International Journal of Wavelets, Multiresolution and Information Processing
In this paper, we will present several new results in finite and countable dimensional separable ... more In this paper, we will present several new results in finite and countable dimensional separable real Hilbert space phase retrieval and norm retrieval by fusion frames. We will characterize of norm retrieval for fusion frames similar norm retrieval for vectors and we will show that only one direction holds for fusion frames. In similar vector case, we will show that every tight fusion frame can do norm retrieval. Also we will show that the unitary operators preserve phase (norm) retrievability of fusion frames. We will make a detailed study of when hyperplanes do norm retrieval and show a general result about it. We will provide numerous examples to show that our results are best possible.
The Gram matrix can be defined for Bessel sequences by combining synthesis with subsequent analys... more The Gram matrix can be defined for Bessel sequences by combining synthesis with subsequent analysis. If different sequences are used and an operator is inserted we reach so called U-cross Gram matrices. This can be seen as reinterpretation of the matrix representation of operators using frames. In this paper we investigate some necessary or suffcient conditions for p-Schatten class properties and the invertibility of U-cross Gram matrices. In particular we study the stability of U-cross Gram matrices.
In this paper, we proposed a new iterative process to approximate fixed point of generalized α-no... more In this paper, we proposed a new iterative process to approximate fixed point of generalized α-nonexpansive mappings and show that the coefficient used in the proposed iterative process play a fundamental role in the rate of convergence. We compare the speed of convergence of new iterative process with other wellknown iterative process by using numerical examples. Finally, by using new iterative process, we obtained some weak and strong convergence theorems for generalized α-nonexpansive mappings in a Banach space.
In this paper, we study the concept of weak linear fuzzy topology on a fuzzy topological vector s... more In this paper, we study the concept of weak linear fuzzy topology on a fuzzy topological vector space as a generalization of usual weak topology. We prove that this fuzzy topology consists of all weakly lower semi-continuous fuzzy sets on a given vector space when K (R or C) endowed with its usual fuzzy topology. In the case that the fuzzy topology of K is different from the usual fuzzy topology, we show that the weak fuzzy topology is not equivalent with the fuzzy topology of weakly lower semi-continuous fuzzy sets.
Motivating the perturbations of frames in Hilbert and Banach spaces, in this paper we introduce t... more Motivating the perturbations of frames in Hilbert and Banach spaces, in this paper we introduce the invariance of Fréchet frames under perturbation. Also we show that for any Fréchet spaces, there is a Fréchet frame and any element in these spaces has a series expansion.
In this paper, we introduce the concept of polar fuzzy sets on fuzzy dual spaces. Using the notio... more In this paper, we introduce the concept of polar fuzzy sets on fuzzy dual spaces. Using the notion of polar fuzzy sets, we define polar linear fuzzy topologies on fuzzy dual spaces and prove the Mackey-Arens type Theorem on fuzzy topological vector spaces
In 2004, Rodŕiguez-Lallena and Ubeda-Flores have introduced a class of bivariate copulas which ge... more In 2004, Rodŕiguez-Lallena and Ubeda-Flores have introduced a class of bivariate copulas which generalizes some known families such as the Farlie-Gumbel-Morgenstern distributions. In 2006, Dolati and Ubeda-Flores presented multivariate generalizations of this class. Then in 2011, Kim et al. generalized RodŕiguezLallena and Ubeda-Flores’ study to any given copula family. But there are some inaccuracies in the study by Kim et al. We mean to consider the interval for the parameter proposed by Kim et al. and show that it is inaccurate.
Frames for operators or k-frames were recently considered by Gavruta (2012) in connection with at... more Frames for operators or k-frames were recently considered by Gavruta (2012) in connection with atomic systems. Also generalized frames are important frames in the Hilbert space of bounded linear operators. Fusion frames, which are a special case of generalized frames have various applications. This paper introduces the concept of generalized fusion frames for operators aka k-g-fusion frames and we get some results for characterization of these frames. We further discuss on duals and Q-duals in connection with k-g-fusion frames. Also we obtain some useful identities for these frames. We also give several methods to construct k-g-fusion frames. The results of this paper can be used in sampling theory which are developed by g-frames and especially fusion frames. In the end, we discuss the stability of a more general perturbation for k-g-fusion frames.
