Book Chapters
Authors: M. Ä°lkhan, E. E. Kara
Chapter: Infinite Systems of Differential Equations in Banach Spaces Constructed by Fibonacci Numbers
Year: 2018
Book: Advances in Summability and Approximation Theory
Editors: S. A. Mohiuddine, T. Acar
Publisher: Springer, Singapore
ISBN:978-981-13-3076-6
Published Papers
M. Ä°lkhan, E. E. Kara, Bourbaki completeness in quasi metric spaces, J. Nonlinear Funct. Anal., (2019) 2019, Article ID 33, 1-15.
M. Ä°lkhan, E. E. Kara, Remarkable applications of measure of non-compactness for infinite system of differential equations, AAM: Intern. J., (2019) Special Issue No. 5, 1-12.
M. Ä°lkhan, E. E. Kara, On statistical convergence in quasi-metric spaces, Demonstr. Math., (2019) 52, 225–236.
V. A. Khan, E.E. Kara, H. Altaf, N. Khan, M. Ahmad, Intuitionistic fuzzy I-convergent Fibonacci difference sequence spaces, Journal of Inequalities and Applications, (2019) 2019(202), 7 pages.
M. İlkhan, S. Demiriz, E. E. Kara, A New Paranormed Sequence Space Defined by Euler Totient Matrix, Karaelmas Science and Engineering Journal​, (2019) 9(2), 277-282.
M. Ä°lkhan, E. E. Kara, A new Banach space defined by Euler totient matrix operator, Operators and Matrices, (2019) 13(2), 527–544.
P. Zengin Alp, E. E. Kara, The new class Lz,p,E of s− type operators, AIMS Mathematics, (2019) 4(3), 779–791.
P. Zengin Alp, E. E. Kara, A new class of operator ideals on the block sequence space l_p(E), Advances and Applications in Mathematical Sciences, (2018) 2018(2), 205-217.
P. Zengin Alp, E. E. Kara, Some equivalent quasinorms on Lφ,E, Facta Univ. (NIS) Ser. Math. Inform., (2018) 33(5), 739-746.
N. Turan, E. E. Kara, M. Ä°lkhan, Quasi statistical convergence in cone metric spaces, Facta Univ. (NIS) Ser. Math. Inform., (2018) 33(4), 613-626.
M. Ä°lkhan, E. E. Kara, P. Zengin Alp, On the spaces of linear operators acting between asymmetric cone normed spaces, Mediterr. J. Math., (2018) 15(136), 12 pages.
M. Abay Tok, E. E. Kara, S. AltundaÄŸ, On the αβ-statistical convergence of the modified discrete operators, Adv. Differ. Equ., (2018) 2018(252), 6 pages.
M. Ä°lkhan, E. E. Kara, Some remarks on completeness and compactness in G-metric spaces, SAUJS, (2018) 22(6), 1893-1900.
M. Ä°lkhan, E. E. Kara, A new type of statistical Cauchy sequence and its relation to Bourbaki completeness, Cogent Mathematics & Statistics, (2018), 5: 1487500, 9 pages.
M. Ä°lkhan, M. AkyiÄŸit, E. E. Kara, On new types of sets via Gamma-open sets in bitopological spaces, Commun. Fac. Sci. Univ. Ank. Series A1, (2018) 67(1), 225-234.
P. Zengin Alp, E. E. Kara, A new class of operator ideals and approximation numbers, NTMSCI, (2018) 6(4), 8-15.
M. Ä°lkhan, M. BaÅŸarır, E. E. Kara, A note on I-convergence and I ∗ -convergence of an infinite product, Creative Math. Inf., (2017) 26(3), 275 - 279.
P. Zengin Alp, M. Ä°lkhan, E. E. Kara, Generalized Stolz mappings, Konuralp J. Math., (2017) 5(2), 12-18.
M. Ä°lkhan, E. E. Kara, Uniform continuity and Cauchy continuity in G-metric spaces, J. Inequal. Special Funct., (2017) 8(3), 59-68.
E.E. Kara, M. DaÅŸtan, M. Ä°lkhan, On Lacunary ideal convergence of some sequences, NTMSCI, (2017) 5(1), 234-242.
S. Demiriz, E. E. Kara, On compactoperators on some sequence spaces related to matrix B(r,s,t), Thai J. Math., (2016) 14(3), 651-666.
M. Başarır, F. Başar, E. E. Kara, On the spaces of Fibonacci difference absolutely p-summable null and convergent sequences, Sarajevo J. Math., (2016) 12(2), 167-182.
