In this paper, we have constructed a sequence of soft points in one set with respect to fixed point another set. The convergence and boundedness these sequences Δ-metric spaces are defined their properties established. Further, the complete introduced by defining Δ-Cauchy sequences.

In this paper, the Schwarz boundary value problem (BVP) for the inhomogeneous Cauchy-Riemann equation in a triangle is investigated explicitly. Firstly, by the technique of parquetingreflection and the Cauchy-Pompeiu representation formula a modified Cauchy-Schwarz representation formula is obtained. Then, the solution of the Schwarz BVP is explicitly solved. In particular, the boundary behavio...

We point out that the initial-value (Cauchy) problem for self-interacting vector fields presents same well-posedness issues as first-order derivative scalar (often referred to $k$-essence). For latter, suitable strategies have been employed in last few years successfully evolve Cauchy at level of infrared theory, without need an explicit ultraviolet completion. argue very techniques can also be...

Statistical convergence has been a prominent research area in mathematics since this concept was independently introduced by Fast and Steinhaus 1951. Afterward, the statistical of double sequences metric spaces fuzzy widely studied. The main goal present study is to introduce concepts Cauchy for intuitionistic spaces. Moreover, characterizes sequence an ordinary convergent subsequence sequence....

For sequences of fuzzy numbers, Nanda 1 studied the sequences of fuzzy numbers and showed that the set of all convergent sequences of fuzzy numbers forms a complete metric space. Kwon 2 introduced the definition of strongly p-Cesàro summability of sequences of fuzzy numbers. Savaş 3 introduced and discussed double convergent sequences of fuzzy numbers and showed that the set of all double conve...

Let the numbers P (r, n, k) be defined by P (r, n, k) := Pr ( H n −H (1) k , · · · , H (r) n −H (r) k ) , where Pr(x1, · · · , xr) = (−1)Yr(−0!x1,−1!x2, · · · ,−(r− 1)!xr) and Yr are the exponential complete Bell polynomials. By observing that the numbers P (r, n, k) generate two Riordan arrays, we establish several general summation formulas, from which series of harmonic number identities are...

In the present work the space  $L_{p;r} $ which is continuously embedded into $L_{p} $  is introduced. The corresponding Hardy spaces of analytic functions are defined as well. Some properties of the functions from these spaces are studied. The analogs of some results in the classical theory of Hardy spaces are proved for the new spaces. It is shown that the Cauchy singular integral operator is...

In this paper, we will provide a simple method for starting with a given finite frame for an $n$-dimensional Hilbert space $mathcal{H}_n$ with nonzero elements and producing a frame which is $epsilon$-nearly Parseval and $epsilon$-nearly unit norm. Also, the concept of the $epsilon$-nearly equal frame operators for two given frames is presented. Moreover, we characterize all bounded invertible ...

PURPOSE To develop a three-dimensional (3D) free-breathing myocardial T1 mapping sequence for assessment of left ventricle diffuse fibrosis after contrast administration. METHODS In the proposed sequence, multiple 3D inversion recovery images are acquired in an interleaved manner. A mixed prospective/retrospective navigator scheme is used to obtain the 3D Cartesian k-space data with fully sam...