<abstract xmlns="http://www.w3.org/1999/xhtml">In 1968, M. G. Maia [16] generalized Banach’s fixed point theorem for a set X endowed with two metrics. In 2014, Ansari [2]introduced the concept of C-class functions and generalized many fixed point theorems in the literature. In this paper, we prove some Maia’s type fixed point results via C-class function in the setting of two metrics space endowed with a binary relation. Our results, generalized and extended many existing fixed point theorems, for generalized contractive and quasi-contractive mappings, in a metric space endowed with binary relation.</abstract>

Maia type fixed point results via C-class function

<abstract xmlns="http://www.w3.org/1999/xhtml">In this note, we discuss the definitions of the difference sequences defined earlier by Kızmaz (1981), Et and Çolak (1995), Malkowsky et al. (2007), Başar (2012), Baliarsingh (2013, 2015) and many others. Several authors have defined the difference sequence spaces and studied their various properties. It is quite natural to analyze the convergence of the corresponding sequences. As a part of this work, a convergence analysis of difference sequence of fractional order defined earlier is presented. It is demonstrated that the convergence of the fractional difference sequence is dynamic in nature and some of the results involved are also inconsistent. We provide certain stronger conditions on the primary sequence and the results due to earlier authors are substantially modified. Some illustrative examples are provided for each point of the modifications. Results on certain operator norms related to the difference operator of fractional order are also determined.</abstract>

On the convergence difference sequences and the related operator norms

<abstract xmlns="http://www.w3.org/1999/xhtml">In this paper we introduce and study the split Horadam quaternions. We give some identities, among others Binet’s formula, Catalan’s, Cassini’s and d’Ocagne’s identities for these numbers.</abstract>

On some properties of split Horadam quaternions

<abstract xmlns="http://www.w3.org/1999/xhtml">The real sequence (x<italic>n</italic>) is maldistributed if for any non-empty interval I, the set {<italic>n</italic> ∈𝕅 : x<italic>n</italic> ∈I} has upper asymptotic density 1. The main result of this note is that the set of all maldistributed real sequences is a residual set in the set of all real sequences (i.e., the maldistribution is a typical property in the sense of Baire categories). We also generalize this result.</abstract>

On topological properties of the set of maldistributed sequences

<abstract xmlns="http://www.w3.org/1999/xhtml">In this note, we recall several connections between the determinant of some tridiagonal matrices and the orthogonal polynomials allowing the relation between Chebyshev polynomials of second kind and Fibonacci numbers. With basic transformations, we are able to recover some recent results on this matter, bringing them into one place.</abstract>

On the connection between tridiagonal matrices, Chebyshev polynomials, and Fibonacci numbers

<abstract xmlns="http://www.w3.org/1999/xhtml">We study a special kind of nil-clean rings, namely those nil-clean rings whose nilpotent elements are difference of two “left-right symmetric” idempotents, and prove that in some various cases they are strongly π-regular. We also show that all nil-clean rings having cyclic unit 2-groups are themselves strongly nil-clean of characteristic 2 (and thus they are again strongly π-regular).</abstract>

A note on nil-clean rings

<abstract xmlns="http://www.w3.org/1999/xhtml">Let T<italic>n</italic> be the class of functions f which are defined by a power series
<disp-formula><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_ausm-2020-0021_eq_001.png"></graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mi>f</mi><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow><mo>=</mo><mi>z</mi><mo>+</mo><msub><mrow><mi>a</mi></mrow><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msub><msup><mrow><mi>z</mi></mrow><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>+</mo><msub><mrow><mi>a</mi></mrow><mi>n</mi></msub><mn>2</mn><msup><mrow><mi>z</mi></mrow><mrow><mi>n</mi><mo>+</mo><mn>2</mn></mrow></msup><mo>+</mo><mo>…</mo></mrow></math><tex-math>f\left( z \right) = z + {a_{n + 1}}{z^{n + 1}} + {a_n}2{z^{n + 2}} + \ldots</tex-math></alternatives></disp-formula>
for every <italic>z</italic> in the closed unit disc <inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_ausm-2020-0021_eq_002.png"></inline-graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>𝕌</mi><mo>¯</mo></mover></math><tex-math>\bar {\mathbb{U}}</tex-math></alternatives></inline-formula>. With m different boundary points <italic>z</italic>s, (s = 1,2,...,m), we consider α<italic>m</italic> ∈ <italic>e</italic>iβ𝒜−j−λf(𝕌), here 𝒜−j−λ is the generalized Alexander integral operator and 𝕌 is the open unit disc. Applying 𝒜−j−λ, a subclass B<italic>n</italic>(α<italic>m</italic>,β,ρ; j, λ) of T<italic>n</italic> is defined with fractional integral for functions f. The object of present paper is to consider some interesting properties of f to be in B<italic>n</italic>(α<italic>m</italic>,β,ρ; j, λ).</abstract>

