known...

Strongly contracting dynamical systems have numerous properties (e.g., incremental ISS), find widespread applications in controls and learning), their study is receiving increasing attention. This work starts with the simple observation that, given a strongly system, its adjoint system also contracting, same rate, respect to dual norm, under time reversal. As main implication of this contractiv...

Some generalizations of Banach's contraction principle, which is a fixed-point theorem for mapping in metric spaces, have developed rapidly recent years. the things that support development generalization are emergence mappings more general than and spaces spaces. The generalized Kannan type one mappings. Furthermore, some b-metric modular bring concept into theorems Kannan-type on been given. ...