Pseudodistances

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Robert Plebaniak - One of the best experts on this subject based on the ideXlab platform.

Kazimierz Włodarczyk - One of the best experts on this subject based on the ideXlab platform.

  • Periodic Point, Endpoint, and Convergence Theorems for Dissipative Set-Valued Dynamic Systems with Generalized Pseudodistances in Cone Uniform and Uniform Spaces
    2015
    Co-Authors: Kazimierz Włodarczyk, Robert Plebaniak
    Abstract:

    the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In cone uniform and uniform spaces, we introduce the three kinds of dissipative set-valued dynamic systems with generalized Pseudodistances and not necessarily lower semicontinuous entropies, we study the convergence of dynamic processes and generalized sequences of iterations of these dissipative dynamic systems, and we establish conditions guaranteeing the existence of periodic points and endpoints of these dissipative dynamic systems and the convergence to these periodic points and endpoints of dynamic processes and generalized sequences of iterations of these dissipative dynamic systems. The paper includes examples. 1

  • Contractions of Banach, Tarafdar, Meir–Keeler, Ćirić–Jachymski–Matkowski and Suzuki types and fixed points in uniform spaces with generalized Pseudodistances
    Journal of Mathematical Analysis and Applications, 2013
    Co-Authors: Kazimierz Włodarczyk, Robert Plebaniak
    Abstract:

    In the uniform spaces (sequentially complete and not sequentially complete), we introduce the concept of the J-families of generalized Pseudodistances, we apply it to construct J-generalized contractions and we provide the conditions guaranteeing the existence and uniqueness of fixed points of these contractions and the convergence to these fixed points of each iterative sequence of these contractions. Our J-generalized contractions essentially extend Banach, Tarafdar, Meir–Keeler, Ciric–Jachymski–Matkowski and Suzuki contractions to uniform spaces with J-families of generalized Pseudodistances. Examples showing a difference between our results and the well-known ones are given. The definitions, the results and the method to investigate uniqueness and iterative approximation of fixed points of the maps presented here are new for maps in uniform and locally convex spaces and even in metric spaces.

  • Fixed points and endpoints of contractive set-valued maps in cone uniform spaces with generalized Pseudodistances
    Fixed Point Theory and Applications, 2012
    Co-Authors: Kazimierz Włodarczyk, Robert Plebaniak
    Abstract:

    We introduce the concept of contractive set-valued maps in cone uniform spaces with generalized Pseudodistances and we show how in these spaces our fixed point and endpoint existence theorem of Caristi type yields the fixed point and endpoint existence theorem for these contractive maps.

  • Generalized uniform spaces, uniformly locally contractive set-valued dynamic systems and fıxed points
    Fixed Point Theory and Applications, 2012
    Co-Authors: Kazimierz Włodarczyk, Robert Plebaniak
    Abstract:

    Motivated by classical Banach contraction principle, Nadler investigated set-valued contractions with respect to Hausdorff distances h in complete metric spaces, Covitz and Nadler (Jr.) investigated set-valued maps which are uniformly locally contractive or contractive with respect to generalized Hausdorff distances H in complete generalized metric spaces and Suzuki investigated set-valued maps which are contractive with respect to distances Qp in complete metric spaces with τ-distances p. Here, we provide more general results which, in particular, include the mentioned ones above. The concepts of generalized uniform spaces, generalized Pseudodistances in these spaces and new distances induced by these generalized Pseudodistances are introduced and a new type of sequential completeness which extended the usual sequential completeness is defined. Also, the new two kinds of set-valued dynamic systems which are uniformly locally contractive or contractive with respect to these new distances are studied and conditions guaranteeing the convergence of dynamic processes and the existence of fixed points of these uniformly locally contractive or contractive set-valued dynamic systems are established. In addition, the concept of the generalized locally convex space as a special case of the generalized uniform space is introduced. Examples illustrating ideas, methods, definitions, and results are constructed, and fundamental differences between our results and the well-known ones are given. The results are new in generalized uniform spaces, uniform spaces, generalized locally convex and locally convex spaces and they are new even in generalized metric spaces and in metric spaces. MSC: 54C60; 47H10; 54E15; 46A03.

  • Contractivity of Leader type and fixed points in uniform spaces with generalized Pseudodistances
    Journal of Mathematical Analysis and Applications, 2012
    Co-Authors: Kazimierz Włodarczyk, Robert Plebaniak
    Abstract:

    Abstract Recently, Jachymski and Joźwik proved that among various classes of contractions which are introduced and studied in the metric fixed point theory, the Leader contractions are greatest general contractions. In this article, we want to show how generalized Pseudodistances in uniform spaces can be used to obtain new and general results of Leader type without complete graph assumptions about maps and without sequentially complete assumptions about spaces, which was not done in the previous publications on this subject. The definitions, results and methods presented here are new for maps in uniform and locally convex spaces and even in metric spaces. Examples showing a difference between our results and the well-known ones are given.

