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2019
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Existence of nonoscillatory solutions of nonlinear neutral differential equation of second order
Existence of nonoscillatory solutions of nonlinear neutral differential equation of second order
en
en
In this paper, some necessary and sufficient conditions have been obtained to ensure the existence of
nonoscillatory solutions which are bounded below and above by bounded functions. These conditions
are more applicable than some known results in the references. An example is included to illustrate the results obtained.
1
8
Hussain Ali
Mohamad
Department of mathematics, College of science for women
University of Baghdad
Iraq
hussainam_math@csw.uobaghdad.edu.iq
Bashar Ahmed
Jawad
Department of Mathematics, Faculty of Computer Science and Mathematics
University of Kufa
Iraq
bashara.hamod@uokufa.edu.iq
Existence of positive solution
neutral differential equations
asymptotic behavior
Article.1.pdf
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[1]
T. Candan, Existence of positive periodic solutions of first-order neutral differential equations, Math. Methods Appl. Sci., 40 (2017), 205-209
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I. Culakov, L. Hanutiakova, R. Olach, Existence for positive solutions of second-order neutral nonlinear differential equations, Appl. Math. Lett., 22 (2009), 1007-1010
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B. Dorociakova, M. Kubjatkova, R. Olach, Existence of Positive Solutions of Neutral Differential Equations, Abstr. Appl. Anal., 2012 (2012), 1-14
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B. Dorociakova, M. Kubjatkova, R. Olach, Uncountably many solutions of first-order neutral nonlinear differential equations, Adv. Difference Equ., 2013 (2013), 1-8
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B. Dorociakova, A. Najmanova, R. Olach , Existence of Nonoscillatory Solutions of First-Order Neutral Differential Equations, Abstr. Appl. Anal., 2011 (2011), 1-9
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B. Dorociakova, R. Olach , Existence of Positive Solutions of Delay Differential Equations, Tatra Mt. Math. Publ., 43 (2009), 63-70
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L. H. Erbe, Q. Kong, B. G. Zhang, Oscillation Theory for Functional Differential Equations, Marcel Dekker, New York (1995)
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E. K. Essel, E. Yankson , On The Existence of Positive Periodic Solutions for Totally Nonlinear Neutral Differential Equations of The Second-Order With Functional Delay, Opuscula Math., 34 (2014), 469-481
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I. Györi, G. Ladas, Oscillation Theory of Delay Differential Equations, The Clarendon Press, Oxford University Press, New York (1991)
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F. Kong, Existence of non-oscillatory solutions of a kind of first-order neutral differential equation, Math. Commun., 22 (2017), 151-164
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H. A. Mohamad, I. Z. Mushtt, Oscillation of Second Order Nonlinear Neutral Differential Equations, Pure Appl. Math. J., 4 (2015), 62-65
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Ö, Öcalan, Existence of positive solutions for a neutral differential equation with positive and negative coefficients, Appl. Math. Lett., 22 (2009), 84-90
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S. Tanaka, Existence of Positive Solutions of Higher Order Nonlinear Neutral Differential Equations, Rocky Mountain J. Math., 30 (2000), 1139-1149
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G. Weiming, C. Jinfa, C. Yuming , Existence of Nonoscillatory Solution of Second Order Neutral Differential Equation, Bull. Inst. Math. Acad. Sin. (N.S.), 2 (2007), 785-795
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A. J. Yang, Z. G. Zhang, W. G. Ge, Existence of Nonoscillatory Solutions of Second-Order Nonlinear Neutral Differential Equations, Indian J. Pure Appl. Math., 39 (2008), 227-235
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Y. H. Yu, H. Z. Wang, Nonoscillatory solutions of second-order nonlinear neutral delay equations, J. Math. Anal. Appl., 311 (2005), 445-456
]
On approximation process by certain modified Dunkl generalization of Szász-Beta type operators
On approximation process by certain modified Dunkl generalization of Szász-Beta type operators
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en
In this paper, we give a generalization of the Szász-Beta type operators generated by Dunkl generalization of exponential
function and obtain convergence properties of these operators by using
Korovkin's theorem and weighted Korovkin-type theorem. We also establish
the order of convergence by using the modulus of smoothness and the weighted
modulus of continuity.
