Quasilinear Spaces Research Articles

Soft quasilinear operators in soft normed quasilinear spaces

In this study, we define soft quasilinear functionals on soft normed quasilinear spaces and we examine some of its qualities. By using the soft quasilinear operator defined in [6] we specify and prove some theorem related to the continuity and boundedness of soft quasilinear operators and functionals. Furthermore, we give some examples in favor of the soft quasilinear functionals.

On Soft Normed Quasilinear Spaces

In this study, we investigate some properties of soft quasi-sequences and present new results. We then study the completeness of soft normed quasilinear space and present an analog of convergence and boundness results of soft quasi sequences in soft normed quasilinear spaces. Moreover, we define regular and singular subspaces of soft quasilinear spaces and draw several conclusions related to these notions. Afterward, we provide examples of these results in soft normed quasilinear spaces generalizing well-known results in soft linear normed spaces. Additionally, we offer new results concerning soft quasi subspaces of soft normed quasilinear spaces. Finally, we discuss the need for further research.

Some new results on soft quasilinear spaces

In this article, we focus on developing new results regarding normed quasilinear spaces. We provide a definition for soft homogenized quasilinear spaces and obtain some related results. Furthermore, we explore the floor of soft normed quasilinear spaces. Using some soft linearity and soft quasilinearity methods, we derive new results and examples. Finally, we also obtain some new consequences that we believe will facilitate the development of quasilinear functional analysis in a soft inner product quasilinear space.

Soft interval spaces and soft interval sequence spaces

In this article, we present the two new kinds of examples of soft quasilinear spaces namely ?gIRn soft interval space? and ?eIs, eIl2, fIl? and fIc0 soft interval sequence spaces?. We give some properties of these spaces. We study completeness of gIRn soft normed quasilinear spaces. Further, we obtain some results on these soft interval spaces and soft interval sequence spaces related to concepts of soft quasilinear dependence-independence and solid-floored.

From quasilinear structures to population dynamics: Global stability analysis of an uncertain nonlinear delay system with interval approach

In this paper, we analyze a new continuous-time epidemic model including nonlinear delay differential equations by using parameters and functions selected from a class of intervals whose algebraic basis is based on quasilinear spaces. The main idea in the model’s generic structure is based on uncertainties in the values of parameters and functions forming the model. Therefore, using an interval coefficient approach rather than the exact value of parameters and functions that define transmissions between the compartments in the population dynamics will better represent the reality. Furthermore, preferring such an approach provides more realistic scenarios for temporal and stability dynamics of a population exposed to a disease. In this study, the quasilinear space is defined to explain the mathematical background of the interval approach in the fictional chain of the model. Next, descriptions belonging to the introduced model are included. After this compartmental system is presented as two systems formed by the lower and upper endpoints of the intervals determining parameters and functions, local and global dynamics related to stabilities of the models are analyzed separately for each. Then, using some interval analysis and functional analysis methods, these results are combined, and a conclusion about the stability of the proposed epidemic model has been reached. Alongside, the performance of the proposed approach is demonstrated by a visual simulation.

Inner Product Fuzzy Quasilinear Spaces and Some Fuzzy Sequence Spaces

It has been shown that the class of fuzzy sets has a quasilinear space structure. In addition, various norms are defined on this class, and it is given that the class of fuzzy sets is a normed quasilinear space with these norms. In this study, we first developed the algebraic structure of the class of fuzzy sets F(ℝn) and gave definitions such as quasilinear independence, dimension, and the algebraic basis in these spaces. Then, with special norms, namely, ‖u‖q = where 1 ≤ q ≤ ∞, we stated that (F(ℝn), ‖u‖q) is a complete normed space. Furthermore, we introduced an inner product in this space for the case q = 2. The inner product must be in the form. For u, v ∈ F(ℝn). We also proved that the parallelogram law can only be provided in the regular subspace, not in the entire of F(ℝn). Finally, we showed that a special class of fuzzy number sequences is a Hilbert quasilinear space.

Inner-product quasilinear spaces with applications in signal processing

If certain characteristics of a non-deterministic signal are known, can some approximate results be obtained concerning the frequency, deterministic autocorrelation or other characteristics of the signal? The mathematical techniques we have developed allow us to obtain some approximate estimations of this type. In this way we use some new mathematical methods so called quasilinear functional analysis. Interval analysis also in the scope of this area and we use complex interval-valued signals in calculations. Especially, in this work, we give some special properties and results of inner-product quasilinear spaces which are generalizations of classical inner-product spaces. By this results we give easy examples of approximate estimations of deterministic autocorrelation of some semi non-deterministic signals or signals with inexact data. Further, we have constructed the space $\mathbb{I}l_{2}$ and we have showed that $\mathbb{I}l_{2}$ is an inner-product quasilinear space. This space provides a basis for an estimation of deterministic autocorrelation of the signals with inexact data.

QUOTIENT SPACES ON QUASI LINEAR SPACES

Trace of quotient spaces is usually seen wherever there is a study of a linear structure. In linear spaces, we use subspaces and their corresponding equivalence relation to define quotient spaces. With the same method, in this paper, we present two generalized structures of quotient space that are defined on quasilinear spaces. One of them is a quasilinear space and the other is a linear space. After that, we try to introduce norms on certain states of these spaces and examin some properties of them. We will also provide examples for better understanding throughout the process.

Soft Quasilinear Spaces and Soft Normed Quasilinear Spaces

In this study, a recent concepts of soft quasilinear spaces and soft proper quasilinear spaces are presented. Further, soft quasi vectors in soft quasilinear spaces are investigated, and several related properties are examined such as quasilinear dependent and quasilinear independent. Also, the concept of soft quasi norm of soft quasilinear spaces is given. Lastly, soft quasilinear operators on soft normed quasilinear spaces are defined, and some results about the bounded soft quasilinear operators and continuous soft quasilinear operators are obtained.