Faculty of Science, Department of Mathematics

Honorary Professor “1 Decembrie 1918” University Alba Iulia

Generalized operator for Alexander integral operator

<abstract xmlns="http://www.w3.org/1999/xhtml">In this paper we introduce the new types of separation axioms called λD − R0 and λD − R1 spaces, by using λD-open set. The notion λD − R0 and λD − R1 spaces are introduced and some of their properties are investigated.</abstract>

Departamento de Ciencias Naturales y Exactas

On λD − R0 and λD − R1 spaces

<abstract xmlns="http://www.w3.org/1999/xhtml">In this work, soft covered ideals in semigroups are constructed and in this concept, soft covered semigroups, soft covered left (right) ideals, soft covered interior ideals, soft covered (generalized) bi-ideals and soft covered quasi ideals of a semigroup are defined. Various properties of these ideals are introduced and the interrelations of these soft covered ideals and the relations of soft anti covered ideals and soft covered ideals are investigated.</abstract>

Department of Mathematics and Science Education

Soft covered ideals in semigroups

<abstract xmlns="http://www.w3.org/1999/xhtml">In this paper, a general form of the Suzuki type function is considered on S- metric space, to get a fixed point. Then we show that our results generalize some old results.</abstract>

Department of Mathematics, Faculty of Science

Some fixed point results on S-metric spaces

<abstract xmlns="http://www.w3.org/1999/xhtml">Let 𝒭 be a commutative ring with identity and 𝒜(𝒭) be the set of ideals with non-zero annihilator. The strongly annihilating-ideal graph of 𝒭 is defined as the graph SAG(𝒭) with the vertex set 𝒜 (𝒭)* = 𝒜 (𝒭) \{0} and two distinct vertices I and J are adjacent if and only if I ∩ Ann(J) ≠ (0) and J ∩ Ann(I) ≠ (0). In this paper, we study the metric dimension of SAG(𝒭) and some metric dimension formulae for strongly annihilating-ideal graphs are given.</abstract>

Department of Mathematics, Science and Research Branch

On the metric dimension of strongly annihilating-ideal graphs of commutative rings

<abstract xmlns="http://www.w3.org/1999/xhtml">New sufficient conditions involving the properties of analytic functions to belong to the class of Carathéodory functions are investigated. Certain univalence and starlikeness conditions are deduced as special cases of main results.</abstract>

On application of differential subordination for Carathéodory functions

<abstract xmlns="http://www.w3.org/1999/xhtml">In this paper we introduce and study a new class of sets, namely γ−countably paracompact sets. We characterize γ−countably paracompact sets and we study some of its basic properties. We obtain that this class of sets is weaker than α−countably paracompact sets and stronger than β−countably paracompact sets.</abstract>

Department of Mathematics, Faculty of science

Department of Mathematics, Faculty of science Yarmouk

Department of Mathematics and General Courses

China Medical University Hospital, China Medical University

On γ−countably paracompact sets

<abstract xmlns="http://www.w3.org/1999/xhtml">Let k be an arbitrary field and Q a tame quiver of type ˜D4. Consider the path algebra kQ and the category of finite dimensional right modules mod-kQ. We determine the Hall polynomials F<italic>xyz</italic> associated to indecomposable modules of defect ∂z =−2, ∂x = ∂y =−1 or dually ∂z = 2, ∂x = ∂y = 1.</abstract>

Faculty of Mathematics and Computer Science

On some Hall polynomials over a quiver of type ˜D4

AHEAD OF PRINT

Volume 15 (2023): Issue 2 (December 2023)

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Volume 14 (2022): Issue 2 (December 2022)

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Volume 7 (2015): Issue 2 (December 2015)

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Volume 6 (2014): Issue 1 (October 2014)

Volume 5 (2013): Issue 2 (December 2013)

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Acta Universitatis Sapientiae, Mathematica

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