9
18
Çiğdem
Atakut
Department of Mathematics, Faculty of Science
Ankara University
Turkey
atakut@science.ankara.edu.tr
Seda
Karateke
Department of Mathematics and Computer Science, Faculty of Science and Letters
Istanbul Arel University
Turkey
sedakarateke34@gmail.com
Ibrahim
Büyükyazıcı
Department of Mathematics, Faculty of Science
Ankara University
Turkey
ibuyukyazici@gmail.com
Dunkl type generalization
Genuine Szász beta operators
modulus of smoothness
Lipschitz functions
Article.2.pdf
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[1]
B. Çekim, Ü . Dinlemez Kantar, I. Yüksel , Dunkl generalization of Szász beta-type operators, Math. Methods Appl. Sci., 40 (2017), 7697-7704
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A. R. Gairola, Deepmala, L. N. Mishra , Rate of approximation by finite iterates of q-Durrmeyer operators , Proc. Nat. Acad. Sci. India Sect. A, 86 (2016), 229-234
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A. R. Gairola, Deepmala, L. N. Mishra , On the q-derivatives of a certain linear positive operators, Iran. J. Sci. Technol. Trans. A Sci., 42 (2018), 1409-1417
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R. B. Gandhi, Deepmala, V. N. Mishra, Local and global results for modified Szász–Mirakjan operators, Math. Method. Appl. Sci., 40 (2017), 2491-2504
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N. ˙Ispir, Ç. Atakut, Approximation by modified Szasz–Mirakjan operators on weighted spaces , Proc. Indian Acad. Sci. Math. Sci., 112 (2002), 571-578
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M. Lésniewicz, L. Rempulska, Approximation by some operators of the Szasz–Mirakjan type in exponential weight spaces , Glas. Mat. Ser. III, 32 (1997), 57-69
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V. N. Mishra, K. Khatri, L. N. Mishra, Deepmala, Inverse result in simultaneous approximation by Baskakov-Durrmeyer- Stancu operators, J. Inequal. Appl., 2013 (2013), 1-11
##[10]
V. N. Mishra, S. Pandey, I. A. Khan, On a modification of Dunkl generalization of Szász Operators via q-calculus, Eur. J. Pure Appl. Math., 10 (2017), 1067-1077
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M. Rosenblum, Generalized Hermite polynomials and the Bose-like oscillator calculus, Oper. Theory Adv. Appl., 73 (1994), 369-396
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S. Sucu, Dunkl analogue of Szász operators, Appl. Math. Comput., 244 (2014), 42-48
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S. Varma, S. Sucu, G. Içöz , Generalization of Szász operators involving Brenke type polynomials, Comput. Math. Appl., 64 (2012), 121-127
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Z. Walczak, On certain modified Szasz–Mirakjan operators for functions of two variables, Demonstratio Math., 33 (2000), 92-100
]
Oscillation criteria for a class of third order neutral distributed delay differential equations with damping
Oscillation criteria for a class of third order neutral distributed delay differential equations with damping
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en
In this paper, the oscillation criteria of a class of third order neutral distributed delay differential equations with damping are investigated. This work is the continuation of the study by Saker [S. H. Saker, Math. Slovaca, \({\bf 56}\) (2006), 433--450] and the extension of the work by Zhang [Q. X. Zhang, L. Gao, Y. H. Yu, Appl. Math. Lett., \({\bf 25}\) (2012), 1514--1519] on oscillation properties of nonlinear third order delay differential
equation. By choosing the appropriate functions and using a generalized Riccati transformation, some new oscillation criteria are presented to insure that every solution of this equation oscillates or converges to zero. The presented results correct and improve the earlier ones in existing literature. Finally, several illustrative examples are included.