Quasilineer Uzaylarda Biquasilineer Fonksiyoneller ve Bazı Sonuçları

Bu çalışmada quasilineer fonksiyonel analizde yeni bir kavram olan biquasilineer fonksiyonel kavramını tanımladık. Bilineer fonksiyonel kavramında olduğu gibi biquasilineer fonksiyonel ve kuadratik form kavramlarında da bir iç çarpım quasilineer uzayına ihtiyaç duyulmadığını gördük. Bu fonksiyonelleri herhangi bir quasilineer uzayında tanımlayabildik. Çalışmamızda bu yeni kavramı verdikten sonra Hilbert quasilineer uzaylarda biquasilineer fonksiyoneller teorisi üzerine dikkate değer bazı örnekler verdik. Ve yine bu teori üzerine bazı teoremler ve ispatlarını çalışmamızda sunduk.

Intervals and (non-)negative numbers

Intervals have a double nature: they can be considered as compact sets ofВ real numbers (set-intervals) or as approximate numbers. A set-interval isВ presented as an ordered pair of two real numbers (interval end-points), whereasВ an approximate number is an ordered pairВ consisting of a real ``exact'' number and a nonnegative error bound.В Thus, differently to the case withВ set-intervals, where both endpoints are real numbers, when operating with approximate numbers,В one should know the algebraic properties of the arithmetic operationsВ over error bounds, that is over nonnegative numbers. ThisВ work is devoted to the algebraic study ofВ the arithmetic operations addition and multiplication by scalars for approximate numbers, resp. forВ errors bounds. Such a setting leads to so-called quasilinear spaces. We formulate andВ prove several new properties of such spaces, which areВ important from computational aspect. In particular, we focus our study on theВ operation ``distance between two nonnegative numbers''.В We show that this operation plays an important role in the study of theВ concept of linear independence of interval vectors, the latter being correctly defined.

A Generalization of the Hahn-Banach Theorem in Seminormed Quasilinear Spaces

A Generalization of the Hahn-Banach Theorem in Seminormed Quasilinear Spaces

Riesz Lemma in Normed Quasilinear Spaces and Its an Application

Aseev (Proc Steklov Inst Math 2:23–52, 1986) started a new field in functional analysis by introducing the concept of normed quasilinear spaces which is a generalization of classical normed linear spaces. Then, we introduced the normed proper quasilinear spaces in addition to the notions of regular and singular dimension of a quasilinear space, Cakan and Yilmaz (J Nonlinear Sci Appl 8:816–836, 2015). In this study, we classify the normed proper quasilinear spaces as “solid-floored” and “non solid-floored”. Thus, some properties of normed proper quasilinear spaces become more comprehensible. Also we present the counterpart of classical Riesz lemma in normed quasilinear spaces.

Retracted: Quasilinear Inner Product Spaces and Hilbert Quasilinear Spaces

Retracted: Quasilinear Inner Product Spaces and Hilbert Quasilinear Spaces

On orthonormal sets in inner product quasilinear spaces

Aseev, S. M [Aseev, S. M., Quasilinear operators and their application in the theory of multivalued mappings, Proc. Steklov Inst. Math., 2 (1986), 23–52] generalized linear spaces by introducing the notion of quasilinear spaces in 1986. Then, special quasilinear spaces which are called ”solid floored quasilinear spaces” were defined and their some properties examined in [C¸ akan, S., Some New Results Related to Theory of Normed Quasilinear Spaces, Ph.D. Thesis, ˙Inon¨ u University, Malatya, 2016]. In fact, this classification was made so as to examine consistent and detailed some properties related ¨ to quasilinear spaces. In this paper, we present some properties of orthogonal and orthonormal sets on inner product quasilinear spaces. At the same time, the mentioned classification is crucial for define some topics such as Schauder basis, complete orthonormal sequence, orthonormal basis and complete set and some related theorems. Also, we try to explain some geometric differences of inner product quasilinear spaces from the inner product (linear) spaces.

On orthonormal sets in inner product quasilinear spaces

On orthonormal sets in inner product quasilinear spaces

Some new results on inner product quasilinear spaces

In this article, we research on the properties of the floor of an element taken from an inner product quasilinear space. We prove some theorems related to this new concept. Further, we try to explore some new results in quasilinear functional analysis. Also, some examples have been given which provide an important information about the properties of floor of an inner product quasilinear space.

New Inner Product Quasilinear Spaces on Interval Numbers

Primarily we examine the new example of quasilinear spaces, namely, “IRninterval space.” We obtain some new theorems and results related to this new quasilinear space. After giving some new notions of quasilinear dependence-independence and basis on quasilinear functional analysis, we obtain some results onIRninterval space related to these concepts. Secondly, we presentIs,Ic0,Il∞, andIl2quasilinear spaces and we research some algebraic properties of these spaces. We obtain some new results and provide an important contribution to the improvement of quasilinear functional analysis.

Some refinement of the triangle inequality in quasi 2-normed spaces

In this paper we establish a generalization of the triangle inequity and the Dunkl-Williams inequality in quasi 2-normed linear spaces.

On the triangle inequality in quasi 2-normed spaces and a new characterization of 2-inner product spaces

In this paper we establish a generalization of the triangle inequality in quasi 2-normed linear spaces. Moreover, we obtained a new characterization of 2-inner product spaces by comparing the 2-angular distance and 2-skew-angular distance with each other.