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1 – 10 of 999Godwin Amechi Okeke and Daniel Francis
This paper aims to prove some fixed-point theorems for a general class of mappings in modular G-metric spaces. The results of this paper generalize and extend several known…
Abstract
Purpose
This paper aims to prove some fixed-point theorems for a general class of mappings in modular G-metric spaces. The results of this paper generalize and extend several known results to modular G-metric spaces, including the results of Mutlu et al. [1]. Furthermore, the authors produce an example to demonstrate the applicability of the results.
Design/methodology/approach
The results of this paper are theoretical and analytical in nature.
Findings
The authors established some fixed-point theorems for a general class of mappings in modular G-metric spaces. The results generalize and extend several known results to modular G-metric spaces, including the results of Mutlu et al. [1]. An example was constructed to demonstrate the applicability of the results.
Research limitations/implications
Analytical and theoretical results.
Practical implications
The results of this paper can be applied in science and engineering.
Social implications
The results of this paper is applicable in certain social sciences.
Originality/value
The results of this paper are new and will open up new areas of research in mathematical sciences.
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Chon Van Le and Uyen Hoang Pham
This paper aims mainly at introducing applied statisticians and econometricians to the current research methodology with non-Euclidean data sets. Specifically, it provides the…
Abstract
Purpose
This paper aims mainly at introducing applied statisticians and econometricians to the current research methodology with non-Euclidean data sets. Specifically, it provides the basis and rationale for statistics in Wasserstein space, where the metric on probability measures is taken as a Wasserstein metric arising from optimal transport theory.
Design/methodology/approach
The authors spell out the basis and rationale for using Wasserstein metrics on the data space of (random) probability measures.
Findings
In elaborating the new statistical analysis of non-Euclidean data sets, the paper illustrates the generalization of traditional aspects of statistical inference following Frechet's program.
Originality/value
Besides the elaboration of research methodology for a new data analysis, the paper discusses the applications of Wasserstein metrics to the robustness of financial risk measures.
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Godwin Amechi Okeke and Daniel Francis
The authors prove the existence and uniqueness of fixed point of mappings satisfying Geraghty-type contractions in the setting of preordered modular G-metric spaces. The authors…
Abstract
Purpose
The authors prove the existence and uniqueness of fixed point of mappings satisfying Geraghty-type contractions in the setting of preordered modular G-metric spaces. The authors apply the results in solving nonlinear Volterra-Fredholm-type integral equations. The results extend generalize compliment and include several known results as special cases.
Design/methodology/approach
The results of this paper are theoretical and analytical in nature.
Findings
The authors prove the existence and uniqueness of fixed point of mappings satisfying Geraghty-type contractions in the setting of preordered modular G-metric spaces. apply the results in solving nonlinear Volterra-Fredholm-type integral equations. The results extend, generalize, compliment and include several known results as special cases.
Research limitations/implications
The results are theoretical and analytical.
Practical implications
The results were applied to solving nonlinear integral equations.
Social implications
The results has several social applications.
Originality/value
The results of this paper are new.
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Keywords
This paper aims to develop a geometry of moral systems. Existing social choice mechanisms predominantly employ simple structures, such as rankings. A mathematical metric among…
Abstract
Purpose
This paper aims to develop a geometry of moral systems. Existing social choice mechanisms predominantly employ simple structures, such as rankings. A mathematical metric among moral systems allows us to represent complex sets of views in a multidimensional geometry. Such a metric can serve to diagnose structural issues, test existing mechanisms of social choice or engender new mechanisms. It also may be used to replace active social choice mechanisms with information-based passive ones, shifting the operational burden.
Design/methodology/approach
Under reasonable assumptions, moral systems correspond to computational black boxes, which can be represented by conditional probability distributions of responses to situations. In the presence of a probability distribution over situations and a metric among responses, codifying our intuition, we can derive a sensible metric among moral systems.
Findings
Within the developed framework, the author offers a set of well-behaved candidate metrics that may be employed in real applications. The author also proposes a variety of practical applications to social choice, both diagnostic and generative.
Originality/value
The proffered framework, derived metrics and proposed applications to social choice represent a new paradigm and offer potential improvements and alternatives to existing social choice mechanisms. They also can serve as the staging point for research in a number of directions.
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In this paper, we use the notion of cyclic representation of a nonempty set with respect to a pair of mappings to obtain coincidence points and common fixed points for a pair of…
Abstract
Purpose
In this paper, we use the notion of cyclic representation of a nonempty set with respect to a pair of mappings to obtain coincidence points and common fixed points for a pair of self-mappings satisfying some generalized contraction- type conditions involving a control function in partial metric spaces. Moreover, we provide some examples to analyze and illustrate our main results.
