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Öğe Best proximity and best periodic points for proximal nonunique contractions(Springer Basel Ag, 2021) Şahin, Hakan; Aslantaş, Mustafa; Altun, İshakTaking into account nonunique fixed point and periodic point results of Ciric (Institut Mathematique 17, 52-58, 1974) and best proximity point results in the literature, we introduce the concept of proximal nonunique contraction for nonself mappings. Then, we obtain some nonunique best proximity point theorems. Further, we describe the concept of best periodic point of nonself mappings and we present some nonunique best periodic point results. We also provide many examples to show that our new concepts are meaningful and to support our theorems. Additionally, we present a new notion for the nonself mapping H called property P-b, and then we provide some results including sufficient conditions to guarantee that H has the property P-b.Öğe Approximation by Some Baskakov-Kantorovich Exponential-Type Operators(Springer Singapore Pte Ltd, 2022) Özsaraç, Fırat; Gupta, Vijay; Aral, AliIn the present paper, we propose the modification of the Baskakov-Kantorovich operators based on mu-integral. Such operators are connected with exponential functions. We estimate moments and establish some direct results in terms of modulus of continuity.Öğe Approximation of operators related to squared Sza acute accent sz-Mirakjan basis functions(Univ Nis, Fac Sci Math, 2023) Rahman, Shagufta; Aral, Ali; Mursaleen, M.The main objective of this paper is to define a sequence of positive linear operators by means of the squared Szasz-Mirakjan basis functions. We estimate the rate of convergence in terms of the modulus of continuity and the class of Lipschitz functions. Furthermore, we have shown the comparison and convergence of these operators with the help of some illustrative graphics.Öğe Approximation Results for Hadamard-Type Exponential Sampling Kantorovich Series(Springer Basel Ag, 2023) Kurşun, Sadettin; Aral, Ali; Acar, TuncerThe present paper deals with construction of a new family of exponential sampling Kantorovich operators based on a suitable fractional-type integral operators. We study convergence properties of newly constructed operators and give a quantitative form of the rate of convergence thanks to logarithmic modulus of continuity. To obtain an asymptotic formula in the sense of Voronovskaja, we consider locally regular functions. The rest of the paper devoted to approximations of newly constructed operators in logarithmic weighted space of functions. By utilizing a suitable weighted logarithmic modulus of continuity, we obtain a rate of convergence and give a quantitative form of Voronovskaja-type theorem via remainder of Mellin-Taylor's formula. Furthermore, some examples of kernels which satisfy certain assumptions are presented and the results are examined by illustrative numerical tables and graphical representations.Öğe Approximation properties of modified Jain-Gamma operators(Vasyl Stefanyk Precarpathian Natl Univ, 2021) Erdoğan, S.; Olgun, A.In the present paper, we study some approximation properties of a modified Jain-Gamma operator. Using Korovkin type theorem, we first give approximation properties of such operator. Secondly, we compute the rate of convergence of this operator bymeans of themodulus of continuity and we present approximation properties of weighted spaces. Finally, we obtain the Voronovskaya type theorem of this operator.Öğe Approximation properties of two dimensional Bernstein-Stancu-Chlodowsky operators(Univ Studi Catania, Dipt Matematica, 2013) Acar, Tuncer; Aral, AliIn this paper, as a generalization of Bernstein-Stancu type operators of two variable, we introduce a new positive linear operator C-n (alpha,alpha,beta,beta,) (f; x, y) called Bernstein-Stancu-Chlodowsky on a triangular domain, with mobile boundaries, which extends to [0,infinity) x [0,infinity) as n -> infinity. We give some shape properties that are preserved and also obtain weighted approximation properties of these operators.Öğe Approximation Properties of Modified Baskakov Gamma Operators(Univ Nis, 2021) Arpagus, Seda; Olgun, AliIn this paper, we have studied an approximation properties of modified Baskakov-Gamma operator. Using Korovkin type theorem, firste we gave the approximation properties of this operator. Secondly, we computed the rate of convergence of this operator by means of the modulus of continuity and we gave an approximation properties of weighted spaces. Finally, we studied the Voronovskaya type theorem of this operator.