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Öğe A unified generalization of some quadrature rules and error bounds(ELSEVIER SCIENCE INC, 2013) Liu, Wenjun; Jiang, Yong; Tuna, AdnanBy introducing a parameter, we give a unified generalization of some quadrature rules, which not only unify the recent results about error bounds for generalized mid-point, trapezoid and Simpson's rules, but also give some new error bounds for other quadrature rules as special cases. Especially, two sharp error inequalities are derived when n is an odd and an even integer, respectively. (C) 2012 Elsevier Inc. All rights reserved.Öğe Chebyshev-Hermite ve Chebyshev-Laguerre tipli denklem sınıflarının genelleştirilmesi ve çözüm yöntemleri(Niğde Üniversitesi, 2000) Tuna, Adnan; Aliyev, Gabilm ÖZET CHEBYSHEV-HERMİTE VE CHEBYSHEV-LAGUERRE TİPLİ DENKLEM SINIFLARININ GENELLEŞTİRİLMESİ VE ÇÖZÜM YÖNTEMLERİ TUNA, Adnan Niğde Üniversitesi Fen Bilimleri Enstitüsü Matematik Ana Bilim Dalı Danışman: Prof. Dr. Gabil ALİYEV Aralık 2000, 110 sayfa Mikrodünyanın doğasında, fiziksel olaylar sonucunda oluşan katsayıları değişen özel tipteki Chebyshev-Hermite ve Chebyshev-Laguerre denklemlerinin çözümleri, özel polinomlar yardımıyla verilerek, bu özel polinomların önemli özellikleri incelendi. Chebyshev-Hermite ve Chebyshev-Laguerre tipindeki denklem sınıfları, operatör dönüşümü yardımıyla genelleştirildi. Ayrıca bu denklem sınıflarının genel çözüm yöntemi verildi. Buradaki denklem sınıflan lineer ve lineer olmayan denklem sınıflarını da kapsamaktadır. Üstel fonksiyon biçiminde olan operatör dönüşümleri için, denklem sınıflarının çözümleri örnek olarak gösterildi. Son olarak, Chebyshev-Hermite, Bessel ve Chebyshev-Laguerre tipindeki denklem sınıflarının çözümleri arasında bağlantının bulunması için gerekli şartlar, operatör biçiminde olan özel dönüşüm yardımıyla oluşturuldu. Anahtar Sözcükler: Chebyshev-Hermite denklemi, Chebyshev-Laguerre denklemi, Chebyshev-Hermite denklemine dönüşen denklem sınıfları, Chebyshev-Laguerre denklemine dönüşen denklem sınıfları.Öğe Diamond-alpha weighted Ostrowski type and Gruss type inequalities on time scales(ELSEVIER SCIENCE INC, 2015) Liu, Wenjun; Tuna, AdnanIn this paper we obtain some weighted Ostrowski type and Gruss type inequalities on time scales by using the recent theory of combined dynamic derivatives on time scales. These results extend some known results in the literature and give some other interesting inequalities as special cases. (C) 2015 Elsevier Inc. All rights reserved.Öğe Exact Solutions of (n+1)-Dimensional Space-Time Fractional Zakharov-Kuznetsov Equation(2018) Ali, Muhammad Nasir; Husnıne, Syed Muhammad; Noor, Sana; Tuna, AdnanIn this article, we study the (n+1)-dimensional space time fractional Zakharov-Kuznetsov equation for calculating the exact solutions. For this purpose fractional derivative is usedn this article, we study the (n+1)-dimensional space time fractional Zakharov-Kuznetsovin the form of modified Riemann-Liouville derivatives. Complex fractional transformation is applied for transforming the nonlinear partial differential equation into anothernonlinear ordinary differential equation. Exact solutions are obtained by using modifiedsimple equation method and (1?G' )-expansion method. Obtained solutions are new andmay be of significant importance in the field of plasma physics to investigate the waves inthe magnetized plasma and in the dust plasma.Öğe Explicit solutions of the nonlinear partial differential equations(PERGAMON-ELSEVIER SCIENCE LTD, 2010) Daghan, Durmus; Donmez, Orhan; Tuna, AdnanThe convection and diffusion process or their mixed states are the Important phenomena in the different physical systems. In order to understand these physical processes, the nonlinear differential equations, Fisher. Burger-Fisher. Benjamin-Bona-Mahony-Burgers (BBMB) and Modified Benjamin-Bona-Mahony (MBBM) are solved to obtain the traveling wave solutions using (G'/G)-expansion method. In this study we give the exact solutions of these equations which describe the dynamics of turbulence created by the Interaction of matters. Our solutions are reduced to the well-known solutions in the literature assigning some special values to the constants in the solutions of these equations. Moreover, we have reached the new exact solutions for these equations mentioned above. We have also analyzed and plotted the results using different integration constants to understand the behavior of solutions. (C) 2009 Elsevier Ltd. All rights reserved.Öğe Generalization of Ostrowski and Ostrowski-Gruss type inequalities on time scales(PERGAMON-ELSEVIER SCIENCE LTD, 2010) Tuna, Adnan; Daghan, DurmusIn this paper, we obtain an Ostrowski and Ostrowski-Gruss type inequality on time scales, which not only provides a generalization of the known results on time scales, but also give some other interesting inequalities as special cases. (C) 2010 Elsevier Ltd. All rights reserved.