Matematik Bölümü Yayın Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413

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Citation Count: Kayar, Zeynep; Kaymakçalan, B. (2022). "Applications of the novel diamond alpha Hardy–Copson type dynamic inequalities to half linear difference equations", Journal of Difference Equations and Applications, Vol.28, No.4, pp.457-484.
Applications of the novel diamond alpha Hardy–Copson type dynamic inequalities to half linear difference equations
(2022) Kayar, Zeynep; Kaymakçalan, Billur; 109448; Çankaya Üniversitesi, Fen-Edebiyat Fakültesi, Matematik Bölümü
This paper is devoted to novel diamond alpha Hardy–Copson type dynamic inequalities, which are (Formula presented.) complements of the classical ones obtained for (Formula presented.) and their applications to difference equations. We obtain two kinds of diamond alpha Hardy–Copson type inequalities for (Formula presented.), one of which is mixed type and established by the convex linear combinations of the related delta and nabla inequalities while the other one is new and is obtained by using time scale calculus rather than algebra. In contrast to the works existing in the literature, these complements are derived by preserving the directions of the classical inequalities. Therefore both kinds of our results unify some of the known delta and nabla Hardy–Copson type inequalities obtained for (Formula presented.) into one diamond alpha Hardy–Copson type inequalities and offer new types of diamond alpha Hardy–Copson type inequalities which have the same directions as the classical ones and can be considered as complementary inequalities. Moreover the application of these inequalities in the oscillation theory of half linear difference equations provides several nonoscillation criteria for such equations.
Citation Count: Pelen, N.N.; Güvenilir, A.F.; Kaymakçalan, B.,"Behavior of the Solutions for Predator-Prey Dynamic Systems With Beddington-Deangelis Type Functional Response On Periodic Time Scales İn Shifts",Abstract and Applied Analysis, Vol. 2016, (2016).
Behavior of the Solutions for Predator-Prey Dynamic Systems With Beddington-Deangelis Type Functional Response On Periodic Time Scales İn Shifts
(Hindawi Limited, 2016) Pelen, Neslihan Nesliye; Güvenilir, Ayşe Feza; Kaymakçalan, Billur; 109448; Çankaya Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü
We consider two-dimensional predator-prey system with Beddington-DeAngelis type functional response on periodic time scales in shifts. For this special case we try to find under which conditions the system has δ ± -periodic solution. © 2016 Neslihan Nesliye Pelen et al.
Citation Count: Kayar, Zeynep; Kaymakcalan, Billur; Pelen, Neslihan Nesliye (2021). "Bennett-Leindler Type Inequalities for Nabla Time Scale Calculus", Mediterranean Journal of Mathematics, Vol. 18, No. 1.
Bennett-Leindler Type Inequalities for Nabla Time Scale Calculus
(2021-02) Kayar, Zeynep; Kaymakcalan, Billur; Pelen, Neslihan Nesliye; 109448; Çankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik Bölümü
In this study, we generalize the converse of Hardy and Copson inequalities, which are known as Bennett and Leindler type inequalities, for nabla time scale calculus. This generalization allows us not only to unify all the related results existing in the literature for an arbitrary time scale but also to obtain new results which are analogous to the results of the delta time scale calculus.
Citation Count: Kayar, Zeynep; Kaymakçalan, Billur; Pelen, Neslihan Nesliye (2022). "Diamond alpha Bennett-Leindler type dynamic inequalities and their applications", Mathematical Methods in the Applied Sciences, Vol. 45, No. 5, pp .2797-2819.
Diamond alpha Bennett-Leindler type dynamic inequalities and their applications
(2022-03-30) Kayar, Zeynep; Kaymakçalan, Billur; Pelen, Neslihan Nesliye; 109448; Çankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik Bölümü
In this paper, two kinds of dynamic Bennett-Leindler type inequalities via the diamond alpha integrals are derived. The first kind consists of eight new integral inequalities which can be considered as mixed type in the sense that these inequalities contain delta, nabla and diamond alpha integrals together due to the fact that convex linear combinations of delta and nabla Bennett-Leindler type inequalities give diamond alpha Bennett-Leindler type inequalities. The second kind involves four new inequalities, which are composed of only diamond alpha integrals, unifying delta and nabla Bennett-Leindler type inequalities. For the second type, choosing alpha=1 or alpha=0 not only yields the same results as the ones obtained for delta and nabla cases but also provides novel results for them. Therefore, both kinds of our results expand some of the known delta and nabla Bennett-Leindler type inequalities, offer new types of these inequalities, and bind and unify them into one diamond alpha Bennett-Leindler type inequalities. Moreover, an application of dynamic Bennett-Leindler type inequalities to the oscillation theory of the second-order half linear dynamic equation is developed and presented for the first time ever.
