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1

Inertial iterative method with self-adaptive step size for finite family of split monotone variational inclusion and fixed point problems in Banach spaces

Ogwo Grace N., Alakoya Timilehin O., Mewomo Oluwatosin T.

Demonstratio Mathematica

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2022

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Vol. 55, nr 1

193--216

EN

In this paper, we propose and study a new inertial iterative algorithm with self-adaptive step size for approximating a common solution of finite family of split monotone variational inclusion problems and fixed point problem of a nonexpansive mapping between a Banach space and a Hilbert space. This method combines the inertial technique with viscosity method and self-adaptive step size for solving the common solution problem. We prove a strong convergence result for the proposed method under some mild conditions. Moreover, we apply our result to study the split feasibility problem and split minimization problem. Finally, we provide some numerical experiments to demonstrate the efficiency of our method in comparison with some well-known methods in the literature. Our method does not require prior knowledge or estimate of the operator norm, which makes it easily implementable unlike so many other methods in the literature, which require prior knowledge of the operator norm for their implementation.

2

Generalized common fixed point theorem for generalized hybrid mappings in Hilbert spaces

Kondo Atsumasa

Demonstratio Mathematica

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2022

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Vol. 55, nr 1

752--759

EN

In this article, we prove a common fixed point theorem for commutative nonlinear mappings that jointly satisfy a certain condition. From the main theorem, a common fixed point theorem for commutative generalized hybrid mappings is derived as a special case. Our novel approach significantly expands the applicable range of mappings for well-known fixed point theorems to be effective. Examples are presented to explicitly illustrate this contribution.

3

Existence results for ABC-fractional BVP via new fixed point results of F-Lipschitzian mappings

Mehmood Nayyar, Khan Israr Ali, Nawaz Muhammad Ayyaz, Ahmad Niaz

Demonstratio Mathematica

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2022

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Vol. 55, nr 1

452--469

EN

In this article, fixed point results for self-mappings in the setting of two metrics satisfying F -lipschitzian conditions of rational-type are proved, where F is considered as a semi-Wardowski function with constant τ∈R instead of τ>0 . Two metrics have been considered, one as an incomplete while the other is orbitally complete. The mapping is taken to be orbitally continuous from one metric to another. Some examples are provided to validate our results. For applications, we present existence results for the solutions of a new type of ABC-fractional boundary value problem.

4

Computation of solution of integral equations via fixed point results

Alqudah Manar A., Garodia Chanchal, Uddin Izhar, Nieto Juan J.

Demonstratio Mathematica

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2022

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Vol. 55, nr 1

772--785

EN

The motive of this article is to study a modified iteration scheme for monotone nonexpansive mappings in the class of uniformly convex Banach space and establish some convergence results. We obtain weak and strong convergence results. In addition, we present a nontrivial numerical example to show the convergence of our iteration scheme. To demonstrate the utility of our scheme, we discuss the solution of nonlinear integral equations as an application, which is again supported by a nontrivial example.

5

The aesthetic geometry of holy places: A case study of intrinsic relations through traces

Miguel Molines-Cano Jose, Almerich-Chulia Ana

Wiadomości Konserwatorskie

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2021

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Nr 68S

26--34

EN

The Santos Juanes Church in Valencia, Spain, is one of the most important religious buildings in the city. Based on this church, this work proposes an analysis that can be extrapolated to other historic buildings where, like this one, no detailed documents on constructive measurement reasons exist. Hence the present work outlines the unpublished hypothesis of how the sequential process of traces on both the plan and section might have been based on the different ancient and medieval architectural treatises. All this will allow the existing intrinsic relations between the shape of the building and its current aesthetics to be obtained through a metric and geometric analysis of the church.

PL

Kościół Santos Juanes w Walencji jest jednym z najważniejszych budynków sakralnych miasta. Na podstawie tej świątyni artykuł proponuje analizę, która może być przeniesiona na inne budynki historyczne, nieposiadające – podobnie jak ona – szczegółowej dokumentacji dotyczącej wymiarów konstrukcyjnych. W związku z tym tekst przedstawia niepublikowaną hipotezę odnośnie do sekwencyjnego rozmierzania zarówno rzutu, jak i przekroju, które mogło być oparte na różnych starożytnych i średniowiecznych traktatach. Wszystko to pozwoli ustalić relacje pomiędzy kształtem budynku i jego obecną estetyką poprzez metryczną i geometryczną analizę kościoła.