Öğe Generalized contraction mapping principle in intuitionistic Menger spaces and application to differential equations(SHANGHAI UNIV, 2007) Kutukcu, Servet; Tuna, Adnan; Yakut, Atakan T.Using the idea of Atanassov, we define the notion of intuitionistic Menger spaces as a netural generalizations of Menger spaces due to Menger. We also obtain a new generalized contraction mapping and utilize this contraction mapping to prove the existance theorems of solutions to differential equations in intuitionistic Menger spaces.Öğe NEW WEIGHTED CEBYSEV-OSTROWSKI TYPE INTEGRAL INEQUALITIES ON TIME SCALES(ELEMENT, 2016) Tuna, Adnan; Liu, WenjunIn this paper we obtain some weighted Cebysev-Ostrowski type integral inequalities on time scales involving functions whose first derivatives belong to L-p (a, b) (1 <= p <= infinity). We also give some other interesting inequalities as special cases.Öğe NEW WEIGHTED OSTROWSKI AND OSTROWSKI-GRUSS TYPE INEQUALITIES ON TIME SCALES(UNIV AL I CUZA, FAC MATH, 2014) Liu, Wenjun; Tuna, Adnan; Jiang, YongIn this paper we derive new weighted Ostrowski and Ostrowski-Gruss type inequalities on time scales. Some other interesting inequalities on time scales are also given as special cases.Öğe On weighted Ostrowski type, Trapezoid type, Gruss type and Ostrowski-Gruss like inequalities on time scales(TAYLOR & FRANCIS LTD, 2014) Liu, Wenjun; Tuna, Adnan; Jiang, YongIn this paper, we first derive a weighted Montgomery identity on time scales and then establish weighted Ostrowski-type, Trapezoid-type, Gruss-type and Ostrowski-Gruss-like inequalities on time scales, respectively. These results not only provide a generalization of the known results, but also give some other interesting inequalities on time scales as special cases.Öğe Ostrowski and generalized trapezoid type inequalities on time scales(Elsevier, 2020) Tuna, Adnan; Nwaeze, Eze R.In this paper, some new Ostrowski and generalized Trapezoid type inequalities on time scales are established. The Ostrowski type inequality is presented via a parameter function g : [0, 1] -> [0, 1]. Our results generalize and extend the results of Dragomir, and Ujevic. Furthermore, we apply our results to the discrete and continuous time scales to obtain some other interesting inequalities as special cases. (C) 2018 Production and hosting by Elsevier B.V. on behalf of King Saud University.Öğe Some new generalizations of Ostrowski type inequalities on time scales involving combination of Delta-integral means(INT SCIENTIFIC RESEARCH PUBLICATIONS, 2014) Jiang, Yong; Ruzgar, Huseyin; Liu, Wenjun; Tuna, AdnanIn this paper we obtain some new generalizations of Ostrowski type inequalities on time scales involving combination of Delta-integral means, i.e., a new Ostrowski type inequality on time scales involving combination of Delta-integral means, two Ostrowski type inequalities for two functions on time scales, and some new perturbed Ostrowski type inequalities on time scales. We also give some other interesting inequalities as special cases. (C)2014 All rights reserved.Öğe SOME RESULTS ON THE STABILITY OF QUASI-LINEAR DYNAMIC SYSTEMS ON TIME SCALES(EUDOXUS PRESS, LLC, 2009) Tuna, Adnan; Kutukcu, ServetIt is shown that we study some results on the stability of Quasilinear dynamic systems on time scales characterized completely by its linear part.Öğe TRAPEZOID-TYPE INEQUALITIES ON TIME SCALES(Univ Prishtines, 2019) Bohner, Martin; Nwaeze, Eze R.; Tuna, AdnanSome trapezoid inequalities were proved in 2004 by B. G. Pachpatte. It is our purpose in this paper to extend these results to time scales. Besides that, two more results are also established. Furthermore, we also apply our results to continuous and discrete calculus to derive some new inequalities as special cases.Öğe Weighted Ostrowski, Ostrowski-Gruss and Ostrowski-Cebysev type inequalities on time scales(KOSSUTH LAJOS TUDOMANYEGYETEM, 2012) Tuna, Adnan; Jiang, Yong; Liu, WenjunIn this paper we derive some weighted Ostrowski, Ostrowski-Gruss and Ostrowski-Cebysev type inequalities on time scales. We also give some other interesting inequalities on time scales as special cases.Öğe WEIGHTED OSTROWSKI, TRAPEZOID AND GRUSS TYPE INEQUALITIES ON TIME SCALES(ELEMENT, 2012) Liu, Wenjun; Tuna, AdnanIn this paper we first derive a weighted Montgomery identity on time scales and then establish weighted Ostrowski, trapezoid and Gruss type inequalities on time scales, respectively. These results not only provide a generalization of the known results, but also give some other interesting inequalities on time scales as special cases.