Citation Count: Kayar, Z.; Kaymakçalan, B. (2022). "Diamond alpha Hardy-Copson type dynamic inequalities", Hacettepe Journal of Mathematics and Statistics, Vol.51, No.1, pp.48-73.
Diamond alpha Hardy-Copson type dynamic inequalities
(2022-02-14) Kayar, Zeynep; Kaymakçalan, Billur; 109448; Çankaya Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü
In this paper two kinds of dynamic Hardy-Copson type inequalities are derived via diamond alpha integrals. The first kind consists of twelve new integral inequalities which can be considered as mixed type in the sense that these inequalities contain delta, nabla and diamond alpha integrals together. The second kind involves another twelve new inequalities, which are composed of only diamond alpha integrals, unifying delta and nabla Hardy-Copson type inequalities. Our approach is quite new due to the fact that it uses time scale calculus rather than algebra. Therefore both kinds of our results unify some of the known delta and nabla Hardy-Copson type inequalities into one diamond alpha Hardy-Copson type inequalities and offer new Hardy-Copson type inequalities even for the special cases.
Citation Count: Kayar, Z.; Kaymakçalan, B. (2023). "Diamond-Alpha Pachpatte Type Dynamic Inequalities Via Convexity", Differential Equations and Dynamical Systems.
Diamond-Alpha Pachpatte Type Dynamic Inequalities Via Convexity
(2023-05) Kayar, Zeynep; Kaymakçalan, Billur; 109448; Çankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik Bölümü
Diamond-alpha Pachpatte type dynamic inequalities, which are convex generalizations of diamond-alpha Hardy−Copson type inequalities, are established to harmonize and bind foregoing related results in the delta and nabla calculi. A noteworthy contribution of the paper is that new diamond-alpha dynamic inequalities as well as their delta and nabla versions are derived by making use of convexity. © 2023, Foundation for Scientific Research and Technological Innovation.
Citation Count: Kayar, Zeynep; Kaymakçalan, Billur (2021). "Extensions of Diamond Alpha Hardy-Copson Type Dynamic İnequalities and Their Applications to Oscillation Theory", Dynamic Systems and Applications, Vol. 30, No. 7.
Extensions of Diamond Alpha Hardy-Copson Type Dynamic İnequalities and Their Applications to Oscillation Theory
(2021-07) Kayar, Zeynep; Kaymakçalan, Billur; 109448; Çankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik Bölümü
This paper is devoted to 0 < ζ < 1 complements of the classical (ζ > 1) diamond alpha Hardy-Copson type dynamic inequalities and their applications to dynamic equations. We obtain two kinds of diamond alpha Hardy-Copson type inequalities for 0 < ζ < 1, one of which is mixed type and established by the convex linear combinations of delta and nabla integrals while the other one is obtained by a new method which uses time scale calculus rather than algebra. In addition to their novelty, these two types are the complements of the classical diamond alpha Hardy-Copson type inequalities. In contrast to the works existing in the literature, these complements are derived by preserving the directions of the classical inequalities. Therefore both kinds of our results unify some of the known delta and nabla Hardy-Copson type inequalities obtained for 0 < ζ < 1 into one diamond alpha Hardy-Copson type inequalities and offer new types of diamond alpha Hardy-Copson type inequalities which have the same directions as the classical ones and can be considered as complementary to such inequalities. Moreover the application of these inequalities in the oscillation theory of half linear dynamic equations provides several nonoscillation criteria for such equations.
Citation Count: El-Deeb, Ahmed A.; Akin, Elvan; Kaymakçalan, B. (2021). "Generalization Of Mitrinović–Pečarić Inequalities On Time Scales", Rocky Mountain Journal of Mathematics, Vol.51, No.6, pp.1909-1918.