E. E. Kara, M. DaÅŸtan, M. Ä°lkhan, On almost ideal convergence with respect to an Orlicz function, Konuralp J. Math., (2016) 4(2), 78-94.
E. E. Kara, M. Ä°lkhan, Lacunary I-convergent and lacunary I-bounded sequence spaces defined by an Orlicz function, Electr. J. Math. Anal. Appl., (2016) 4(2), 150-159.
E. E. Kara, M. Ä°lkhan, Some properties of generalized Fibonacci sequence spaces, Linear and Multilinear Algebra, (2016) 64(11), 2208-2223.
S. Demiriz, E. E. Kara, Some new paranormed difference sequence spaces derived by Fibonacci numbers, Miskolc Mathematical Notes, (2015) 16(2), 907-923.
E. E. Kara, M. Başarır, M. Mursaleen, Compactness of matrix operators on some sequence spaces derived by Fibonacci numbers, Kragujevac J. Math., (2015) 39(2), 217-230.
M. Candan, E. E. Kara, A study on topological and geometrical characteristics of new Banach sequence space, Gulf J. Math., (2015) 3(4), 67-84.
S. Demiriz, E. E. Kara, M. Başarır, On the Fibonacci almost convergent sequence spaces and Fibonacci core, KYUNGPOOK Math. J., (2015) 55(2), 355-372.
E. E. Kara, M. Ä°lkhan, On a new class of s-type operators, Konuralp J. Math., (2015) 3(1), 1-11.
E. E. Kara, M. Ä°lkhan, On some paranormed A-Ideal convergent sequence spaces defined by Orlicz function, Asian J. Math. Comput. Res., (2015) 4(4), 183-194.
E. E. Kara, M. Ä°lkhan, On some Banach sequence spaces derived by a new band matrix, British J. Math. Comput. Sci., (2015) 9(2), 141-159.
M. Başarır, E. E. Kara, Ş. Konca, On some new weighted Euler sequence spaces and compact operators, Math. Inequal. Appl., (2014) 17(2), 649-664.
E. E. Kara, K. ElmaaÄŸaç, On the u-difference almost sequence space and matrix transformations, Inter. J. Modern Math. Sci., (2013) 8(1), 57-66.
M. Başarır, E. E. Kara, On the mth order difference sequence space of generalized weighted mean and compact operators, Acta Math. Sci., (2013) 33(3), 797-813.
E. E. Kara, Some topological and geometrical properties of new Banach sequence spaces, J. Inequal. Appl., (2013) 2013(38), 15 pages.
M. Başarır, Ş. Konca, E. E. Kara, Some generalized difference statistically convergent sequence spaces in 2-normed space, J. Inequal. Appl., (2013) 2013(177), 10 pages.
M. Başarır, E. E. Kara, On compact operators on the Riesz B^m difference sequence spaces II, Iran. J. Sci. Technol. Trans. A, (2012) 36(A), 371-376.
M. Başarır, E. E. Kara, On the B difference sequence space derived by generalized weighted mean and compact operators, J. Math. Anal. Appl., (2012) 391(1), 67-81.
E. E. Kara, M. Başarır, An application of Fibonacci numbers into infinite Toeplitz matrices, Caspian J. Math. Sci., (2012) 1(1), 1-6.
E. E. Kara, M. Başarır, On compact operators and some Euler B^m difference sequence spaces, J. Math. Anal. Appl., (2011) 379(2), 499-511.
M. Başarır, E. E. Kara, On compact operators on the Riesz B^m difference sequence space, Iran. J. Sci. Technol. Trans. A, (2011) 35(A4), 279-285.
M. Başarır, E. E. Kara, On some difference sequence spaces of weighted means and compact operators, Annals Funct. Anal., (2011) 2(2), 114-129.
E. E. Kara, M. Öztürk, M. BaÅŸarır, Some topological and geometric properties of generalized Euler sequence space, Math. Slovaca, (2010) 60(3), 385-398.
International Conference Proceedings
2018
E. E. Kara, M. Ä°lkhan, Some geometric properties of a new Banach sequence space, 7th International Eurasian Conference on Mathematical Sciences and Applications (IECMSA-2018), August 28-31, 2018, Kyiv-Ukraine.
M. Ä°lkhan, E. E. Kara, Compactness of matrix operators on the Banach space l_p(T), 7th International Eurasian Conference on Mathematical Sciences and Applications (IECMSA-2018), August 28-31, 2018, Kyiv-Ukraine.