Öğe Approximation Properties Of Modified Gauss-Weierstrass Integral Operators In Exponential Weighted Lp Spaces(Univ Nis, 2021) Yılmaz, BaşarIn this paper, we deal with modified Gauss-Weierstrass integral operators from exponentially weighted spaces L-p,L-a (R) into L-p,L-2a (R). We give the rate of convergence in terms of weighted modulus of continuity. Moreover, we prove weighted approximation of functions belonging to the space L-p,L-a (R) by these operators with the help of a Korovkin type theorem. Finally, we give pointwise approximation of such functions by these operators at generalized Lebesgue points.Öğe A new type of R-contraction and its best proximity points(Amer Inst Mathematical Sciences-Aims, 2024) Aslantaş, Mustafa; Şahin, Hakan; Altun, Ishak; Saadoon, Taif Hameed SaadoonIn this paper, we aim to overcome the problem given by Abkar et al. [Abstr. Appl. Anal., 2013 (2013), 189567], and so to obtain real generalizations of fixed point results in the literature. In this direction, we introduce a new class of functions, which include R-functions. Thus, we present a new type of R-contraction and weaken R-contractions that have often been studied recently. We also give a new definition of the P-property. Hence, we obtain some best proximity point results, including fixed point results for the new kind of R-contractions. Then, we provide an example to show the effectiveness of our results. Finally, inspired by a nice and interesting technique, we investigate the existence of a best proximity point of the homotopic mappings with the help of our main result.Öğe A New Result of Presic Type Theorems with Applications to Second Order Boundary Value Problems(Univ Nis, Fac Sci Math, 2021) Altun, İshak; Qasim, Muhammad; Olgun, MuratIn this paper, taking into account the recent contractive technique we present a new result of Presic type fixed point theorems. Then, we provide a comparative example to put forth the validity of our theoretical result. Finally, considering a special case of the main theorem, we give some existence results for the second order two point boundary value problems.Öğe A new approach to Leonardo number sequences with the dual vector and dual angle representation(Amer Inst Mathematical Sciences-Aims, 2024) Babadağ, Faik; Atasoy, AliIn this paper, we introduce dual numbers with components including Leonardo number sequences. This novel approach facilitates our understanding of dual numbers and properties of Leonardo sequences. We also investigate fundamental properties and identities associated with Leonardo number sequences, such as Binet's formula and Catalan's, Cassini's and D'ocagne's identities. Furthermore, we also introduce a dual vector with components including Leonardo number sequences and dual angles. This extension not only deepens our understanding of dual numbers, it also highlights the interconnectedness between numerical sequences and geometric concepts. In the future it would be valuable to replicate a similar exploration and development of our findings on dual numbers with Leonardo number sequences.Öğe A new approach to Mannheim curve in Euclidean 3-space(Tamkang Univ, 2023) Uçum, Ali; Camcı, Çetin; İlarslan, KazımIn this article, a new approach is given for Mannheim curves in 3 -dimensional Euclidean space. Thanks to this approach, the necessary and suffi-cient conditions including the known results have been obtained for a curve to be Mannheim curve in E3. In addition, related examples and graphs are given by show-ing that Salkowski and anti-Salkowski curves can be the examples of Mannheim curves and their mates. Finally, the Mannheim partner curves are characterized in E3.Öğe A New Class of Bertrand Curves in Euclidean 4-Space(Mdpi, 2022) Li, Yanlin; Uçum, Ali; İlarslan, Kazım; Camcı, ÇetinBertrand curves are a pair of curves that have a common principal normal vector at any point and are related to symmetry properties. In the present paper, we define the notion of (1, 3)-V Bertrand curves in Euclidean 4-space. Then we find the necessary and sufficient conditions for curves in Euclidean 4-space to be (1, 3)-V Bertrand curves. Some related examples are given.