Moosa Gabeleh - One of the best experts on this subject based on the ideXlab platform.

Roxana Smarandache - One of the best experts on this subject based on the ideXlab platform.

  • ITW - Free Pseudodistance Growth Rates for Spatially Coupled LDPC Codes over the BEC
    2018 IEEE Information Theory Workshop (ITW), 2018
    Co-Authors: Cunlu Zhou, David G. M. Mitchell, Roxana Smarandache
    Abstract:

    The minimum pseudoweight is an important parameter related to the decoding performance of LDPC codes with iterative message-passing decoding. In this paper, we consider ensembles of periodically time-varying spatially coupled LDPC (SC-LDPC) codes and the pseudocodewords arising from their finite graph covers of a fixed degree. We show that for certain (J,K)-regular SC-LDPC code ensembles and a fixed cover degree, the typical minimum pseudoweight of the unterminated (and associated tail-biting/terminated) SC-LDPC code ensembles grows linearly with the constraint (block) length as the constraint (block) length tends to infinity. We prove that one can bound the the free pseudodistance growth rate over a BEC from below (respectively, above) using the associated tail-biting (terminated) SC-LDPC code ensemble and show empirically that these bounds coincide for a sufficiently large period, which gives the exact free pseudodistance growth rate for the SC-LDPC ensemble considered.

  • Free Pseudodistance Growth Rates for Spatially Coupled LDPC Codes over the BEC
    2018 IEEE Information Theory Workshop (ITW), 2018
    Co-Authors: Cunlu Zhou, David G. M. Mitchell, Roxana Smarandache
    Abstract:

    The minimum pseudoweight is an important parameter related to the decoding performance of LDPC codes with iterative message-passing decoding. In this paper, we consider ensembles of periodically time-varying spatially coupled LDPC (SC-LDPC) codes and the pseudocodewords arising from their finite graph covers of a fixed degree. We show that for certain (J,K)-regular SC-LDPC code ensembles and a fixed cover degree, the typical minimum pseudoweight of the unterminated (and associated tail-biting/terminated) SC-LDPC code ensembles grows linearly with the constraint (block) length as the constraint (block) length tends to infinity. We prove that one can bound the the free pseudodistance growth rate over a BEC from below (respectively, above) using the associated tail-biting (terminated) SC-LDPC code ensemble and show empirically that these bounds coincide for a sufficiently large period, which gives the exact free pseudodistance growth rate for the SC-LDPC ensemble considered.

Panos E. Livadas - One of the best experts on this subject based on the ideXlab platform.

  • The Kobayashi and Carathe´odory Pseudodistances for complex analytic manifolds
    Information Sciences, 1994
    Co-Authors: Panos E. Livadas
    Abstract:

    Pseudodistances defined on analytic Banach manifolds permit one to obtain a number of results on that space by purely topological methods. In addition, they enable one to give geometric insight into function theoretic results. In this paper, we extend the notion of a complex analytic manifold to a complex analytic Banach manifold over a complex Banach space. Then we show that if M is a complex analytic Banach manifold, then the Kobayashi pseudodistance is the largest for which every holomorphic mapping from the unit disk of the complex plane into a complex analytic Banach manifold is distance decreasing, whereas the Caratheodory pseudodistance is the smallest pseudodistance from which every holomorphic mapping from the complex analytic manifold to the unit disk of the complex plane is distance decreasing.

  • the kobayashi and carathe odory Pseudodistances for complex analytic manifolds
    Information Sciences, 1994
    Co-Authors: Panos E. Livadas
    Abstract:

    Pseudodistances defined on analytic Banach manifolds permit one to obtain a number of results on that space by purely topological methods. In addition, they enable one to give geometric insight into function theoretic results. In this paper, we extend the notion of a complex analytic manifold to a complex analytic Banach manifold over a complex Banach space. Then we show that if M is a complex analytic Banach manifold, then the Kobayashi pseudodistance is the largest for which every holomorphic mapping from the unit disk of the complex plane into a complex analytic Banach manifold is distance decreasing, whereas the Caratheodory pseudodistance is the smallest pseudodistance from which every holomorphic mapping from the complex analytic manifold to the unit disk of the complex plane is distance decreasing.

  • The Kobayashi and Carathéodory Pseudodistances for complex analytic manifolds
    Information Sciences, 1994
    Co-Authors: Panos E. Livadas
    Abstract:

    Information Sciences 76 (1994) 43-56. doi:10.1016/0020-0255(94)90066-3Received by publisher: 1991-10-25Harvest Date: 2016-01-04 12:19:50DOI: 10.1016/0020-0255(94)90066-3Page Range: 43-5

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