E. E. Kara, M. Ä°lkhan, Infinite systems of differential equations in Banach spaces constructed by Fibonacci numbers, 7th International Eurasian Conference on Mathematical Sciences and Applications (IECMSA-2018), August 28-31, 2018, Kyiv-Ukraine.
M. Ä°lkhan, E. E. Kara, Solvability of infinite systems of differential equations in some BK spaces, 5th International Conference on Recent Advances in Pure and Applied Mathematics (ICRAPAM 2018), July 23-27, 2018, Trabzon-Turkey.
M. Ä°lkhan, E. E. Kara, Compact operators on some new sequence spaces, International Conference on Mathematics: An Istanbul Meeting for World Mathematicians (ICOMATH 2018), July 3-6, 2018, Ä°stanbul-Turkey.
R. Özçelik, E. E. Kara, M. Ä°lkhan, Some contraction mappings on Branciari b-metric spaces, International Conference on Mathematics: An Istanbul Meeting for World Mathematicians (ICOMATH 2018), July 3-6, 2018, Ä°stanbul-Turkey.
M. Ä°lkhan, N. ÅžimÅŸek, E. E. Kara, Applications of measure of non-compactness to the infinite system of differential equations in some Banach spaces, International Conference on Mathematical Advances and Applications (ICOMAA-2018), May 11-13, 2018, Ä°stanbul-Turkey.
M. Ä°lkhan, E. E. Kara, Norms and lower bounds for some matrix operators, International Conference on Mathematical Advances and Applications (ICOMAA-2018), May 11-13, 2018, Ä°stanbul-Turkey.
M. Ä°lkhan, P. Zengin Alp, E. E. Kara, On Riesz Fibonacci sequence spaces, International Conference on Mathematics and Related Sciences (ICMRS 2018), April 30-May 4, 2018, Antalya-Turkey.
E. E. Kara, M. Ä°lkhan, A new sequence space isomorphic to l_p, International Conference on Mathematics and Related Sciences (ICMRS 2018), April 30-May 4, 2018, Antalya-Turkey.
M. Ä°lkhan, E. E. Kara, Hausdorff measure of non-compactness of matrix operators on some new spaces, International Conference on Mathematics and Related Sciences (ICMRS 2018), April 30-May 4, 2018, Antalya-Turkey.
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2017
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E. E. Kara, M. Ä°lkhan, A new property between compactness and completeness in generalized metric spaces, 6th International Eurasian Conference on Mathematical Sciences and Applications (IECMSA-2017), August 15-18, 2017, Budapest, Hungary.
M. Ä°lkhan, E. E. Kara, Some effective results related to the new statistical Cauchy sequence, 6th International Eurasian Conference on Mathematical Sciences and Applications (IECMSA-2017), August 15-18, 2017, Budapest, Hungary.
N. Turan, E. E. Kara, On quasi statistical convergence in cone metric spaces, International Conference on Applied Analysis and Mathematical Modeling (ICAAMM-2017), July 03-07, 2017, Ä°stanbul-Turkey.
P. Zengin Alp, E. E. Kara, On operator ideals via generalized approximation numbers, International Conference on Applied Analysis and Mathematical Modeling (ICAAMM-2017), July 03-07, 2017, Ä°stanbul-Turkey.
M. Ä°lkhan, P. Zengin Alp, E. E. Kara, On boundedness and continuity of linear operators between asymmetric cone normed spaces, International Conference on Applied Analysis and Mathematical Modeling (ICAAMM-2017), July 03-07, 2017, Ä°stanbul-Turkey.
P. Zengin Alp, M. Ä°lkhan, E. E. Kara, A new version of Stolz mappings, International Conference on Applied Analysis and Mathematical Modeling (ICAAMM-2017), July 03-07, 2017, Ä°stanbul-Turkey.
M. Ä°lkhan, E. E. Kara, On asymmetric cone normed spaces, International Conference on Mathematics and Engineering (ICOME-2017), May 10-12, 2017, Ä°stanbul-Turkey.
E. E. Kara, M. Ä°lkhan, Generalizing asymmetric convergence and Cauchy conditions using asymptotic density, International Conference on Mathematics and Engineering (ICOME-2017), May 10-12, 2017, Ä°stanbul-Turkey.
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2016
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M. Ä°lkhan, E. E. Kara, A new type measure of noncompactness, International Congress on Fundamental and Applied Sciences (ICFAS-2016), August 22-26, 2016, Ä°stanbul-Turkey.
