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Content available remote On θ-generalized demimetric mappings and monotone operators in Hadamard spaces
Our main interest in this article is to introduce and study the class of θ-generalized demimetric mappings in Hadamard spaces. Also, a Halpern-type proximal point algorithm comprising this class of mappings and resolvents of monotone operators is proposed, and we prove that it converges strongly to a fixed point of a θ-generalized demimetric mapping and a common zero of a finite family of monotone operators in a Hadamard space. Furthermore, we apply the obtained results to solve a finite family of convex minimization problems, variational inequality problems and convex feasibility problems in Hadamard spaces.
Content available remote On the proximal point algorithm and demimetric mappings in CAT(0) spaces
In this paper, we introduce and study the class of demimetric mappings in CAT(0) spaces. We then propose a modified proximal point algorithm for approximating a common solution of a finite family of minimization problems and fixed point problems in CAT(0) spaces. Furthermore, we establish strong convergence of the proposed algorithm to a common solution of a finite family of minimization problems and fixed point problems for a finite family of demimetric mappings in complete CAT(0) spaces. A numerical example which illustrates the applicability of our proposed algorithm is also given. Our results improve and extend some recent results in the literature.
In this paper, we introduce the concept of (CLRS)-property for mappings F : X x X → X and S : X → X (wherein X stands for a partial metric space) and utilize the same to prove two common fixed point theorems for two pairs of mappings in partial metric spaces. We also furnish two examples to illustrate our main theorems.
It is shown that the graph of the sum of two Lipschitz mappings of the real line into a normed space of infinite dimension, whose graphs have tangents, need not have a tangent. Moreover, it turns out that the contingent of the graph of their linear combination may depend on the coefficients of that combination in quite "nonlinear" way.
Content available remote Supra b-compact and supra b-Lindelöf spaces
In this paper we introduce the notion of supra b-compact spaces and investigate its several properties and characterizat eions. Also we introduce and study the notion of supra b-Lindelöf spaces.
Content available remote A Companion of the generalized trapezoid inequality and applications
A sharp companion of the generalized trapezoid inequality is introduced. Applications to quadrature formula are pointed out.
Content available remote Metodyka konstruowania odwzorowań anamorficznych
Stosowanie powiększenia anamorficznego stanowi ciekawą i użyteczną alternatywę dla map o jednolitej skali i może znaleźć szerokie zastosowanie, przy tworzeniu różnego rodzaju map obszarów o zróżnicowanym przestrzennym rozkładzie informacji. Tego typu odwzorowania są dedykowane głównie do tworzenia dynamicznych (interaktywnych) map elektronicznych, ze wskazaniem na mapy mobilne. Przykładem wykorzystania tego typu prezentacji mogą być mapy nawigacyjne, w których pożądanym jest dostarczanie szczegółowej (w większej skali) prezentacji w pobliżu aktualnego punktu położenia użytkownika - np. aktualnej pozycji na trasie podróży, przy zapewnieniu jednoczesnego ogólnego oglądu dalszej okolicy (w mniejszej skali). Mogą być one również okazjonalnie stosowane do map papierowych - np. turystycznych. Dokładne poznanie właściwości odwzorowań anamorficznych pozwala na świadome ich stosowanie i praktyczne wykorzystanie. Stanowiło również podstawę do stworzenia algorytm ów pozwalających na dynamiczną transformację anamorficzną mapy wektorowej. Wypracowane rozwiązania oraz wnioski i spostrzeżenia z analizy wyników zastosowania odwzorowań anamorficznych w prezentacjach opartych na ogólnie dostępnych danych wektorowych VMap L2 i TBD pozwolą na stosowanie ich do tworzenia map tematycznych wykorzystujących dane VMap L2 i TBD jako dane referencyjne.