19
28
M. H.
Wei
School of Mathematics and Statistics
Yulin University
China
wei_meihua@163.com
M. L.
Zhang
School of Mathematics and Statistics
Yulin University
China
X. L.
Liu
School of Mathematics and Statistics
Yulin University
China
Y. H.
Yu
Academy of Mathematics and System Sciences
Chinese Academy of Sciences
China
Oscillation criteria
third order
distributed delay
damping
Riccati transformation
Article.3.pdf
[
[1]
R. P. Agarwal, M. Bohner, T. X. Li, C. H. Zhang, Hille and Nehari type criteria for third-order delay dynamic equations, J. Difference Equ. Appl., 19 (2013), 1563-1579
##[2]
R. P. Agarwal, M. Bohner, T. X. Li, C. H. Zhang , Oscillation of third-order nonlinear delay differential equations , Taiwanese J. Math., 17 (2013), 545-558
##[3]
M. F. Aktas, A. Tiryaki, A. Zafer, Oscillation criteria for third order nonlinear functional differential equations, Appl. Math. Lett., 23 (2010), 756-762
##[4]
M. Bohner, S. R. Grace, I. Sager, E. Tunc , Oscillation of third-order nonlinear damped delay differential equations, Appl. Math. Comput., 278 (2016), 21-32
##[5]
L. Erbe, T. S. Hassan, A. Peterson, Oscillation of third order nonlinear functional dynamic equations on time scales, Differ. Equ. Dyn. Syst., 18 (2010), 199-227
##[6]
L. Erbe, T. S. Hassan, A. Peterson, Oscillation of third-order functional dynamic equations with mixed arguments on time scales, J. Appl. Math. Comput., 34 (2010), 353-371
##[7]
L. Erbe, A. Peterson, S. H. Saker, Hille and Nehari type criteria for third order dynamic equations, J. Math. Anal. Appl., 329 (2007), 112-131
##[8]
S. R. Grace, Oscillation criteria for third-order nonlinear delay differential equations with damping, Opuscula Math., 35 (2015), 485-497
##[9]
S. R. Grace, J. R. Graef, M. A. El-Beltagy, On the oscillation of third order neutral delay dynamic equations on time scales , Comput. Math. Appl., 63 (2012), 775-782
##[10]
S. R. Grace, J. R. Graef, E. Tunc, On the oscillation of certain third order nonlinear dynamic equations with a nonlinear damping term, Math. Slovaca, 67 (2017), 501-508
##[11]
Z. L. Han, T. X. Li, S. R. Sun, F. J. Cao, Oscillation criteria for third order nonlinear delay dynamic equations on time scales, Ann. Polon. Math., 99 (2010), 143-156
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T. S. Hassan, Oscillation of third order nonlinear delay dynamic equations on time scales, Math. Comput. Modelling, 49 (2009), 1573-1586
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T. X. Li, Z. L. Han, S. R. Sun, Y. Zhao , Oscillation results for third order nonlinear delay dynamic equations on time scales, Bull. Malays. Math. Sci. Soc., (2), 34 (2011), 639-648
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T. X. Li, Y. V. Rogovchenko, On asymptotic behavior of solutions to higher-order sublinear Emden-Fowler delay differential equations, Appl. Math. Lett., 67 (2017), 53-59
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S. Padhi, S. Pati , Theory of third-order differential equations, Springer, New Delhi (2014)
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Y.-C. Qiu, A. Zada, H. Y. Qin, T. X. Li, Oscillation criteria for nonlinear third-order neutral dynamic equations with damping on time scales, J. Funct. Spaces, 2017 (2017), 1-8
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Y. V. Rogovchenko, Oscillation theorems for second-order equations with damping, Nonlinear Anal., 41 (2000), 1005-1028
##[18]
S. H. Saker , Oscillation criteria of third-order nonlinear delay differential equations, Math. Slovaca, 56 (2006), 433-450
##[19]
S. H. Saker, P. Y. H. Pang, R. P. Agarwal, Oscillation theorems for second order functional differential equations with damping, Dynam. Systems Appl., 12 (2003), 307-321
##[20]
Y. B. Sun, Z. Han, Y. Sun, Y. Pan , Oscillation theorems for certain third order nonlinear delay dynamic equations on time scales, Electron. J. Qual. Theory Differ. Equ., 75 (2011), 1-14
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A. Tiryaki, M. F. Aktas, Oscillation criteria of a certain class of third order nonlinear delay differential equations with damping, J. Math. Anal. Appl., 325 (2007), 54-68
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A. Tiryaki, S. (Yaman) Pasinliogu, Oscillatory behaviour of a class of nonlinear differential equations of third order, Acta Math. Sci. Ser. B Engl. Ed., 21 (2001), 182-188
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A. Tiryaki, A. Zafer, Oscillation criteria for second-order nonlinear differential equations with damping, Turkish J. Math., 24 (2000), 185-196
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Q. X. Zhang, L. Gao, Y. H. Yu, Oscillation criteria for third-order neutral differential equations with continuously distributed delay, Appl. Math. Lett., 25 (2012), 1514-1519
]
Mönch type Leray--Schauder alternatives for maps satisfying weakly countable compactness conditions
Mönch type Leray--Schauder alternatives for maps satisfying weakly countable compactness conditions
en
en
In this paper we discuss
weakly Mönch type maps and obtain Leray--Schauder alternatives for
such maps.
