Atomic system in fuzzy Hilbert space is introduced and the existence of the fuzzy atomic systems for a strongly fuzzy bounded linear operator is studied. The notion of a K-frame in fuzzy Hilbert space is presented and some of their characterizations are given. We will see that fuzzy frame operator of a fuzzy K-frame in fuzzy Hilbert space is invertible under some sufficient condition and validates this by giving some examples. Fuzzy K-frame property in fuzzy Hilbert space preserve by a strongly fuzzy bounded linear operator is established. We will describe stability condition of fuzzy K-frame in fuzzy Hilbert space under some perturbations. We construct new types of fuzzy K-frame using fuzzy K-frame in fuzzy Hilbert space. Further, it is seen that scalar combinations and product of two fuzzy K-frames is also a fuzzy K-frame in fuzzy Hilbert space

The concept of fixed point plays a crucial role in various fields of applied mathematics. The aim of this paper is to establish the existence of a unique fixed point of some type of functions which satisfy a new contraction principle, namely, TSR-contraction principle in various types of probabilistic metric spaces. The proposed contraction mapping is different from our traditional definitions of contraction mapping.

The main aim of this paper is to find a unique common fixed point for six functions in a Menger probabilistic generalized metric space. For this purpose, we have defined the compatibility of three functions and established some required theorems.

This paper develops the theory of soft normed spaces and soft linear operators, extending classical functional analysis to the framework of soft sets. We define soft norms and soft operator norms, and explore the properties of soft bounded and soft continuous linear operators. Key results include the equivalence of soft boundedness and soft continuity, and the characterization of the soft operator norm, including positivity, homogeneity, subadditivity, and submultiplicativity. We also show that a linear operator is soft continuous on the entire space if and only if it is soft continuous at a single point. These results provide a rigorous foundation for soft functional analysis, enabling applications in uncertainty modeling, decision-making, and other fields requiring flexible handling of imprecise information.

In this paper, we introduce the concept of various types fuzzy delta $(\delta)$ compactness such as Quasi fuzzy delta compact, Quasi fuzzy countably delta compact, Weakly fuzzy delta compact, $a$-delta compact, Strong fuzzy delta compact, Ultra fuzzy delta compact and Fuzzy delta compact and characterize these types of fuzzy delta compactness using the notion of fuzzy upper limit of net of some types of delta $(\delta)$ closed sets.

The aim of this paper is to introduce the concept of Delta-Compact spaces along with some basic properties of it. Here, we try to establish the behavior of Delta-Compact spaces under the continuous mapping. Finally, we define another concept namely, Locally Delta-Compactness.

The main aim of this paper is to define a weakest topology $\sigma$ on a linear topological space $(E, \tau)$ such that each $\delta$-continuous functional on $(E, \tau)$ is $\delta$-continuous functional on $(E, \sigma)$ and to find out the relation between the set of these $\delta$-continuous functionals on $(E, \tau)$ and the set of all $\delta$-continuous functionals on $(E, \sigma)$. Also we find out the closure of a subset $A$ of $E$ on that weakest topology by the $\delta$-closure of $A$ with respect to the given topology.

The main aim of this paper is to establish the concepts of soft seminorm and soft norm with the help of balanced, absorbing and convex soft sets. Also, we have established equivalent concepts of soft seminorm as well as of soft norm.

In the era of Industry 4.0, Internet of Things (IoT) has been a crucial component in shaping smart cities and advancing urbanisation. With the ever-rising demand of customers, it is getting tougher to handle numerous IoT end devices with consistent reliability and responsiveness. While CAT-M1 and Nb-IoT architectures could handle faster transfer rates and boarder communication protocols, lower lat...

