Abstract: Recently a new type of very general relational
structures, the so called (L-)complete propelattices, was introduced.
These significantly generalize complete lattices and completely lattice
L-ordered sets, because they do not assume the technically very
strong property of transitivity. For these structures also the main part
of the original Tarski’s fixed point theorem holds for (L-fuzzy) isotone
maps, i.e., the part which concerns the existence of fixed points and
the structure of their set. In this paper, fundamental properties of
(L-)complete propelattices are recalled and the so called L-fuzzy
relatively isotone maps are introduced. For these maps it is proved
that they also have fixed points in L-complete propelattices, even if
their set does not have to be of an awaited analogous structure of
a complete propelattice.
Abstract: In this paper, we introduce a two-step iterative algorithm to prove a strong convergence result for approximating common fixed points of three contractive-like operators. Our algorithm basically generalizes an existing algorithm..Our iterative algorithm also contains two famous iterative algorithms: Mann iterative algorithm and Ishikawa iterative algorithm. Thus our result generalizes the corresponding results proved for the above three iterative algorithms to a class of more general operators. At the end, we remark that nothing prevents us to extend our result to the case of the iterative algorithm with error terms.
Abstract: In this paper, we prove a strong convergence result using a recently introduced iterative process with contractive-like operators. This improves andgeneralizes corresponding results in the literature in two ways: iterativeprocess is faster, operators are more general. At the end, we indicatethat the results can also be proved with the iterative process witherror terms.
Abstract: The hidden-point bar method is useful in many
surveying applications. The method involves determining the
coordinates of a hidden point as a function of horizontal and vertical
angles measured to three fixed points on the bar. Using these
measurements, the procedure involves calculating the slant angles,
the distances from the station to the fixed points, the coordinates of
the fixed points, and then the coordinates of the hidden point. The
propagation of the measurement errors in this complex process has
not been fully investigated in the literature. This paper evaluates the
effect of the bar geometry on the position accuracy of the hidden
point which depends on the measurement errors of the horizontal and
vertical angles. The results are used to establish some guidelines
regarding the inclination angle of the bar and the location of the
observed points that provide the best accuracy.
Abstract: In this paper, we consider an iteration process for
approximating common fixed points of two asymptotically quasinonexpansive
mappings and we prove some strong and weak convergence
theorems for such mappings in uniformly convex Banach
spaces.
Abstract: In this paper, we use a one-step iteration scheme to approximate common fixed points of two quasi-asymptotically nonexpansive mappings. We prove weak and strong convergence theorems in a uniformly convex Banach space. Our results generalize the corresponding results of Yao and Chen [15] to a wider class of mappings while extend those of Khan, Abbas and Khan [4] to an improved one-step iteration scheme without any condition and improve upon many others in the literature.
Abstract: By incorporating a prey refuge, this paper proposes new discrete Leslie–Gower predator–prey systems with and without Allee effect. The existence of fixed points are established and the stability of fixed points are discussed by analyzing the modulus of characteristic roots.
Abstract: Equations with differentials relating to the inverse of an unknown function rather than to the unknown function itself are solved exactly for some special cases and numerically for the general case. Invertibility combined with differentiability over connected domains forces solutions always to be monotone. Numerical function inversion is key to all solution algorithms which either are of a forward type or a fixed point type considering whole approximate solution functions in each iteration. The given considerations are restricted to ordinary differential equations with inverted functions (ODEIs) of first order. Forward type computations, if applicable, admit consistency of order one and, under an additional accuracy condition, convergence of order one.