Öğe A new approach to Jacobsthal, Jacobsthal-Lucas numbers and dual vectors(Amer Inst Mathematical Sciences-Aims, 2023) Babadağ, FaikThis paper gives a detailed study of a new generation of dual Jacobsthal and dual Jacobsthal-Lucas numbers using dual numbers. Also some formulas, facts and properties about these numbers are presented. In addition, a new dual vector called the dual Jacobsthal vector is presented. Some properties of this vector apply to various properties of geometry which are not generally known in the geometry of dual space. Finally, this study introduces the dual Jacobsthal and the dual Jacobsthal-Lucas numbers with coefficients of dual numbers. Some fundamental identities are demonstrated, such as the generating function, the Binet formulas, the Cassini's, Catalan's and d'Ocagne identities for these numbers.Öğe Degenerate Pochhammer symbol, degenerate Sumudu transform, and degenerate hypergeometric function with applications(Hacettepe Univ, Fac Sci, 2021) Yağcı, Oğuz; Şahin, RecepIn the paper, we first define a degenerate Pochhammer symbol by using the degenerate gamma function and investigate its properties. By using the degenerate Pochhammer symbol, we introduce and investigate a degenerate hypergeometric function. We also define a degenerate Sumudu transform and investigate its properties by using degenerate exponential function. Finally, we give certain the integral representations, derivative formulas, integral transforms, factional calculus applications, and generating functions of the degenerate hypergeometric function.Öğe Embeddings between weighted Tandori and Cesàro function spaces(Ankara Univ, Fac Sci, 2021) Ünver Yıldız, TuğçeWe characterize the weights for which the two-operator inequalityÖğe Solution of fractional kinetic equations involving generalized Hurwitz-Lerch Zeta function using Sumudu transform(Ankara Univ, Fac Sci, 2021) Yağcı, Oğuz; Şahin, RecepFractional kinetic equations (FKEs) comprising a large array of special functions have been extensively and successfully applied in specification and solving many significant problems of astrophysics and physics. In this present work, our aim is to demonstrate solutions of (FKEs) of the generalized Hurwitz-Lerch Zeta function by applying the Sumudu transform. In addition to these, solutions of (FKEs) in special conditions of generalised Hurwitz-Lerch Zeta function have been derived.Öğe Canal Surface Whose Center Curve is a Hyperbolic Curve with Hyperbolic Frame(Int Electronic Journal Geometry, 2021) Uçum, AliIn this paper, we obtain the parametrization of the canal surfaces whose center curves are the hyperbolic curves on the hyperbolic space H-2 in E-1(3). The parametrization of the canal surface is expressed according to the hyperbolic frame given in [10]. Then, the parallel surface of this surface is studied. Also, we define the notion of the associated canal surface. Lastly, we give the geometric properties of these surfaces such that Weingarten surface, (X, Y)-Weingarten surface and linear Weingarten surface.Öğe Bivariate Bernstein polynomials that reproduce exponential functions(Ankara Univ, Fac Sci, 2021) Bozkurt, Kenan; Özsaraç, Fırat; Aral, AliIn this paper, we construct Bernstein type operators that reproduce exponential functions on simplex with one moved curved side. The operator interpolates the function at the corner points of the simplex. Used function sequence with parameters alpha and beta not only are gained more modeling flexibility to operator but also satisfied to preserve some exponential functions. We examine the convergence properties of the new approximation processes. Later, we also state its shape preserving properties by considering classical convexity. Finally, a Voronovskaya-type theorem is given and our results are supported by graphics.Öğe Quantitative estimates for Jain-Kantorovich operators(Ankara Univ, Fac Sci, 2016) Deniz, EmreBy using given arbitrary sequences, beta(n) > 0, n is an element of N with the property that lim(n ->infinity)n beta(n) 0 lim(n ->infinity)n beta(n) = 0, we give a Kantorovich type generalization of Jain operator based on the a Poisson disrtibition. Fristly we give the quantitative Voronovskaya type theorem. Then we also obtain the Griiss Voronovskaya type theorem in quantitative form.We show that they have an arbitrary good order of weighted approximation.