29
34
Donal
O'Regan
School of Mathematics, Statistics and Applied Mathematics
National University of Ireland
Ireland
donal.oregan@nuigalway.ie
Essential maps
fixed points
nonlinear alternatives
Mönch-type maps
Article.4.pdf
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[1]
A. Ben Amar, D. O’Regan, Topological fixed point theory for singlevalued and multivalued mappings with applications, Springer, Cham (2016)
##[2]
T. Cardinali, P. Rubbioni, Multivalued fixed point theorems in terms of weak topology and measure of weak noncompactness, J. Math. Anal. Appl., 405 (2013), 409-415
##[3]
A. Granas, J. Dugundji , Fixed Point Theory, Springer-Verlag, New York (2003)
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H. Mönch, Boundary value problems for nonlinear ordinary differential equations in Banach spaces, Nonlinear Anal., 4 (1980), 985-999
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D. O’Regan, Mönch type results for maps with weakly sequentially closed graphs, Dynam. Systems Appl., 24 (2015), 129-134
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D. O’Regan , Coincidence results for compositions of multivalued maps based on countable compactness principles, Applicable Analysis, 2018 (2018), 1-11
##[7]
D. O’Regan, Maps with weakly sequentially closed graphs satisfying compactness conditions on countable sets, Pure Appl. Func. Anal., (to appear.), -
]
On asymptotically lacunary statistical equivalent functions via ideals
On asymptotically lacunary statistical equivalent functions via ideals
en
en
The goal of this paper is to introduce \(\mathcal{I}_\theta\)-asymptotically statistical equivalent by taking nonnegative two real-valued Lebesgue measurable functions \( \gamma\left( \nu\right) \) and \( \mu\left( \nu\right)\) in
the interval \(\left( 1,\infty \right)\) instead of sequences and we establish some inclusion relations.
35
40
Ekrem
Savaş
Department of Mathematics
Usak University
Turkey
ekremsavas@yahoo.com
Asymptotical equivalent functions
ideal convergence
lacunary sequence
\(\mathcal{I}\)-statistical convergence
Article.5.pdf
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[1]
P. Das, E. Savas, S. K. Ghosal, On generalizations of certain summability methods using ideals, Appl. Math. Lett., 24 (2011), 1509-1514
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J. A. Fridy , On Statistical Convergence, Analysis, 5 (1985), 301-313
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P. Kostyrko, M. Macaj, T. Salat, M. Sleziak, J–Convergence and Extremal J–Limit Points, Math. Slovaca, 55 (2005), 443-464
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P. Kostyrko, W. Wilczyński, T. Salat, J–Convergence, Real Anal. Exchange, 26 (2000), 669-686
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R. F. Patterson, On Asymptotically Statistically Equivalent Sequences, Demonstr. Math., 36 (2003), 149-153
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R. F. Patterson, E. Savas, On Asymptotically Lacunary Statistical Equivalent Sequences, Thai J. Math., 4 (2006), 267-272
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E. Savas, On J–Asymptotically Lacunary Statistical Equivalent Sequences, Adv. Difference Equ., 2013 (2013), 1-7
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E. Savas, On Asymptotically J–Lacunary Statistical Equivalent Sequences of order \(\alpha\), The 2014 International Conference on Pure Mathematics–Applied Mathematics Venice, Italy (2014)
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E. Savas, Generalized summability methods of functions using ideals, AIP Conference Proceedings, V. 1676 (2015)
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E. Savas, On generalized statistically convergent functions via ideals, Appl. Math., 10 (2016), 943-947
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E. Savas, P. Das, A generalized statistical convergence via ideals, Appl. Math. Lett., 24 (2011), 826-830
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E. Savas, P. Das, S. Dutta, A note on strong matrix summability via ideals, Appl. Math. Lett., 25 (2012), 733-738
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E. Savas, H. Gumus, A generalization on I–asymptotically lacunary statistical equivalent sequences, J. Inequal. Appl., 2013 (2013), 1-9
]
Chaotic behavior in real dynamics and singular values of family of generalized generating function of Apostol-Genocchi numbers
Chaotic behavior in real dynamics and singular values of family of generalized generating function of Apostol-Genocchi numbers
en
en
Chaotic behavior in the real dynamics and singular values of a two-parameter family of generalized generating function of Apostol-Genocchi numbers, \(f_{\lambda,a}(z)=\lambda \frac{2z}{e^{az}+1}\),
\(\lambda, a\in \mathbb{R} \backslash \{0\}\), are investigated. The real fixed points of \(f_{\lambda,a}(z)\) and their nature are studied. It is seen that bifurcation and chaos occur in the real dynamics of \(f_{\lambda,a}(z)\). It is also found that the function \(f_{\lambda,a}(z)\) has infinitely many singular values for \(a>0\) and \(a<0\). The critical values of \(f_{\lambda,a}(z)\) lie inside the open disk, the annulus and exterior of the open disk at center origin for \(a>0\) and \(a<0\).