Generalization Of Mitrinović–Pečarić Inequalities On Time Scales
(2021-12) El-Deeb, Ahmed A.; Akin, Elvan; Kaymakçalan, Billur; 109448; Çankaya Üniversitesi, Fen-Edebiyat Fakültesi, Matematik Bölümü
We prove some new inequalities of Mitrinović–Pečarić inequalities for convex functions on an arbitrary time scale using delta integrals. These inequalities extend and improve some known dynamic inequalities in the literature. The main results will be proved by using Hölder and Jensen inequalities and a simple consequence of Keller’s and Poetzsche’s chain rules on time scales. c Rocky Mountain Mathematics Consortium
Citation Count: Kayar, Zeynep; Kaymakçalan, Billur; Pelen, Neslihan Nesliye. Generalized diamond alpha bennett-leindler-type dynamic inequalities, in Dynamic Calculus and Equations on Time Scales, pp. 259-293, 2023.
Generalized diamond alpha bennett-leindler-type dynamic inequalities
(2023-09-18) Kayar, Zeynep; Kaymakçalan, Billur; Pelen, Neslihan Nesliye; 109448; Çankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik Bölümü
The dual results; delta and nabla inequalities and their special cases; continuous and discrete inequalities are unified into diamond alpha case and new forms of such results as well as new diamond alpha Bennett-Leindler-type dynamic inequalities are established by developing a novel method, which does not require the Integration by Parts Formula and the Fundamental Theorem of Calculus. These theorems are standard arguments in the proofs of Bennett-Leindler-type dynamic inequalities in the delta and nabla approaches but do not follow naturally in the diamond alpha calculus.
Citation Count: Kayar, Zeynep; Kaymakçalan, B. (2021). "Hardy—Copson type inequalities for nabla time scale calculus", Turkish Journal of Mathematics, Vol.45, No.2, pp.1040-1064.
Hardy—Copson type inequalities for nabla time scale calculus
(2021) Kayar, Zeynep; Kaymakçalan, Billur; 109448; Çankaya Üniversitesi, Fen-Edebiyat Fakültesi, Matematik Bölümü
This paper is devoted to the nabla unification of the discrete and continuous Hardy-Copson type inequalities. Some of the obtained inequalities are nabla counterparts of their delta versions while the others are new even for the discrete, continuous, and delta cases. Moreover, these dynamic inequalities not only generalize and unify the related ones in the literature but also improve them in the special cases.
Citation Count: Pelen, Neslihan Nesliye; Guvenilir, A. Feza; Kaymakcalan, Billur, "Necessary and sufficient condition for existence of periodic solutions of predator-prey dynamic systems with Beddington-DeAngelis-type functional response", Advances in Difference Equations, (2016).
Necessary and sufficient condition for existence of periodic solutions of predator-prey dynamic systems with Beddington-DeAngelis-type functional response
(Springer Open, 2016-01-22) Pelen, Neslihan Nesliye; Güvenilir, Ayşe Feza; Kaymakçalan, Billur; 109448; Çankaya Üniversitesi, Fen-Edebiyat Fakültesi, Matematik Bölümü
We consider two-dimensional predator-prey systems with Beddington-DeAngelis-type functional response on periodic time scales. For this special case, we try to find the necessary and sufficient conditions for the considered system when it has at least one w-periodic solution. This study is mainly based on continuation theorem in coincidence degree theory and will also give beneficial results for continuous and discrete cases. Especially, for the continuous case, by using the study of Cui and Takeuchi (J. Math. Anal. Appl. 317: 464-474, 2006), to obtain the globally attractive w-periodic solution of the given system, an inequality is given as a necessary and sufficient condition. Additionally, for the continuous case in this study, the open problem given in the discussion part of the study of Fan and Kuang (J. Math. Anal. Appl. 295: 15-39, 2004) is solved.
Citation Count: Kayar, Zeynep; Kaymakçalan, Billur (2024). "On the complementary nabla Pachpatte type dynamic inequalities via convexity", Kuwait Journal of Science, Vol. 51, No. 1.
On the complementary nabla Pachpatte type dynamic inequalities via convexity
(2024-01) Kayar, Zeynep; Kaymakçalan, Billur; 109448; Çankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik Bölümü
Pachpatte type inequalities are convex generalizations of the well-known Hardy-Copson type inequalities. As Hardy-Copson type inequalities and convexity have numerous applications in pure and applied mathematics, combining these concepts will lead to more significant applications that can be used to develop certain branches of mathematics such as fuctional analysis, operator theory, optimization and ordinary/partial differential equations. We extend classical nabla Pachpatte type dynamic inequalities by changing the interval of the exponent δ from δ > 1 to δ < 0. Our results not only complement the classical nabla Pachpatte type inequalities but also generalize complementary nabla Hardy-Copson type inequalities. As the case of δ < 0 has not been previously examined, these complementary inequalities represent a novelty in the nabla time scale calculus, specialized cases in continuous and discrete scenarios, and in the dual outcomes derived in the delta time scale calculus.