In this paper, we investigate the Polya-Knopp type inequality for Sugeno integrals in two cases. ... more In this paper, we investigate the Polya-Knopp type inequality for Sugeno integrals in two cases. In the first case, we suppose that the inner integral is the standard Riemann integral and the remaining two integrals are of Sugeno type. In the second case, all involved integrals are Sugeno integral. We present several examples illustrating the validity of our theorems. Finally, we prove a Hardy-Knopp type inequality for Sugeno integral.
In this paper, generalizations of the Feng Qi type integral inequalities for pseudo-integrals are... more In this paper, generalizations of the Feng Qi type integral inequalities for pseudo-integrals are proved. There are considered two cases of the real semiring with pseudo-operations: One, when pseudo-operations are defined by monotone and continuous function $g$ (then the pseudo-integrals reduces $g$-integral), and the second with a semiring $([a, b],\max,\odot)$, where the pseudo-multiplication $\odot$ is generated.
An idea of fuzzy norm on a linear space introduced by Katsaras [11] in 1984. He studied fuzzy top... more An idea of fuzzy norm on a linear space introduced by Katsaras [11] in 1984. He studied fuzzy topological vector spaces. Following his pioneering work, Felbin [6] offered in 1992 an alternative definition of a fuzzy norm linear space (FNLS). With this definition of fuzzy normed linear space, it has been possible to introduce a notion of fuzzy bounded linear operator over fuzzy normed linear spaces to define “fuzzy norm” for such an operator. In [6], Felbin introduced an idea of fuzzy bounded operators and defined a fuzzy norm for such an operator which was erroneous as it shown in Example 3.1 of [3]. Xiao and Zhu ([14], [15]) studied various properties of Felbin-type fuzzy normed linear spaces. They gave a new definition for the norm of the bounded operators. A different definition of a fuzzy bounded linear operator and a “fuzzy norm” for such an operator was introduced by Bag and Samanta [3]. Finally, we note that the definition of the fuzzy norm of an operator was given in [3] and...
International Journal of Wavelets, Multiresolution and Information Processing
In this paper, we will present several new results in finite and countable dimensional separable ... more In this paper, we will present several new results in finite and countable dimensional separable real Hilbert space phase retrieval and norm retrieval by fusion frames. We will characterize of norm retrieval for fusion frames similar norm retrieval for vectors and we will show that only one direction holds for fusion frames. In similar vector case, we will show that every tight fusion frame can do norm retrieval. Also we will show that the unitary operators preserve phase (norm) retrievability of fusion frames. We will make a detailed study of when hyperplanes do norm retrieval and show a general result about it. We will provide numerous examples to show that our results are best possible.
The Gram matrix can be defined for Bessel sequences by combining synthesis with subsequent analys... more The Gram matrix can be defined for Bessel sequences by combining synthesis with subsequent analysis. If different sequences are used and an operator is inserted we reach so called U-cross Gram matrices. This can be seen as reinterpretation of the matrix representation of operators using frames. In this paper we investigate some necessary or suffcient conditions for p-Schatten class properties and the invertibility of U-cross Gram matrices. In particular we study the stability of U-cross Gram matrices.
In this paper, we proposed a new iterative process to approximate fixed point of generalized α-no... more In this paper, we proposed a new iterative process to approximate fixed point of generalized α-nonexpansive mappings and show that the coefficient used in the proposed iterative process play a fundamental role in the rate of convergence. We compare the speed of convergence of new iterative process with other wellknown iterative process by using numerical examples. Finally, by using new iterative process, we obtained some weak and strong convergence theorems for generalized α-nonexpansive mappings in a Banach space.
In this paper, we study the concept of weak linear fuzzy topology on a fuzzy topological vector s... more In this paper, we study the concept of weak linear fuzzy topology on a fuzzy topological vector space as a generalization of usual weak topology. We prove that this fuzzy topology consists of all weakly lower semi-continuous fuzzy sets on a given vector space when K (R or C) endowed with its usual fuzzy topology. In the case that the fuzzy topology of K is different from the usual fuzzy topology, we show that the weak fuzzy topology is not equivalent with the fuzzy topology of weakly lower semi-continuous fuzzy sets.