M. Ä°lkhan, E. E. Kara, Some new spaces of lacunary ideal convergent sequences, International Congress on Fundamental and Applied Sciences (ICFAS-2016), August 22-26, 2016, Ä°stanbul-Turkey.
E. E. Kara, M. Ä°lkhan, Ideal convergent sequence spaces via Orlicz function, 5th International Eurasian Conference on Mathematical Sciences and Applications (IECMSA-2016), August 16-19, 2016, Belgrade, Serbia.
M. Ä°lkhan, E. E. Kara, New type open sets in bitopological spaces, 5th International Eurasian Conference on Mathematical Sciences and Applications (IECMSA-2016), August 16-19, 2016, Belgrade, Serbia.
M. DaÅŸtan, M. Ä°lkhan, E. E. Kara, New type of Lacunary ideal convergent sequence spaces,5th International Eurasian Conference on Mathematical Sciences and Applications (IECMSA-2016), August 16-19, 2016, Belgrade, Serbia.
M. Ä°lkhan, P. Zengin Alp, E. E. Kara, Cofinally quasi Cauchy continuity, 5th International Eurasian Conference on Mathematical Sciences and Applications (IECMSA-2016), August 16-19, 2016, Belgrade, Serbia.
E. E. Kara, M. Başarır, M. İlkhan, Ideal Cauchy condition for infinite products, 2nd International Conference on Analysis and Applications (ICAA2016), July 12-15, 2016, Kırşehir, Turkey.
M. İlkhan, E. E. Kara, Some properties of generalized metric spaces, 2nd International Conference on Analysis and Applications (ICAA2016), July 12-15, 2016, Kırşehir, Turkey.
2015
M. Ä°lkhan, M. AkyiÄŸit, E. E. Kara, On gamma P-open sets in bitopological spaces, 4th International Eurasian Conference on Mathematical Sciences and Applications (IECMSA-2015), August 31- September 03, 2015, Athens, Greece .
M. DaÅŸtan, M. Ä°lkhan, E. E. Kara, Almost I-convergent sequence spaces defined by Orlicz function, 4th International Eurasian Conference on Mathematical Sciences and Applications (IECMSA-2015), August 31- September 03, 2015, Athens, Greece .
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2014
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M. Ä°lkhan, E. E. Kara, On some new difference sequence spaces, Karatekin Mathematics Days 2014, June 11-13, 2014, Çankırı, Turkey.
2013
S. Demiriz, E. E. Kara, M. Başarır, Some matrix transformations on the Fibonacci almost convergence sequence space, Algerian-Turkish International Days on Mathematics, September 11-14, 2013, İstanbul, Turkey.
E. E. Kara, S. Demiriz, Some new paranormed Fibonacci difference sequence spaces, 2st International Eurasian Conference on Mathematical Sciences and Applications (IECMSA-2013), August 26-29, 2013, Sarajevo, Bosnia.
2012
E. E. Kara, M. Başarır, M. Mursaleen, Compact operators on the Fibonacci difference sequence spaces l_p (F) and l_infinity(F). 1st International Eurasian Conference on Mathematical Sciences and Applications (IECMSA-2012), September 03-07, 2012, Pristhine, Kosovo.
E. E. Kara, S. Demiriz, On some new paranormed B-difference sequence spaces derived by generalized weighted mean matrix, 1st International Eurasian Conference on Mathematical Sciences and Applications (IECMSA-2012), September 03-07, 2012, Pristhine, Kosovo.
Ş. Konca, E. E. Kara, M. Başarır, Some generalized difference statistically convergent sequence spaces in 2-normed space, International Congress in Honour of Professor H.M. Srivastava, August 22-26, 2012, Bursa-Turkey.
2011
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E. E. Kara, M. Başarır, On the space of p summable B-difference sequences derived by weighted mean, International Conference on Applied Analysis and Algebra (ICAAA-2011), June 28-July 2, 2011, İstanbul-Turkey.
E. E. Kara, M. Başarır, On compact operators and some m -difference sequence spaces derived by weighted mean, Conference on Summability and Applications 2011, May 12-13, 2011 İstanbul-Turkey.
National Conference Proceedings
M. Ä°lkhan, E. E. Kara (2014): Some geometric properties of weighted Euler sequence space e_w (teta), XII. Geometri Sempozyumu, Bilecik Åžeyh Edebali University, Bilecik, Turkey.
E. E. Kara, M. Başarır (2010): Compact operators and matrix transformations on some B m Euler difference sequence spaces, XXIII. Ulusal Matematik Sempozyumu, Erciyes University, Kayseri, Turkey.