In this paper, we obtain a complete characterization for the norm and the minimum norm attainment sets of bounded linear operators on a real Banach spaces at a vector in the unit sphere, using approximate 𝜖-Birkhoff-James orthogonality techniques. As an application of the results, we obtained a useful characterization of
bounded linear operators on a real Banach spaces. Also, using approximate 𝜖-Birkhoff -James orthogonality proved that a Banach space is a reflexive if and only if for any closed hyperspace of , there exists a rank one linear operator such that , for some vectors in and such that 𝜖 .Mathematics subject classification (2010): 46B20, 46B04, 47L05.

The purpose of this paper is to introduce and study the concepts of fuzzy generalized open sets, fuzzy generalized closed sets, generalized continuous fuzzy proper functions and prove results about these concepts.

We consider some nonlinear partial differential equations in higher dimensions, the negative order of the Calogero-Bogoyavelnskii-Schiff (nCBS) equationin (2+1) dimensions, the combined of the Calogero-Bogoyavelnskii-Schiff equation and the negative order of the Calogero-Bogoyavelnskii-Schiff equation (CBS-nCBS) in (2+1) dimensions, and two models of the negative order Korteweg de Vries (nKdV) equations in (3+1) dimensions. We show that these equations can be reduced to the  same class of ordinary differential equations via wave reduction variable. Solutions in terms of symmetrical Fibonacci and Lucas functions are presented by implementation of the modified Kudryashov method.

In this paper we introduce the idea of the commutator of two fuzzy subsets of a group and study the concept of the commutator of two fuzzy subsets of a group .We introduce and study some of its properties .

Fingerprint recognition is one among oldest procedures of identification. An important step in automatic fingerprint matching is to mechanically and dependably extract features. The quality of the input fingerprint image has a major impact on the performance of a feature extraction algorithm. The target of this paper is to present a fingerprint recognition technique that utilizes local features for fingerprint representation and matching. The adopted local features have determined: (i) the energy of Haar wavelet subbands, (ii) the normalized of Haar wavelet subbands. Experiments have been made on three completely different sets of features which are used when partitioning the fingerprint into overlapped blocks. Experiments are conducted on

   Hiding secret information in the image is a challenging and painstaking task in computer security and steganography system. Certainly, the absolute intricacy of attacks to security system makes it more attractive.in this research on steganography system involving information hiding,Huffman codding used to compress the secret code before embedding which provide high capacity and some security. Fibonacci decomposition used to represent the pixels in the cover image, which increase the robustness of the system. One byte used for mapping all the pixels properties. This makes the PSNR of the system higher due to random distribution of embedded bits. Finally, three kinds of evaluation are applied such as PSNR, chi-square attack, a

In this paper the research introduces a new definition of a fuzzy normed space then the related concepts such as fuzzy continuous, convergence of sequence of fuzzy points and Cauchy sequence of fuzzy points are discussed in details.

    In this work, we study a new class of meromorphicmultivalent functions, defined by fractional differ-integral operator.We obtain some geometricproperties, such ascoefficient inequality, growth and distortion bounds, convolution properties, integral representation, radii of starlikeness, convexity, extreme pointsproperties, weighted mean and arithmetic meanproperties.

In this paper, the linear system of Fredholm integral equations is solving using Open Newton-Cotes formula, which we use five different types of Open Newton-Cotes formula to solve this system.  Compare the results of suggested method with the results of another method (closed Newton-Cotes formula)    Finally, at the end of each method, algorithms and programs developed and written in MATLAB (version 7.0) and we give some numerical examples, illustrate suggested method