41
50
Mohammad
Sajid
College of Engineering
Qassim University
Saudi Arabia
msajd@qu.edu.sa
Fixed points
critical values
singular values
bifurcation
chaos
Lyapunov exponents
Article.6.pdf
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M. Akbari, M. Rabii, Real cubic polynomials with a fixed point of multiplicity two, Indag. Math. (N.S.), 26 (2015), 64-74
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H. Jolany, H. Sharifi, R. E. Alikelaye, Some results for the Apostol-Genocchi polynomials of higher order, Bull. Malays. Math. Sci. Soc., (2), 36 (2013), 465-479
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M. Sajid, Real and complex dynamics of one parameter family of meromorphic functions, Far East J. Dyn. Syst., 19 (2012), 89-105
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M. Sajid, On real fixed points of one parameter family of function \(\frac{x }{b^x-1}\), Tamkang J. Math., 46 (2015), 61-65
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M. Sajid, Singular values and fixed points of family of generating function of Bernoulli’s numbers, J. Nonlinear Sci. Appl., 8 (2015), 17-22
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M. Sajid, Singular Values of One Parameter Family \(\lambda \frac{b^z-1 }{z}\), J. Math. Comput. Sci., 15 (2015), 204-208
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M. Sajid, Singular values of one parameter family of generalized generating function of Bernoulli’s numbers, Appl. Math. Inf. Sci., 9 (2015), 2921-2924
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M. Sajid, A. S. Alsuwaiyan, Chaotic behavior in the real dynamics of a one parameter family of functions, Int. J. Appl. Sci. Eng., 12 (2014), 283-301
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M. Sajid, G. P. Kapoor, Dynamics of a family of non-critically finite even transcendental meromorphic functions, Regul. Chaotic Dyn., 9 (2004), 143-162
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M. Sajid, G. P. Kapoor , Dynamics of transcendental meromorphic functions \((z + \mu)e^z/(z + \mu + 4)\) having rational Schwarzian derivative , Dynam. Syst., 22 (2007), 323-337
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F.-F. Zhang, S.-T. Liu, W.-Y. Yu, Modified projective synchronization with complex scaling factors of uncertain real chaos and complex chaos, Chinese Physics B, 22 (2013), 141-151
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J. H. Zheng, On fixed-points and singular values of transcendental meromorphic functions, Sci. China Math., 53 (2010), 887-894
]
The weight inequalities on Reich type theorem in \(b\)-metric spaces
The weight inequalities on Reich type theorem in \(b\)-metric spaces
en
en
In this note, we give a generalization of the Reich type theorem in \(b\)-metric spaces by using weight inequalities. Here, the existence of nonunique fixed points is ensured. Other known fixed point results in the literature are derived.
51
57
Zoran D.