Citation Count: Grace, Said R.; Agarwal, Ravi P.; Kaymakçalan, Billur. (2011). "Oscillation criteria for even order dynamic equations on time-scales", International Journal of Pure and Applied Mathematics, Vol.72, No.4, pp.591-597.
Oscillation criteria for even order dynamic equations on time-scales
(2011) Grace, Said R.; Agarwal, Ravi P.; Kaymakçalan, Billur; 109448; Çankaya Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü
Some new criteria for the oscillation of even order linear dynamic equations on time-scales of the form xΔn(t) + q(t)x(t) = 0 are established.
Citation Count: Pelen, Neslihan Nesliye; Güvenilir, Ayşe Feza; Kaymakçalan, Billur, "Quantum calculus with the notion δ±-periodicity and its applications", Advanced Technologies of Quantum Key Distribution, No.9, (2018).
Quantum calculus with the notion δ±-periodicity and its applications
(2018-05-30) Pelen, Neslihan Nesliye; Güvenilir, Ayşe Feza; Kaymakçalan, Billur; 109448; Çankaya Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü
The relation between the time scale calculus and quantum calculus and the δ ± -periodicity in quantum calculus with the notion is considered. As an application, in two-dimensional predator–prey system with Beddington-DeAngelis-type functional response on periodic time scales in shifts is used.
Citation Count: Kayar, Zeynep; Kaymakçalan, Billur (2022). "Some Extended Nabla and Delta Hardy-Copson Type Inequalities with Applications in Oscillation Theory", BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, Vol. 48, No. 5, pp. 2407-2439.
Some Extended Nabla and Delta Hardy-Copson Type Inequalities with Applications in Oscillation Theory
(2022-10) Kayar, Zeynep; Kaymakçalan, Billur; 109448; Çankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik Bölümü
We extend classical nabla and delta Hardy-Copson type inequalities from zeta > 1 to 0 < zeta < 1 and also use these novel inequalities to find necessary and sufficient condition for the nonoscillation of the related half linear dynamic equations. Since ordinary differential equations and difference equations are special cases of dynamic equations, our results cover these equations as well. Moreover, the obtained inequalities are not only novel but also unify the continuous and discrete cases for which the case 0 < zeta < 1 has not been considered so far.
Citation Count: Pelen, N.N., Güvenilir, A.F., Kaymakçalan, B. (2017). Some results on predator-prey dynamic systems with beddington-deangelis type functional response on time scale calculus. Dynamic System and Applications, 26(1), 167-181.
Some results on predator-prey dynamic systems with beddington-deangelis type functional response on time scale calculus
(Dynamic Publishers, 2017-03) Pelen, Neslihan Nesliye; Güvenilir, Ayşe Feza; Kaymakçalan, Billur; 157065; 106920; 109448; Çankaya Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bilgisayar Bölümü
We consider two dimensional predator-prey system with Beddington-DeAngelis type functional response on time scales. For this special case, we try to find under which conditions the system is permanent and globally attractive. This study gives beneficial results for continuous and discrete cases and also for solving open problems related to the dynamical properties of the systems which include the species that have unusual life cycle.
Citation Count: Kayar, Zeynep; Kaymakçalan, B. (2022). "The complementary nabla Bennett-Leindler type inequalities", Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Vol.71, No.2, pp.349-376.
The complementary nabla Bennett-Leindler type inequalities
(2022-06-30) Kayar, Zeynep; Kaymakçalan, Billur; 109448; Çankaya Üniversitesi, Fen-Edebiyat Fakültesi, Matematik Bölümü
We aim to find the complements of the Bennett-Leindler type inequalities in nabla time scale calculus by changing the exponent from 0 < ζ < 1 to ζ > 1. Different from the literature, the directions of the new inequalities, where ζ > 1 , are the same as that of the previous nabla Bennett-Leindler type inequalities obtained for 0 < ζ < 1 . By these settings, we not only complement existing nabla Bennett-Leindler type inequalities but also generalize them by involving more exponents. The dual results for the delta approach and the special cases for the discrete and continuous ones are obtained as well. Some of our results are novel even in the special cases.

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