6

On θ-generalized demimetric mappings and monotone operators in Hadamard spaces

Ogwo Grace N., Izuchukwu Chinedu, Aremu Kazeem O., Mewomo Oluwatosin T.

Demonstratio Mathematica

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2020

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Vol. 53, nr 1

95--111

EN

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.

7

An iterative algorithm for the system of split mixed equilibrium problem

Karahan Ibrahim, Jolaoso Lateef Olakunle

Demonstratio Mathematica

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2020

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Vol. 53, nr 1

309--324

EN

In this article, a new problem that is called system of split mixed equilibrium problems is introduced. This problem is more general than many other equilibrium problems such as problems of system of equilibrium, system of split equilibrium, split mixed equilibrium, and system of split variational inequality. A new iterative algorithm is proposed, and it is shown that it satisfies the weak convergence conditions for nonexpansive mappings in real Hilbert spaces. Also, an application to system of split variational inequality problems and a numeric example are given to show the efficiency of the results. Finally, we compare its rate of convergence other algorithms and show that the proposed method converges faster.

8

On the proximal point algorithm and demimetric mappings in CAT(0) spaces

Aremu K. O., Izuchukwu C., Ugwunnadi G. C., Mewomo O. T.

Demonstratio Mathematica

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2018

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Vol. 51, nr 1

277--294

EN

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.

9

Common fixed point theorems for mappings under (CLRS)-property in partial metric spaces

Rao K. P. R., Imdad M., Siva Parvathi K. V.

Demonstratio Mathematica

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2016

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Vol. 49, nr 3

357--371

EN

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.

10

On the contingent of the graph of the sum of two mappings

Turowska M.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

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2013

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Vol. 18

55--66

EN

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.

11

Supra b-compact and supra b-Lindelöf spaces

Mustafa J. M.

Journal of Mathematics and Applications

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2013

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Vol. 36

79--83

EN

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.

12

A Companion of the generalized trapezoid inequality and applications

Alomari M. W.

Journal of Mathematics and Applications

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2013

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Vol. 36

5--15

EN

A sharp companion of the generalized trapezoid inequality is introduced. Applications to quadrature formula are pointed out.

13

Metodyka konstruowania odwzorowań anamorficznych

Grabarczyk-Walus S.

Roczniki Geomatyki

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2009

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T. 7, z. 4

37-46

PL

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.

EN

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.

14

A common fixed point theorem in non-Archimedean Menger pm-spaces

Kutukcu S., Sharma S.

Demonstratio Mathematica

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2009

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Vol. 42, nr 4

837-849

EN

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.

15

On (m, n)-Jordan derivations and commutativity of prime rings

Vukman J.

Demonstratio Mathematica

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2008

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Vol. 41, nr 4

773-778

16

Generalized three-step iteration schemes and common fixed points of three asymptotically quasi-nonexpansive mappings

Rashwan R., Hakim A.

Demonstratio Mathematica

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2008

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Vol. 41, nr 4

895-908

EN

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.

17

Fixed point results in complete metric spaces

Latif A., Albar W.

Demonstratio Mathematica

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2008

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Vol. 41, nr 1

145-150

EN

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.

18

A generalized Ostrowski type inequality for a random variable whose probability density function belongs to L-infinity[a,b].

Rafiq A., Mir N., Zafar F.

Demonstratio Mathematica

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2008

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Vol. 41, nr 3

723-732

EN

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.

19

k-Fold symmetrical mappings and loewner chains

Hamada H., Kohr G.

Demonstratio Mathematica

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2007

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Vol. 40, nr 1

85-94

EN

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.

20

Identities with two automorphisms on semiprime rings

Kosi-Ulbl I.

Demonstratio Mathematica

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2007

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Vol. 40, nr 1

37-42

EN

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.