19 research outputs found

    Common fixed point theorems for cyclic contractive mappings in partial cone b-metric spaces and applications to integral equations

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    In this paper, we introduce the concept of partial cone b-metric spaces as a generalization of partial metric, cone metric and b-metric spaces and establish some topological properties of partial cone b-metric spaces. Moreover, we also prove some common fixed point theorems for cyclic contractive mappings in such spaces. Our results generalize and extend the main results of Huang and Zhang [Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl., 332:1468–1476, 2007], Stanić et al. [Common fixed point under contractive condition of Ćirić's type on cone metric type spaces, Fixed Point Theory Appl., 2012:35, 2012] and Latif et al. [Fixed point results for generalized (α,ψ)‐Meir–Keeler contractive mappings and applications, J. Inequal. Appl., 2014:68, 2014]. Some examples and an application are given to support the usability of the obtained results

    Existence theorem for integral inclusions by a fixed point theorem for multivalued implicit-type contractive mappings

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    In this article, we introduce fixed point theorems for multivalued mappings satisfying implicit-type contractive conditions based on a special form of simulation functions. We also provide an application of our result in integral inclusions. Our outcomes generalize/extend many existing fixed point results

    Some New Results on Coincidence Points for Multivalued Suzuki-Type Mappings in Fairly Complete Spaces

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    In this paper, we introduce Suzuki-type generalized and modified proximal contractive mappings. We establish some coincidence and best proximity point results in fairly complete spaces. Also, we provide coincidence and best proximity point results in partially ordered complete metric spaces for Suzuki-type generalized and modified proximal contractive mappings. Furthermore, some examples are presented in each section to elaborate and explain the usability of the obtained results. As an application, we obtain fixed-point results in metric spaces and in partially ordered metric spaces. The results obtained in this article further extend, modify and generalize the various results in the literature.This research was funded by Basque Government through Grant IT1207/19

    Fixed Point Theory and Related Topics

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    Approximation Theory and Related Applications

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    In recent years, we have seen a growing interest in various aspects of approximation theory. This happened due to the increasing complexity of mathematical models that require computer calculations and the development of the theoretical foundations of the approximation theory. Approximation theory has broad and important applications in many areas of mathematics, including functional analysis, differential equations, dynamical systems theory, mathematical physics, control theory, probability theory and mathematical statistics, and others. Approximation theory is also of great practical importance, as approximate methods and estimation of approximation errors are used in physics, economics, chemistry, signal theory, neural networks and many other areas. This book presents the works published in the Special Issue "Approximation Theory and Related Applications". The research of the world’s leading scientists presented in this book reflect new trends in approximation theory and related topics

    Bifurcation analysis of the Topp model

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    In this paper, we study the 3-dimensional Topp model for the dynamicsof diabetes. We show that for suitable parameter values an equilibrium of this modelbifurcates through a Hopf-saddle-node bifurcation. Numerical analysis suggests thatnear this point Shilnikov homoclinic orbits exist. In addition, chaotic attractors arisethrough period doubling cascades of limit cycles.Keywords Dynamics of diabetes · Topp model · Reduced planar quartic Toppsystem · Singular point · Limit cycle · Hopf-saddle-node bifurcation · Perioddoubling bifurcation · Shilnikov homoclinic orbit · Chao

    Postquantum Br\`{e}gman relative entropies and nonlinear resource theories

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    We introduce the family of postquantum Br\`{e}gman relative entropies, based on nonlinear embeddings into reflexive Banach spaces (with examples given by reflexive noncommutative Orlicz spaces over semi-finite W*-algebras, nonassociative Lp_p spaces over semi-finite JBW-algebras, and noncommutative Lp_p spaces over arbitrary W*-algebras). This allows us to define a class of geometric categories for nonlinear postquantum inference theory (providing an extension of Chencov's approach to foundations of statistical inference), with constrained maximisations of Br\`{e}gman relative entropies as morphisms and nonlinear images of closed convex sets as objects. Further generalisation to a framework for nonlinear convex operational theories is developed using a larger class of morphisms, determined by Br\`{e}gman nonexpansive operations (which provide a well-behaved family of Mielnik's nonlinear transmitters). As an application, we derive a range of nonlinear postquantum resource theories determined in terms of this class of operations.Comment: v2: several corrections and improvements, including an extension to the postquantum (generally) and JBW-algebraic (specifically) cases, a section on nonlinear resource theories, and more informative paper's titl

    Some fixed point results based on contractions of new types for extended b-metric spaces

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    The construction of contraction conditions plays an important role in science for formulating new findings in fixed point theories of mappings under a set of specific conditions. The aim of this work is to take advantage of the idea of extended b-metric spaces in the sense introduced by Kamran et al. [A generalization of b-metric space and some fixed point theorems, Mathematics, 5 (2017), 1–7] to construct new contraction conditions to obtain new results related to fixed points. Our results enrich and extend some known results from b-metric spaces to extended b-metric spaces. We construct some examples to show the usefulness of our results. Also, we provide some applications to support our results

    Error Bounds of Gaussian Quadratures for One Class of Bernstein-Szego Weight Functions

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    We consider the action of the automorphism group I(n) of Zn on the set of k−sets of Zn in the natural way. Although elementary in its nature, it has not been fully analyzed and understood yet. The vast class of enumerative and computational problems problems is related to this action. For example, the number of orbits on the set of k−sets of Zn is one of them that we are interested in. Those enumerative problems are mainly resolved by application of P olya's theory

    Recent Developments of Function Spaces and Their Applications I

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    This book includes 13 papers concerning some of the recent progress in the theory of function spaces and its applications. The involved function spaces include Morrey and weak Morrey spaces, Hardy-type spaces, John–Nirenberg spaces, Sobolev spaces, and Besov and Triebel–Lizorkin spaces on different underlying spaces, and they are applied in the study of problems ranging from harmonic analysis to potential analysis and partial differential equations, such as the boundedness of paraproducts and Calderón operators, the characterization of pointwise multipliers, estimates of anisotropic logarithmic potential, as well as certain Dirichlet problems for the Schrödinger equation
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