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Öğe Almost Picard Operators(Amer Inst Physics, 2019) Altun, Ishak; Hancer, Hatice AslanThe concept of Picard operator is one of the most important concept of fixed point theory. As known, a self mapping T of a metric space X is called Picard operator (PO) if it has unique fixed point and every Picard iteration sequence converges to this fixed point. There are some weaker forms of PO in the literature as weakly Picard operator (WPO) and pseudo Picard operator (PPO). In this study, we present a new kind of PO as almost Picard operator (APO) and we show the differences from the others. Then we show that every continuous P-contractive self mapping of a compact metric space is APO. Also we present some open problems.Öğe Tauberian theorems for the weighted mean method of summability of integrals(Amer Inst Physics, 2019) Canak, Ibrahim; Ozsarac, FiratLet q be a positive weight function on R+ := [0, infinity) which is integrable in Lebesgue's sense over every finite interval (0, x) for 0 < x < infinity, in symbol: q is an element of L-loc(1)(R+) such that Q(x) := integral(x)(0)(t)dt # 0 for each x > 0, Q(0) = 0 and Q(x) -> infinity as x -> infinity. Given a real or complex-valued function f is an element of L-loc(1)(R+), we define s(x) := integral(x)(0) f(t)dt and tau((0))(q)(x) := s(x), tau((m))(q)(x) := 1/Q(x) integral(x)(0) tau((m 1))(q)(t)q(t)dt (x > 0, m = 1, 2, ...), provided that Q(x) > 0. We say that integral(infinity)(0) f(x)dx is summable to L by the m-th iteration of weighted mean method determined by the function q(x), or for short, ((N) over bar, q, m) integrable to a finite number L if lim(x ->infinity) tau((m))(q)(x) = L. In this case, we write s(x) -> L((N) over bar, q, m). It is known that if the limit lim(x ->infinity) s(x) = L exists, then lim(x ->infinity) tau((m))(q)(x) = L also exists. However, the converse of this implication is not always true. Some suitable conditions together with the existence of the limit lim(x ->infinity) tau((m))(q)(x), which is so called Tauberian conditions, may imply convergence of lim(x ->infinity) s(x). In this paper, one- and two-sided Tauberian conditions in terms of the generating function and its generalizations for ((N) over bar, q, m) summable integrals of real- or complex-valued functions have been obtained. Some classical type Tauberian theorems given for Cesaro summability (C, 1) and weighted mean method of summability ((N) over bar, q) have been extended and generalized.Öğe Generalized Lupas Operators(Amer Inst Physics, 2018) Ilarslan, Hatice Gill Ince; Aral, Ali; Bascanbaz-Tunca, GulenIn this work, by taking a continuously differentiable, increasing and unbounded function rho, we consider an extension of the Lupas operator L-n in the form L-n (f o rho(-1)) o rho for convenient functions f on [0, infinity). We give weighted approximation, Voronovskaya type theorem, quantitative estimates for the local approximation.Öğe New Results for General Helix in Euclidean 3-space(Amer Inst Physics, 2018) Ilarslan, KazimFinding parametric equation of a space curve is not easy task when its curvature functions are given. It is well known that this problem is known as fundamental theorem of a space curve. If the curvature functions are functions of arc-length, the solution of this problem is usually impossible. In this study, we discuss the answer of the problem when the curve is a general helix in Euclidean 3-space. By using slope axis of general helix, we get parametric equations of a general helix. Also, we give some examples and their figures.Öğe An Extension of Some Lauricella Hypergeometric Functions(Amer Inst Physics, 2013) Sahin, RecepIn this paper, we present an extension of Lauricella hypergeometric functions, which is motivated by the extended Beta function.
