Abstract In this work we study the Ulam–Hyers stability of a differential equation. Its proof is based on Banach fixed point theorem in some space continuous functions equipped with norm $\|\cdot \|_{\infty }$ ∥ ⋅ ∞ . Moreover, ge...

*Correspondence: [email protected] 2Department of Applied Mathematics, Central South University, Lushan South Road 932, Changsha, Hunan 410083, P.R. China Full list of author information is available at the end of the article Abstract In this paper, we present some new existence and uniqueness results for nonlinear fractional differential equations with a kind of general irregular boundary co...

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...

We provide sufficient conditions for sums of two unbounded operators on a Banach space to be (pre-)generators of contraction semigroups. Necessary conditions and applications to positive semigroups on Banach lattices are also presented.

In this paper, the authors introduce two new classes of series type additive functional Equations (FEs). The first class equations is derived from sum squares alternative and second one obtained cubes series. solution FE investigated using principle mathematical induction. beauty method lies in fact that it satisfies property as well Banach spaces are widely-used very helpful to analyse stabili...

The development in the qualitative theory of fractional differential equations is accompanied by discrete analog which has been studied intensively recent past. Suitable fixed point theorem to be selected study boundary value due properties exhibited difference operators. This article aims at investigating stability results sense Hyers and Ulam with application Mittag–Leffler function hybrid or...

In this study we provide several significant generalisations of Banach contraction principle where the Lipschitz constant is substituted by real-valued control function that a comparison function. We non-stationary variants fixed-point. particular, article looks into “trajectories maps defined systems” which are regarded as generalizations traditional iterated system (IFS). The importance forwa...

The concept of partial metric which is a generalized metric space was introduced by Matthews 1 in 1994, inwhich the distance between two identical elements needs not be zero. The existence of fixed point for contraction-type mappings on such spaces was considered by many authors 1–12 . A modified version of a Banach contraction mapping principle, more suitable to solve certain problems arising ...

Perov studied the Banach contraction principle in framework of a generalized metric space and presented condition where contractive constant is replaced by matrix with nonnegative entries spectral radius less than 1. Azam et al. notion rectangular cone following idea Branciari, Huang Zhang replacing triangular inequality inequality. Motivated work Abbas Vetro Radenovi´c, purpose this paper to i...