Motivating the perturbations of frames in Hilbert and Banach spaces, in this paper we introduce t... more Motivating the perturbations of frames in Hilbert and Banach spaces, in this paper we introduce the invariance of Fréchet frames under perturbation. Also we show that for any Fréchet spaces, there is a Fréchet frame and any element in these spaces has a series expansion.
In this paper, we introduce the concept of polar fuzzy sets on fuzzy dual spaces. Using the notio... more In this paper, we introduce the concept of polar fuzzy sets on fuzzy dual spaces. Using the notion of polar fuzzy sets, we define polar linear fuzzy topologies on fuzzy dual spaces and prove the Mackey-Arens type Theorem on fuzzy topological vector spaces
In 2004, Rodŕiguez-Lallena and Ubeda-Flores have introduced a class of bivariate copulas which ge... more In 2004, Rodŕiguez-Lallena and Ubeda-Flores have introduced a class of bivariate copulas which generalizes some known families such as the Farlie-Gumbel-Morgenstern distributions. In 2006, Dolati and Ubeda-Flores presented multivariate generalizations of this class. Then in 2011, Kim et al. generalized RodŕiguezLallena and Ubeda-Flores’ study to any given copula family. But there are some inaccuracies in the study by Kim et al. We mean to consider the interval for the parameter proposed by Kim et al. and show that it is inaccurate.
Frames for operators or k-frames were recently considered by Gavruta (2012) in connection with at... more Frames for operators or k-frames were recently considered by Gavruta (2012) in connection with atomic systems. Also generalized frames are important frames in the Hilbert space of bounded linear operators. Fusion frames, which are a special case of generalized frames have various applications. This paper introduces the concept of generalized fusion frames for operators aka k-g-fusion frames and we get some results for characterization of these frames. We further discuss on duals and Q-duals in connection with k-g-fusion frames. Also we obtain some useful identities for these frames. We also give several methods to construct k-g-fusion frames. The results of this paper can be used in sampling theory which are developed by g-frames and especially fusion frames. In the end, we discuss the stability of a more general perturbation for k-g-fusion frames.
In this paper, we investigate the Polya-Knopp type inequality for Sugeno integrals in two cases. ... more In this paper, we investigate the Polya-Knopp type inequality for Sugeno integrals in two cases. In the first case, we suppose that the inner integral is the standard Riemann integral and the remaining two integrals are of Sugeno type. In the second case, all involved integrals are Sugeno integral. We present several examples illustrating the validity of our theorems. Finally, we prove a Hardy-Knopp type inequality for Sugeno integral.
In this paper, generalizations of the Feng Qi type integral inequalities for pseudo-integrals are... more In this paper, generalizations of the Feng Qi type integral inequalities for pseudo-integrals are proved. There are considered two cases of the real semiring with pseudo-operations: One, when pseudo-operations are defined by monotone and continuous function $g$ (then the pseudo-integrals reduces $g$-integral), and the second with a semiring $([a, b],\max,\odot)$, where the pseudo-multiplication $\odot$ is generated.
An idea of fuzzy norm on a linear space introduced by Katsaras [11] in 1984. He studied fuzzy top... more An idea of fuzzy norm on a linear space introduced by Katsaras [11] in 1984. He studied fuzzy topological vector spaces. Following his pioneering work, Felbin [6] offered in 1992 an alternative definition of a fuzzy norm linear space (FNLS). With this definition of fuzzy normed linear space, it has been possible to introduce a notion of fuzzy bounded linear operator over fuzzy normed linear spaces to define “fuzzy norm” for such an operator. In [6], Felbin introduced an idea of fuzzy bounded operators and defined a fuzzy norm for such an operator which was erroneous as it shown in Example 3.1 of [3]. Xiao and Zhu ([14], [15]) studied various properties of Felbin-type fuzzy normed linear spaces. They gave a new definition for the norm of the bounded operators. A different definition of a fuzzy bounded linear operator and a “fuzzy norm” for such an operator was introduced by Bag and Samanta [3]. Finally, we note that the definition of the fuzzy norm of an operator was given in [3] and...
Uploads
Papers