Ambarzumyan type theorem for a quadratic Sturm-Liouville operator

We consider a quadratic Sturm-Liouville problem. In this paper, some uniqueness theorems are extended to the case in which the governing second-order ordinary differential equation contains both q(x) and p(x) instead of only q(x) . It is shown that if the spectrum is the same as the spectrum belonging to the zero potential, then the functions q(x) and p(x) are zero.Bu çalışmada bir kuadratik Sturm-Liouville problemi ele alındı. Bazı teklik teoremleri, içerisinde sadece değil hem hemde bulunduran ikinci mertebeden adi diferensiyel denklem olması durumuna genişletildi. Spektrum eğer sıfır potansiyeline ait olan spektrum ile aynı ise, ve fonksiyonlarının sıfır olduğu gösterildi

Incomplete inverse spectral and nodal problems for differential pencils

[[abstract]]We prove uniqueness theorems for so-called half inverse spectral problem (and also for some its modification) for second order differential pencils on a finite interval with Robin boundary conditions. Using the obtained result we show that for unique determination of the pencil it is sufficient to specify the nodal points only on a part of the interval slightly exceeding its half.[[notice]]補正完畢[[incitationindex]]SCI[[booktype]]紙本[[booktype]]電子

Uniform Lacunary Statistical Convergence on Time Scales

We introduce (θ,m)-uniform lacunary density of any set and (θ,m)-uniform lacunary statistical convergence on an arbitrary time scale. Moreover, (θ,m)-uniform strongly p-lacunary summability and some inclusion relations about these new concepts are also presented.</p

Uniform Lacunary Statistical Convergence on Time Scales

We introduce (θ,m)-uniform lacunary density of any set and (θ,m)-uniform lacunary statistical convergence on an arbitrary time scale. Moreover, (θ,m)-uniform strongly p-lacunary summability and some inclusion relations about these new concepts are also presented.</p