scholarly journals On a New Class of Fractional Difference-Sum Operators with Discrete Mittag-Leffler Kernels

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 772 ◽  
Author(s):  
Thabet Abdeljawad ◽  
Arran Fernandez
Keyword(s):  
Iteration Process ◽  
Laplace Transforms ◽  
Fractional Difference ◽  
Binomial Theorem ◽  
Semigroup Property ◽  
New Class ◽  
Fundamental Properties

We formulate a new class of fractional difference and sum operators, study their fundamental properties, and find their discrete Laplace transforms. The method depends on iterating the fractional sum operators corresponding to fractional differences with discrete Mittag–Leffler kernels. The iteration process depends on the binomial theorem. We note in particular the fact that the iterated fractional sums have a certain semigroup property, and hence, the new introduced iterated fractional difference-sum operators have this semigroup property as well.

scholarly journals ωb-Topological Vector Spaces

2020 ◽  
Vol 19 ◽  
Keyword(s):  
Vector Space ◽  
Topological Vector Space ◽  
Vector Spaces ◽  
Closed Set ◽  
Topological Vector Spaces ◽  
New Class ◽  
Fundamental Properties ◽  
General Properties

The purpose of the present paper is to introduce the new class of ω b - topological vector spaces. We study several basic and fundamental properties of ω b - topological and investigate their relationships with certain existing spaces. Along with other results, we prove that transformation of an open (resp. closed) set in aω b - topological vector space is ω b - open (resp. closed). In addition, some important and useful characterizations of ω b - topological vector spaces are established. We also introduce the notion of almost ω b - topological vector spaces and present several general properties of almost ω b - topological vector spaces.

scholarly journals Positivity and stabilization of fractional 2D linear systems described by the Roesser model

2010 ◽  
Vol 20 (1) ◽  
pp. 85-92 ◽  
Author(s):  
Tadeusz Kaczorek ◽  
Krzysztof Rogowski
Keyword(s):  
Linear Systems ◽  
State Feedback ◽  
Sufficient Conditions ◽  
Roesser Model ◽  
Fractional Difference ◽  
Fractional Systems ◽  
New Class ◽  
Discrete Time Systems ◽  
Necessary And Sufficient ◽  
Time Systems

Positivity and stabilization of fractional 2D linear systems described by the Roesser modelA new class of fractional 2D linear discrete-time systems is introduced. The fractional difference definition is applied to each dimension of a 2D Roesser model. Solutions of these systems are derived using a 2DZ-transform. The classical Cayley-Hamilton theorem is extended to 2D fractional systems described by the Roesser model. Necessary and sufficient conditions for the positivity and stabilization by the state-feedback of fractional 2D linear systems are established. A procedure for the computation of a gain matrix is proposed and illustrated by a numerical example.

scholarly journals Remarks on Pre-I-Regular Pre-I-Open Sets

2014 ◽  
Vol 2014 ◽  
pp. 1-4
Author(s):  
R. Sajuntha
Keyword(s):  
Equivalence Relation ◽  
Closed Sets ◽  
New Class ◽  
Fundamental Properties ◽  
Open Set ◽  
Regular Sets

We deal with the new class of pre-I-regular pre-I-open sets in which the notion of pre-I-open set is involved. We characterize these sets and study some of their fundamental properties. We also present other notions called extremally pre-I-disconnectedness, locally pre-I-indiscreetness, and pre-I-regular sets by utilizing the notion of pre-I-open and pre-I-closed sets by which we obtain some equivalence relation for pre-I-regular pre-I-open sets.

scholarly journals On weak and strong convergence of an explicit iteration process for a total asymptotically quasi-I-nonexpansive mapping in Banach space

Filomat ◽  
2014 ◽  
Vol 28 (8) ◽  
pp. 1699-1710
Author(s):  
Hukmi Kiziltunc ◽  
Yunus Purtas
Keyword(s):  
Banach Space ◽  
Nonexpansive Mapping ◽  
Strong Convergence ◽  
Iterative Process ◽  
Iteration Process ◽  
Nonempty Closed Convex Subset ◽  
Weak And Strong Convergence ◽  
New Class ◽  
Convergence Results ◽  
Definition Of

In this paper, we introduce a new class of Lipschitzian maps and prove some weak and strong convergence results for explicit iterative process using a more satisfactory definition of self mappings. Our results approximate common fixed point of a total asymptotically quasi-I-nonexpansive mapping T and a total asymptotically quasi-nonexpansive mapping I, defined on a nonempty closed convex subset of a Banach space.

scholarly journals Fuzzy integral inequalities on coordinates of convex fuzzy interval-valued functions

2021 ◽  
Vol 18 (5) ◽  
pp. 6552-6580
Author(s):  
Muhammad Bilal Khan ◽  
◽  
Pshtiwan Othman Mohammed ◽  
Muhammad Aslam Noor ◽  
Khadijah M. Abualnaja ◽  
...  
Keyword(s):  
Order Relation ◽  
Strong Relationship ◽  
Double Integral ◽  
New Class ◽  
Fundamental Properties ◽  
Starting Point ◽  
Special Cases ◽  
Fuzzy Order ◽  
Interval Valued ◽  
Fuzzy Interval

