A Study of Fuzzy Sequence Spaces

The purpose of this chapter is to introduce and study some new ideal convergence sequence spaces FSJθT, FS0JθT and FS∞JθT on a fuzzy real number F defined by a compact operator T. We investigate algebraic properties like linearity, solidness and monotinicity with some important examples. Further, we also analyze closedness of the subspace and inclusion relations on the said spaces.

Multivalent Prestarlike Functions with Respect to Symmetric Points

A class of p-valent functions of complex order is defined with the primary motive of unifying the concept of prestarlike functions with various other classes of multivalent functions. Interesting properties such as inclusion relations, integral representation, coefficient estimates and the solution to the Fekete–Szegő problem are obtained for the defined function class. Further, we extended the results using quantum calculus. Several consequences of our main results are pointed out.

Some classes of sequence spaces defined by a Musielak-Orlicz function

In the present paper we introduce the sequence spaces c0{ℳ, Λ , p, q}, c{ℳ, Λ, p, q} and l ∞ {ℳ, Λ, p, q} defined by a Musielak-Orlicz function ℳ = (ℳk). We study some topological properties and prove some inclusion relations between these spaces.

On inclusion properties of discrete Morrey spaces

We discuss a necessary condition for inclusion relations of weak type discrete Morrey spaces which can be seen as an extension of the results in [H. Gunawan, E. Kikianty and C. Schwanke, Discrete Morrey spaces and their inclusion properties, Math. Nachr. 291 2018, 8–9, 1283–1296] and [D. D. Haroske and L. Skrzypczak, Morrey sequence spaces: Pitt’s theorem and compact embeddings, Constr. Approx. 51 2020, 3, 505–535]. We also prove a proper inclusion from weak type discrete Morrey spaces into discrete Morrey spaces. In addition, we give a necessary condition for this inclusion. Some connections between the inclusion properties of discrete Morrey spaces and those of Morrey spaces are also discussed.

Properties of Certain Classes of Holomorphic Functions Related to Strongly Janowski Type Function

Most subclasses of univalent functions are characterized with functions that map open unit disc ∇ onto the right-half plane. This concept was later modified in the literature with those mappings that conformally map ∇ onto a circular domain. Many researchers were inspired with this modification, and as such, several articles were written in this direction. On this note, we further modify this idea by relating certain subclasses of univalent functions with those that map ∇ onto a sector in the circular domain. As a result, conditions for univalence, radius results, growth rate, and several inclusion relations are obtained for these novel classes. Overall, many consequences of findings show the validity of our investigation.

Sequence spaces defined via Euler method and matrix transformations

A blend of matrix summability and Euler summability transformation methods is used to define Lacunary sequence spaces defined over n-normed space. Then we present the properties of this space and finally, some inclusion relations are presented.

Poisson like matrix operator and its application in p-summable space

The incomplete gamma function Γ(a, u) is defined by Γ ( a , u ) = ∫ u ∞ t a − 1 e − t d t , $$\Gamma(a,u)=\int\limits_{u}^{\infty}t^{a-1}\textrm{e}^{-t}\textrm{d} t,$$ where u > 0. Using the incomplete gamma function, we define a new Poisson like regular matrix P ( μ ) = ( p n k μ ) $\mathfrak{P}(\mu)=(p^{\mu}_{nk})$ given by p n k μ = n ! Γ ( n + 1 , μ ) e − μ μ k k ! ( 0 ≤ k ≤ n ) , 0 ( k > n ) , $$p^{\mu}_{nk}= \begin{cases} \dfrac{n!}{\Gamma(n+1,\mu)}\dfrac{\textrm{e}^{-\mu}\mu^k}{k!} \quad &(0\leq k\leq n), \\[1ex] 0\quad & (k>n), \end{cases}$$ where μ > 0 is fixed. We introduce the sequence space ℓ p ( P ( μ ) ) $\ell_p(\mathfrak{P}(\mu))$ for 1 ≤ p ≤ ∞ and some topological properties, inclusion relations and generalized duals of the newly defined space are discussed. Also we characterize certain matrix classes and compact operators related to the space ℓ p ( P ( μ ) ) $\ell_p(\mathfrak{P}(\mu))$ . We obtain Gurarii’s modulus of convexity and investigate some geometric properties of the new space. Finally, spectrum of the operator P ( μ ) $\mathfrak{P}(\mu)$ on sequence space c 0 has been investigated.

on ideal convergence of triple sequences in intuitionistic Fuzzy normed space defined by compact operator

The main purpose of this article is to introduce and study some new spaces of I-convergence of triple sequences in intuitionistic fuzzy normed space defined by compact operator i.e 3SI (μ,ν)(T ) and 3SI0(μ,ν)(T ) and examine some fundamental properties, fuzzy topology and verify inclusion relations lying under these spaces.

NEW GENERALIZED CIESARO SPACE WITH SOME TOPOLOGICAL PROPERTIES

The sequence space introduced by M. Et and have studied its various properties. The aim of the present paper is to introduce the new pranormed generalized difference sequence space. and , We give some topological properties and inclusion relations on these spaces. 2010 AMS Mathematical Subject Classification: 46A45; 40C05.