Since 1964, when I.A. Perov introduced the so-called generalized metric space where d(x,y) is an element of vector Rm, many researchers have considered various contractive conditions in this type space. In paper, we generalize, extend and unify some those established results. We are primarily concerned with examining existence a fixed point mapping from X to itself, but if (x,y) belongs relatio...

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...

‎inspired by the work of suzuki in‎ ‎[t. suzuki‎, ‎a generalized banach contraction principle that characterizes metric completeness‎, proc‎. ‎amer‎. ‎math‎. ‎soc. ‎136 (2008)‎, ‎1861--1869]‎, ‎we prove a fixed point theorem for contractive mappings‎ ‎that generalizes a theorem of geraghty in [m.a‎. ‎geraghty‎, ‎on contractive mappings‎, ‎proc‎. ‎amer‎. ‎math‎. ‎soc., ‎40 (1973)‎, ‎604--608]‎an...

Let R be a 2-torsion free ring and L a Lie ideal of R. An additive mapping F : R ! R is called a generalized derivation on R if there exists a derivation d : R to R such that F(xy) = F(x)y + xd(y) holds for all x y in R. In the present paper we describe the action of generalized derivations satisfying several conditions on Lie ideals of semiprime rings.

In this study, we examine the existence and Hyers–Ulam stability of a coupled system generalized Liouville–Caputo fractional order differential equations with integral boundary conditions connection to Katugampola integrals. first third theorems, Leray–Schauder alternative Krasnoselskii’s fixed point theorem are used demonstrate solution. The Banach theorem’s concept contraction mapping is in s...

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. ...

We consider the linear Volterra equation

In this paper, we show that contraction operations preserve the homology of nD generalized maps, under some conditions. This result extends the similar one given for removal operations in [6]. Removal and contraction operations are used to propose an efficient algorithm that compute homology generators of nD generalized maps. Its principle consists in simplifying a generalized map as much as po...

We study locally compact contractive local groups, that is, locally compact local groups with a contractive pseudo-automorphism. We prove that if such an object is locally connected, then it is locally isomorphic to a Lie group. We also prove a related structure theorem for locally compact contractive local groups which are not necessarily locally connected. These results are local analogues of...

This paper is concerned with p ≥ 2 -cyclic self-mappings T : ⋃i∈p Ai → ⋃ i∈p Ai in a metric space X, d , with Ai ⊂ X, T Ai ⊆ Ai 1 for i 1, 2, . . . , p, under a general contractive condition which includes as particular cases several of the existing ones in the literature. The existence and uniqueness of fixed points and best proximity points is discussed as well as the convergence to them of t...