Pummelo (Citrus grandis Osbeck.), the giant among the citrus, is one of the major monoembryonic species and is well known as the ancestor of grapefruit. The present investigation was carried out with twelve genotypes of pummelo with three replications in each during 2016-17considering nineteen characters like leaf characters, flowering and fruit morphological, physical and chemical characters from ‘citrus descriptor’ (cited by IPGRI, Rome, Italy).Among different morphological characters of leaf, fruit, pulp and seed the pattern of variation was more in characters like leaf lamina margin, leaf apex, fruit shape, fruit base, fruit skin colour, pulp colour and seed shape. The above-mentioned morphological characters are generally highly heritable characters and identity of individual types which may lead to chance of getting desirable types. Early flowering and maximum yield obtained in Type-1.The wide variation of fruit yield showed due to number of fruits per plant and other yield attributing characters. Less number of seeds in a fruit was obtained in Type-9. Significant variation in ascorbic acid (34.98 – 62.61 mg/100 ml juice) was obtained among different pummelo germplasm. From the present investigation, it can be concluded that there is a wide range of variation among different pummelo germplasm. Few types can be exploited for commercial cultivation in new alluvial zone of West Bengal like-Type-1, Type-2, Type-3, Type-5, Type-9 and Type-10 and Type-11.

Cooperative spectrum sensing (CSS) is an efficient method to detect vacant spectrum of a primary user (PU) by combining sensing information of multiple cognitive radios (CRs) in presence of fading. In this paper, effects of perfect and imperfect channel state information (CSI) on CSS network is evaluated. The proposed network is operated over Nakagami-q (Hoyt) and Nakagami-n (Rician) fading affecting both reporting (R) and sensing (S) channels. The CRs which employ energy detectors (EDs) are selected on the basis of CSI between them and a fusion center (FC). The knowledge on the quality of R-channels is estimated at FC using a channel estimator. The estimated CSI is either perfect when there is no error in the estimator, or imperfect when errors are present. Accordingly, CRs are selected under both perfect CSI and imperfect CSI cases. All CRs use the decision statistics obtained by EDs and make one-bit binary decisions about the availability of a PU. Selected CRs only transmit decision information to the FC. The miss detection probability and error rate of network under two cases of selection are evaluated by operating majority and maximal ratio combining rules at the FC. Performance is analyzed for different channel and network parameters and comparison between fusion rules for different fading channels is also highlighted.

Molodtsov introduced the concept of soft set theory, which can be used as a generic mathematical tool for dealing with uncertainty. In fact, it is free from the difficulties that have troubled the usual theoretical approaches. Roy and Samanta [13, 14, 15] defined several basic notions on soft set and studied many properties. In continuation of [13, 14, 15], here we have introduced soft topological vector space and studied few basic properties related to soft topological vector spaces. For introduction of soft topological vector space, there is need to define soft vector space and soft product topological space, which has been encountered in this paper.

The aim of this paper is to define the balanced softset and absorbing soft set over a linear space and construct someuseful theorem depending upon these concepts

The aim of this paper is to construct a topology on a soft set. Also the concepts of soft base, soft subbase are introduced and some important theorems are established.

In consonant with the prime object of this paper as to initiate the concept of hyperquotient structure, necessarily and essentially the notion of hyperquotient sets is the basic to begin with subsequently what comes as the formations of norm on this spaces with the assistance oered by the norm on hypervector spaces. In conclusion, an adequate condition for a normed hyperquotient space to be Banach space has been constituted by us.

In this paper, common xed point theorems have been studied in fuzzy symmetric space instead of fuzzy metric space. Using weakly compatibility, property (E:A: ), we have generalized the common xed point theorems for a pair of weakly compatible self mappings, for four self mappings in fuzzy symmetric space. Also we have established the unique common xed point for four self mappings in this space.

The aim of this paper is to construct a topology on a fuzzy soft set. Also the concepts of fuzzy soft base, fuzzy soft subbase are introduced here and established some important theorems. 2010 AMS Classification: 54A40, 06D72

The main aim of this paper is to generalize the concept of vector space by the hyperstructure. We generalize some definitions such as hypersubspaces, linear combination, Hamel basis, linearly dependence and linearly independence. A few important results like deletion theorem, extension theorem, dimension theorem have been established in this hypervector space.

In this paper, we introduce cone normed linear space, study the cone convergence with respect to cone norm. Finally, we prove the completeness of a finite dimensional cone normed linear space.