Some functionals for copulas

In this paper we study some functionals operating on the set of then-copulas defined on[0,1]n. Conditions under which such functionals are well defined are determined and some counterexamples are described. The study of the fixed points (n-copulas) for these functionals is also considered, and, finally, some open problems are presented.

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AN AFFIRMATIVE ANSWER TO QUASI-CONTRACTION'S OPEN PROBLEM UNDER SOME LOCAL CONSTRAINTS IN JS-METRIC SPACES

Mathematical Modelling and Analysis ◽

10.3846/mma.2019.027 ◽

2019 ◽

Vol 24 (3) ◽

pp. 445-456

Author(s):

Sanaz Pourrazi ◽

Farshid Khojasteh ◽

Mojgan Javahernia ◽

Hasan Khandani

Keyword(s):

Fixed Point ◽

Fixed Points ◽

Open Problem ◽

Metric Spaces ◽

Hausdorff Metric ◽

Affirmative Answer ◽

Point Property ◽

Open Problems ◽

Local Constraints ◽

Strict Fixed Point

In this work, we first present JS-Pompeiu-Hausdorff metric in JS metric spaces and then introduce well-behaved quasi-contraction in order to find an affirmative answer to quasi-contractions’ open problem under some local constraints in JS-metric spaces. In the literature, this problem solved when the constant modules α ∈ [0,1/2] and when α ∈ (1/2,1], finding conditions by which the set of all fixed points be non-empty, has remained open yet. Moreover, we support our result by a notable example. Finally, by taking into account the approximate strict fixed point property we present some worthwhile open problems in these spaces.

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Approximating Common Fixed Points of Nonspreading-Type Mappings and Nonexpansive Mappings in a Hilbert Space

Abstract and Applied Analysis ◽

10.1155/2012/594218 ◽

2012 ◽

Vol 2012 ◽

pp. 1-18 ◽

Cited By ~ 1

Author(s):

Kyung Soo Kim

Keyword(s):

Hilbert Space ◽

Fixed Points ◽

Iterative Scheme ◽

Nonexpansive Mappings ◽

Common Fixed Points ◽

Open Problems ◽

Fundamental Properties ◽

Nonspreading Mappings

We obtain some fundamental properties fork-strictly pseudo-nonspreading mappings in a Hilbert space. We study approximation of common fixed points ofk-strictly pseudo-nonspreading mappings and nonexpansive mappings in a Hilbert space by using a new iterative scheme. Furthermore, we suggest some open problems.

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Lambda theories allowing terms with a finite number of fixed points

Mathematical Structures in Computer Science ◽

10.1017/s0960129515000419 ◽

2015 ◽

Vol 27 (3) ◽

pp. 405-427

Author(s):

BENEDETTO INTRIGILA ◽

RICHARD STATMAN

Keyword(s):

Finite Number ◽

Fixed Points ◽

A New Approach to Proinov-Type Fixed-Point Results in Non-Archimedean Fuzzy Metric Spaces

Mathematics ◽

10.3390/math9233001 ◽

2021 ◽

Vol 9 (23) ◽

pp. 3001

Author(s):

Mi Zhou ◽

Naeem Saleem ◽

Xiaolan Liu ◽

Andreea Fulga ◽

Antonio Francisco Roldán López de Hierro

Keyword(s):

Fixed Point ◽

Fixed Points ◽

Existence And Uniqueness ◽

Metric Spaces ◽

Complete Metric Space ◽

Open Problems ◽

Fuzzy Metric Spaces ◽

Auxiliary Functions ◽

Fuzzy Metric ◽

Contractivity Condition

Very recently, by considering a self-mapping T on a complete metric space satisfying a general contractivity condition of the form ψ(d(Tx,Ty))≤φ(d(x,y)), Proinov proved some fixed-point theorems, which extended and unified many existing results in the literature. Accordingly, inspired by Proinov-type contraction conditions, Roldán López de Hierro et al. introduced a novel family of contractions in fuzzy metric spaces (in the sense of George and Veeramani), whose main advantage is the very weak constraints imposed on the auxiliary functions that appear in the contractivity condition. They also proved the existence and uniqueness of fixed points for the discussed family of fuzzy contractions in the setting of non-Archimedean fuzzy metric spaces. In this paper, we introduce a new family of fuzzy contractions based on Proinov-type contractions for which the involved auxiliary functions are not supposed to satisfy any monotonicity assumptions; further, we establish some new results about the existence and uniqueness of fixed points. Furthermore, we show how the main results in the above-mentioned paper can be deduced from our main statements. In this way, our conclusions provide a positive partial solution to one of the open problems posed by such authors for deleting or weakening the hypothesis of the nondecreasingness character of the auxiliary functions.

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Fixed Points of Almost Generalized (a, y)- Contractions with Rational Expressions

Mathematical Journal of Interdisciplinary Sciences ◽

10.15415/mjis.2017.52008 ◽

2017 ◽

Vol 5 (2) ◽

pp. 101-120

Author(s):

GVR BABU

Keyword(s):

Fixed Points ◽

Rational Expressions

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Topics in Quaternion Linear Algebra

10.23943/princeton/9780691161853.001.0001 ◽

2014 ◽

Cited By ~ 19

Author(s):

Leiba Rodman

Keyword(s):

Linear Algebra ◽

Complex Analysis ◽

Dimensional Space ◽

Applied Mathematics ◽

Three Dimensional ◽

Number System ◽

Graduate Course ◽

Open Problems ◽

Unpublished Research ◽

Reference Tool

Quaternions are a number system that has become increasingly useful for representing the rotations of objects in three-dimensional space and has important applications in theoretical and applied mathematics, physics, computer science, and engineering. This is the first book to provide a systematic, accessible, and self-contained exposition of quaternion linear algebra. It features previously unpublished research results with complete proofs and many open problems at various levels, as well as more than 200 exercises to facilitate use by students and instructors. Applications presented in the book include numerical ranges, invariant semidefinite subspaces, differential equations with symmetries, and matrix equations. Designed for researchers and students across a variety of disciplines, the book can be read by anyone with a background in linear algebra, rudimentary complex analysis, and some multivariable calculus. Instructors will find it useful as a complementary text for undergraduate linear algebra courses or as a basis for a graduate course in linear algebra. The open problems can serve as research projects for undergraduates, topics for graduate students, or problems to be tackled by professional research mathematicians. The book is also an invaluable reference tool for researchers in fields where techniques based on quaternion analysis are used.

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