Most often, the aim of designing and selecting suitable cartographical transformation is as accurate as possible projection of reality, expressing the aspiration to achieve minimum deformation. A task quite often encountered in cartography is to present areas with uneven distribution of objects and phenomena. Anamorphical projections make it possible to present areas of particular interest in an enlarged scale, while continuity of the whole presentation is preserved. This work presents theory and classification of anamorphical projections as well as metric properties, especially deformation. Precise recognition of anamorphical projection properties allows their deliberate use. Works on anamorphical transformation methodology and their practical employment in cartographical presentations based on generally available vector data VMapL2 as well TBD were also presented. Theoretical considerations allowed building the algorithms presented in the paper. Results of anamorphical transformation are shown and discussed in the paper. The aim of the research is to obtain optimal type and parameters of anamorphical transformation. Anamorphical presentations could find wide application in mobile digital maps based on VMapL2 and TBD vector data. Good example of application could be navigation maps where we usually need more detailed information about present location, while continuity of the whole map is preserved.
Content available remote A common fixed point theorem in non-Archimedean Menger pm-spaces
In the present work, we introduce two types of compatible maps in non-Archimedean Menger PM-spaces and obtain a common fixed point theorem for six maps.
In this paper, we study strong convergence theorems for a generalized three-step iterative scheme with errors to approximate common fixed points of three asymptotically quasi-nonexpansive mappings in real Banach spaces. Our results generalize and improve upon the corresponding results in [1], [2], [3], [4], [5], [6], [7], [9], [13] and [16]. As an application of our results, we give and prove strong convergence theorems in uniformly convex Banach spaces.
Content available remote Fixed point results in complete metric spaces
Using the concept of w-distance, we prove fixed point theorems for multivalued contractive maps. Consequently, we improve and extend the corresponding fixed point results due to Feng and Liu, Nadler and many of others.
We establish here an inequality of Ostrowski type for a random variable whose probability density function belongs to L-infinity[a, b], in terms of the cumulative distribution function and expectation. The inequality is then applied to generalized beta random variable.
Content available remote k-Fold symmetrical mappings and loewner chains
Let B be the unit ball in Cn with respect to an arbitrary norm on Cn. In this paper, we give a necessary and su.cient condition that a Loewner chain f(z, t), such that {e-tf(z, t)}t is more than or equal to 0 is a normal family on B, is k-fold symmetrical. As a corollary, we give a necessary and su.cient condition that a normalized locally biholomorphic mapping on B is spirallike of type and k-fold symmetrical. When alpha = 0, this result solves a natural problem that is similar to an open problem posed by Liczberski. We also give two examples of k-fold symmetrical Loewner chains.
Content available remote Identities with two automorphisms on semiprime rings
In this paper we investigate identities with two automorphisms on semiprime rings. We prove the following result: Let T, S : R approaches R be automorphisms where R is a 2-torsion free semiprime ring satisfying the relation T(x)x = xS(x) for all x is an element of R. In this case the mapping x approaches T(x) - x maps R into its center and T = S.
Content available remote Functions convex in the positive direction of the imaginary axis
The aim of this paper is to present a new method of the proof of an analytic characterization of functions convex in the positive direction of the imaginary axis.
The new concept of weak commutativity of type (KB) is used to prove some fixed point theorems for set and single-valued mappings. We show that continuity of any mapping is not necessary for the existence of common fixed point. We also show that completeness of the whole space can be replaced by a weaker condition.
Content available remote Rotative mappings in metric spaces of hyperbolic type
The aim of this paper is to give some conditions providing existence of fixed points for k-lipschitzian and uniformly k-lipschitzian mappings which are n-rotative with n ≥ 2 in complete metric spaces of hyperbolic type.
Content available remote Remarks on almost locally connected spaces
Some preservation theorems for almost local connectedness are proved.
Content available remote Fixed point theorems for weakly inward multivalued maps on a convex metric space
We prove the existence of fixed point for weakly contractive multivalued maps satisfying the inwardness condition in the framework of a convex metric space. Fixed point theorems for multivalued contraction mapping taking the closed values are also obtained. These theorems extend several known results.
Content available remote Coincidence points for multivalued maps on non-starsharped domain
We improve recent results of Shahzad [Demonstratio Math. 36 (2003), 427-431].
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