Mitrović
Nonlinear Analysis Research Group
Ton Duc Thang University
Vietnam
zoran.mitrovic@tdtu.edu.vn
Hassen
Aydi
Department of Mathematics, College of Education in Jubail
Imam Abdulrahman Bin Faisal University
Saudi Arabia
hmaydi@iau.edu.sa
Mohd Salmi Md
Noorani
School of mathematical Sciences, Faculty of Science and Technology
Universiti Kebangsaan Malaysia
Malaysia
msn@ukm.my
Haitham
Qawaqneh
School of mathematical Sciences, Faculty of Science and Technology
Universiti Kebangsaan Malaysia
Malaysia
haitham.math77@gmail.com
Fixed point
\(b\)-metric space
weight inequalities
Article.7.pdf
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[1]
A. Aghajani, M. Abbas, J. R. Roshan, Common fixed point of generalized weak contractive mappings in partially ordered b-metric spaces, Math. Slovaca, 64 (2014), 941-960
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H. Aydi, R. Banković, I. Mitrović, M. Nazam, Nemytzki-Edelstein-Meir-Keeler type results in b-metric spaces , Discrete Dyn. Nat. Soc., 2018 (2018), 1-7
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H. Aydi, M.-F. Bota, E. Karapinar, S. Mitrović, A fixed point theorem for set-valued quasi-contractions in b-metric spaces, Fixed Point Theory Appl., 2012 (2012), 1-8
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H. Aydi, M.-F. Bota, E. Karapinar, S. Moradi, A common fixed point for weak \(\phi\)-contractions on b-metric spaces, Fixed Point Theory, 13 (2012), 337-346
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H. Aydi, A. Felhi, S. Sahmim, Common fixed points via implicit contractions on b-metric-like spaces, J. Nonlinear Sci. Appl., 10 (2017), 1524-1537
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I. A. Bakhtin, The contraction mapping principle in quasimetric spaces, Funct. Anal. Ulianowsk Gos. Ped. Inst., 30 (1989), 26-37
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P. S. Bullen, D. S. Mitrinović, P. M. Vasić, Means and Their Inequalities, D. Reidel Publishing Co., Dordrecht (1988)
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N. Hussain, Z. D. Mitrović , On multi-valued weak quasi-contractions in b-metric spaces, J. Nonlinear Sci. Appl., 10 (2017), 3815-3823
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E. Karapinar, Revisiting the Kannan Type Contractions via Interpolation Adv. Theory, J. Nonlinear Anal. Appl., 2 (2018), 85-87
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E. Karapinar, R. Agarwal, H. Aydi, Interpolative Reich-Rus-Ćirić Type Contractions on Partial Metric Spaces , Mathematics, 60 (2018), 1-7
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R. Miculescu, A. Mihail, New fixed point theorems for set-valued contractions in b-metric spaces , J. Fixed Point Theory Appl., 19 (2017), 2153-2163
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Z. Mustafa, M. M. M. Jaradat, H. Aydi, A. Alrhayyel, Some common fixed points of six mappings on \(G_b\)-metric spaces using (E.A) property, Eur. J. Pure Appl. Math., 11 (2018), 90-109
##[17]
H. A. Qawaqneh, M. S. M. Noorani, W. Shatanawi, Fixed Point Results for Geraghty Type Generalized F-contraction for Weak alpha-admissible Mapping in Metric-like Spaces, Eur. J. Pure Appl. Math., 11 (2018), 702-716
##[18]
H. Qawaqneh, M. S. M. Noorani, W. Shatanawi, Fixed Point Theorems for (\(\alpha,k,\theta\))-Contractive Multi-Valued Mapping in b-Metric Space and Applications, Int. J. Math. Comput. Sci., 14 (2019), 263-283
##[19]
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On a subclass of bi-univalent functions associated with the \(q\)-derivative operator
On a subclass of bi-univalent functions associated with the \(q\)-derivative operator
en
en
In this paper, we consider a new subclass of analytic and bi-univalent functions associated with \(q\)-Ruscheweyh differential
operator in the open unit disk \(\mathbb{U}\). For functions belonging to the class \(\Sigma_q(\lambda,\phi)\), we obtain estimates on the first two Taylor-Maclaurin coefficients. Further, we derive another subclass of analytic and bi-univalent functions as a special consequences of the results.
58
64
Huda
Aldweby
Department of Mathematics, Faculty of Science
Al Asmarya Islamic University
Libya
hu.aldweby@asmarya.edu.ly
Maslina
Darus
Centre of Modelling and Data Science, Faculty of Science and Technology
Universiti Kebangsaan
Malaysia
maslina@ukm.edu.my
Bi-univalent functions
\(q\)-derivative
coefficient estimates
\(q\)-starlike functions
Article.8.pdf
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