<abstract> <p>In this study, we introduce and study new fuzzy-interval integral is known as fuzzy-interval double integral, where the integrand is fuzzy-interval-valued functions (FIVFs). Also, some fundamental properties are also investigated. Moreover, we present a new class of convex fuzzy-interval-valued functions is known as coordinated convex fuzzy-interval-valued functions (coordinated convex FIVFs) through fuzzy order relation (FOR). The FOR $\left(\preccurlyeq \right)$ and fuzzy inclusion relation (⊇) are two different concepts. With the help of fuzzy-interval double integral and FOR, we have proved that coordinated convex fuzzy-IVF establish a strong relationship between Hermite-Hadamard (<italic>HH</italic>-) and Hermite-Hadamard-Fejér (<italic>HH</italic>-Fejér) inequalities. With the support of this relation, we also derive some related <italic>HH</italic>-inequalities for the product of coordinated convex FIVFs. Some special cases are also discussed. Useful examples that verify the applicability of the theory developed in this study are presented. The concepts and techniques of this paper may be a starting point for further research in this area.</p> </abstract>

scholarly journals Beta- Star- Continuity and Beta- Star- Contra- Continuity

2021 ◽  
Vol 7 ◽  
pp. 43-66
Author(s):  
Raja Mohammad Latif
Keyword(s):  
Continuous Functions ◽  
General Topology ◽  
Topological Spaces ◽  
New Class ◽  
Fundamental Properties ◽  
Open Set ◽  
Class Of Functions

In 2014 Mubarki, Al-Rshudi, and Al- Juhani introduced and studied the notion of a set in general topology called β*-open set and investigated its fundamental properties and studied the relationships between β*-open set and other topological sets including β*-continuity in topological spaces. We introduce and investigate several properties and characterizations of a new class of functions between topological spaces called β*- open, β*- closed, β*- continuous and β*- irresolute functions in topological spaces. We also introduce slightly β*- continuous, totally β*- continuous and almost β*- continuous functions between topological spaces and establish several characterizations of these new forms of functions. Furthermore, we also introduce and investigate certain ramifications of contra continuous and allied functions, namely, contra β*- continuous, and almost contra β*-continuous functions along with their several properties, characterizations and natural relationships. Moreover, we introduce new types of closed graphs by using β*- open sets and investigate its properties and characterizations in topological spaces.

scholarly journals Plasmonic nanolasers: fundamental properties and applications

Nanophotonics ◽  
2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Ren-Min Ma ◽  
Si-Yi Wang
Keyword(s):  
Scaling Laws ◽  
Diffraction Limit ◽  
Stimulated Emission ◽  
Optical Diffraction ◽  
Low Loss ◽  
Physical Size ◽  
New Class ◽  
Fundamental Properties ◽  
Threshold Gain ◽  
Mode Volume

Abstract Plasmonic nanolasers are a new class of coherent emitters where surface plasmons are amplified by stimulated emission in a plasmonic nanocavity. In contrast to lasers, the physical size and mode volume of plasmonic nanolasers can shrink beyond the optical diffraction limit, and can be operated with faster speed and lower power consumption. It was initially proposed by Bergman and Stockman in 2003, and first experimentally demonstrated in 2009. Here we summarize our studies on the fundamental properties and applications of plasmonic nanolasers in recent years, including dark emission characterization, scaling laws, quantum efficiency, quantum threshold, gain and loss optimization, low loss plasmonic materials, sensing, and eigenmode engineering.

scholarly journals On certain types of notions via preopen sets

2006 ◽  
Vol 37 (4) ◽  
pp. 391-398
Author(s):  
Saeid Jafari
Keyword(s):  
Equivalence Relations ◽  
New Class ◽  
Fundamental Properties ◽  
Preopen Set

In this paper, we deal with the new class of pre-regular $p$-open sets in which the notion of preopen set is involved. We characterize these sets and study some of their fundamental properties. We also present two other notions called extremally $p$-discreteness and locally $p$-indiscreteness by utilizing the notions of preopen and preclosed sets by which we obtain some equivalence relations for pre-regular $p$-open sets. Moreover, we define the notion of regular $p$-open sets by utilizing the notion of pre-regular $p$-open sets. We investigate some of the main properties of these sets and study their relations to pre-regular $p$-open sets.

On q-Analogues of Sumudu Transform

2013 ◽  
Vol 21 (1) ◽  
pp. 239-259 ◽  
Author(s):  
Durmuş Albayrak ◽  
Sunil Dutt Purohit ◽  
Faruk Uçar
Keyword(s):  
Infinite Series ◽  
Laplace Transforms ◽  
Convolution Theorem ◽  
Convergence Conditions ◽  
Fundamental Properties ◽  
Interesting Connection ◽  
Sumudu Transform ◽  
Sumudu Transforms

Abstract The present paper introduces q-analogues of the Sumudu transform and derives some distinct properties, for example its convergence conditions and certain interesting connection theorems involving q-Laplace transforms. Furthermore, certain fundamental properties of q-Sumudu transforms like, linearity, shifting theorems, differentiation and integration etc. have also been investigated. An attempt has also been made to obtain the convolution theorem for the q-Sumudu transform of a function which can be expressed as a convergent infinite series.

A new semigroup obtained via known ones

2019 ◽  
Vol 12 (06) ◽  
pp. 2040008
Author(s):  
Nurten Urlu Özalan ◽  
A. Sinan Çevik ◽  
Eylem Güzel Karpuz
Keyword(s):  
Finiteness Conditions ◽  
New Class ◽  
Fundamental Properties

The goal of this paper is to establish a new class of semigroups based on both Rees matrix and completely [Formula: see text]-simple semigroups. We further present some fundamental properties and finiteness conditions for this new semigroup structure.

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