Design/methodology/approach
Theoretical method.
Findings
We establish some coincidence points and common fixed point results in partial metric spaces.
Originality/value
Results of this study are new and interesting.
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H. Fukhar-ud-din and A.R. Khan
The purpose of this paper is to introduce the implicit midpoint rule (IMR) of nonexpansive mappings in 2- uniformly convex hyperbolic spaces and study its convergence. Strong and
Abstract
The purpose of this paper is to introduce the implicit midpoint rule (IMR) of nonexpansive mappings in 2- uniformly convex hyperbolic spaces and study its convergence. Strong and
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Tran Ngoc Tam, Nguyen Minh Hai and Bantaojai Thanatporn
The purpose of this paper is to study the Hölder calmness of solutions to equilibrium problems and apply it to economics.
Abstract
Purpose
The purpose of this paper is to study the Hölder calmness of solutions to equilibrium problems and apply it to economics.
Design/methodology/approach
The authors obtain the Hölder calmness by using an effective approach. More precisely, under the key assumption of strong convexity, sufficient conditions for the Hölder continuity of solution maps to equilibrium problems are established.
Findings
A new result in stability analysis for equilibrium problems and applications in economics is archived.
Originality/value
The authors confirm that the paper has not been published previously, is not under consideration for publication elsewhere and is not being simultaneously submitted elsewhere.
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Rishabh Ranjan, P.N. Pandey and Ajit Paul
In this paper, the authors prove that the Douglas space of second kind with a generalised form of special (α, β)-metric F, is conformally invariant.
Abstract
Purpose
In this paper, the authors prove that the Douglas space of second kind with a generalised form of special (α, β)-metric F, is conformally invariant.
Design/methodology/approach
For, the authors have used the notion of conformal transformation and Douglas space.
Findings
The authors found some results to show that the Douglas space of second kind with certain (α, β)-metrics such as Randers metric, first approximate Matsumoto metric along with some special (α, β)-metrics, is invariant under a conformal change.
Originality/value
The authors introduced Douglas space of second kind and established conditions under which it can be transformed to a Douglas space of second kind.
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Ghodratallah Fasihi-Ramandi and Shahroud Azami
In this paper, we consider the Heisenberg groups which play a crucial role in both geometry and theoretical physics.
Abstract
Purpose
In this paper, we consider the Heisenberg groups which play a crucial role in both geometry and theoretical physics.
Design/methodology/approach
In the first part, we retrieve the geometry of left-invariant Randers metrics on the Heisenberg group H2n+1, of dimension 2n + 1. Considering a left-invariant Randers metric, we give the Levi-Civita connection, curvature tensor, Ricci tensor and scalar curvature and show the Heisenberg groups H2n+1 have constant negative scalar curvature.
Findings
In the second part, we present our main results. We show that the Heisenberg group H2n+1 cannot admit Randers metric of Berwald and Ricci-quadratic Douglas types. Finally, the flag curvature of Z-Randers metrics in some special directions is obtained which shows that there exist flags of strictly negative and strictly positive curvatures.
Originality/value
In this work, we present complete Reimannian geometry of left invarint-metrics on Heisenberg groups. Also, some geometric properties of left-invarainat Randers metrics will be studied.
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H.M. Manjunatha, S.K. Narasimhamurthy and Zohreh Nekouee
The purpose of this paper is to study the Bertotti–Kasner space-time and its geometric properties.
Abstract
Purpose
The purpose of this paper is to study the Bertotti–Kasner space-time and its geometric properties.
Design/methodology/approach
This paper is based on the features of λ-tensor and the technique of six-dimensional formalism introduced by Pirani and followed by W. Borgiel, Z. Ahsan et al. and H.M. Manjunatha et al. This technique helps to describe both the geometric properties and the nature of the gravitational field of the space-times in the Segre characteristic.
Findings
The Gaussian curvature quantities specify the curvature of Bertotti–Kasner space-time. They are expressed in terms of invariants of the curvature tensor. The Petrov canonical form and the Weyl invariants have also been obtained.
Originality/value
The findings are revealed to be both physically and geometrically interesting for the description of the gravitational field of the cylindrical universe of Bertotti–Kasner type as far as the literature is concerned. Given the technique of six-dimensional formalism, the authors have defined the Weyl conformal
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