We introduce the notion of weaving continuous controlled K-g-fusion frame in Hilbert space. Some characterizations of weaving continuous controlled K-g-fusion frame have been presented. We extend some of the recent results of woven K-g-fusion frame and controlled K-g-fusion frame to woven continuous controlled K-g-fusion frame. Finally, a perturbation result of woven continuous controlled K-g-fusion frame has been studied.

The idea of best approximation in linear n-normed space is presented and some examples showing various possibilities of best approximations in linear n-normed space is given. Also, we study strictly convex n-norm and enquire about the uniqueness of best approximations in n-normed linear space. Furthermore, best approximations in n-Hilbert space is discussed. Moreover, the notion of a Banach algebra in n-Banach space is presented and some examples are discussed. A set-theoretic property of invertible and non-invertible elements in a n-Banach algebra is explained and then topological divisor of zero in n-Banach algebra is defined. Finally, we introduce the notion of a complex homeomorphism in a n-Banach algebra and derive Gleason, Kahane, Zelazko type theorem with the help of complex b-homeomorphism in the case of n-Banach algebra.

In continuation of the paper [3], we discuss various consequences of Hahn-Banach theorem for bounded b-linear functional in linear n-normed space and describe the notion of reflexivity of linear nnormed space with respect to bounded b-linear functional. The concepts of strong convergence and weak convergence of a sequence of vectors with respect to bounded b-linear functionals in linear n-normed space have been introduced and some of their properties are being discussed.

The concept of a bi-g-fusion frame for a Hilbert space, which is a generalizations of a controlled g-fusion frame, is introduced and an example is given. Finally, bi-g-fusion frame in tensor product of Hilbert spaces is considered.

We introduce the notion of a continuous biframe in a Hilbert space which is a generalization of discrete biframe in Hilbert space. Representation theorem for this type of generalized frame is verified and some characterizations of this biframe with the help of a invertible operator is given. Here we also introduce the concept of continuous biframe for the tensor products of Hilbert spaces and give an example. Further, we study dual continuous biframe and continuous biframe Bessel multiplier in Hilbert spaces and their tensor products.

In this paper, the notion of soft normal int-field over a field has been introduced. We have established a correspondence, called Soft Galois correspondence, between the soft intermediate int-fields of a finite Galois extension and the soft intgroups of the Galois group corresponding to the field extension. We have generalized some results of Galois theory in the environment of soft set theory.

. We present the notion of continuous controlled K-g-fusion frame in a Hilbert space which is generalization of discrete controlled K-g-fusion frame. We discuss some characterizations of a continuous controlled K-g-fusion frame. A relationship between a continuous controlled K-g-fusion frame and a quotient operator has been studied. Finally, stability of a continuous controlled g-fusion frame has been described.

In respect of b-linear functional, Riesz representation theorem in n-Hilbert space have been proved. We define b-sesquilinear functional in n-Hilbert space and establish the polarization identities. A generalized form of the Schwarz inequality in n-Hilbert space is being discussed. Finally, a generalized version of Riesz representation theorem with respect to b-sesquilinear functional in n-Hilbert space have been developed.

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.

We introduce the notion of a retro Banach frame relative to a bounded $b$-linear functional in $n$-Banach space and see that the sum of two retro Banach frames in $n$-Banach space with different reconstructions operators is also a retro Banach frame in $n$-Banach space. Also, we define retro Banach Bessel sequence with respect to a bounded $b$-linear functional in $n$-Banach space. A necessary and sufficient condition for the stability of retro Banach frame with respect to bounded $b$-linear functional in $n$-Banach space is being obtained. Further, we prove that retro Banach frame with respect to bounded $b$-linear functional in $n$-Banach space is stable under perturbation of frame elements by positively confined sequence of scalars. In $n$-Banach space, some perturbation results of retro Banach frame with the help of bounded $b$-linear functional in $n$-Banach space have been studied. Finally, we give a sufficient condition for finite sum of retro Banach frames to be a retro Banach frame in $n$-Banach space. At the end, we discuss retro Banach frame with respect to a bounded $b$-linear functional in Cartesian product of two $n$-Banach spaces.

Some results in linear\;$n$-normed space have been discussed.\,Several nice properties of bounded\;$b$-linear functional in linear\;$n$-normed space are presented.\,We see that the collection of all bounded\;$b$-linear functionals after introducing suitable operations, is a normed space.

We introduce the definition of intuitionistic fuzzy pseudo-norm and study some properties of convergence and [Formula: see text]-convergence in intuitionistic fuzzy pseudo-normed linear spaces.

In this paper, focus is on the study of spectrum and the spectral properties of bounded linear operators in intuitionistic fuzzy pseudo normed linear spaces(IFPNLS). It is done by studying regular value, resolvent set, spectrum of a linear operator in IFPNLS. Also, some properties of spectrum and resolvent of strongly intuitionistic fuzzy bounded(IFB) linear operators in IFPNLS are being developed. It is observed that, for a linear operator P in an IFPNLS, the resolvent set rho(P) and spectrum sigma(P) are nonempty, rho(P) is open and sigma(P) is closed set.

The concept of K-g-frame in Cartesian product of two Hilbert spaces is being studied.We will see that the Cartesian product of two K-g-frames is also a K-g-frame.The concept of K-g-frame operator on Cartesian product of two Hilbert spaces is being presented and results of it are being established.Finally, we give a perturbation result on K-g-frame in Cartesian product of two Hilbert spaces.

In this paper we consider some functional equations for studying their Hyers-Ulam-Rassias stability. This stability has been studied for a variety of mathematical structures. Our framework of dis-cussion is intuitionistic fuzzy normed linear space. We consider both Archimedean and non-Archimedean varieties of such spaces. The approach to the present problem is a fixed point approach, that is, we obtain our results by applications of an extension of the Banach contraction mapping principle on generalized metric spaces where infinite distances are allowable.

Generalized fusion frame and some of their properties in tensor product of Hilbert spaces are described. Also, the canonical dual g-fusion frame in tensor product of Hilbert spaces is considered. Finally, the frame operator for a pair of g-fusion Bessel sequences in tensor product of Hilbert spaces is presented.

We introduce the notion of a $g$-atomic subspace for a bounded linear operator and construct several useful resolutions of the identity operator on a Hilbert space using the theory of $g$-fusion frames. Also, we shall describe the concept of frame operator for a pair of $g$-fusion Bessel sequences and some of their properties.

Concepts of g-fusion frame and gf-Riesz basis in a Hilbert to a Banach space is being presented. Some properties of g-fusion frame and gf-Riesz basis in Banach space have been developed. We discuss perturbation results of g-fusion frame in a Banach space. Finally, we construct g-p-fusion frames in Cartesian product of Banach spaces and tensor product of Banach spaces.

Banach's fixed point theorem in linear n-normed space is being developed. Also, we present several theorems on fixed points in linear n-normed space.