المؤلفون: Muhammad Adil Khan, Asadullah Sohail, Hidayat Ullah, Tareq Saeed

المصدر: Mathematics; Volume 11; Issue 8; Pages: 1957

مصطلحات موضوعية: convex function, 6-convex function, Jensen’s inequality, Hölder inequality, power means, quasi-arithmetic means, information theory, Zipf–Mandelbrot entropy

وصف الملف: application/pdf

Relation: Difference and Differential Equations; https://dx.doi.org/10.3390/math11081957

الاتاحة: https://doi.org/10.3390/math11081957

المؤلفون: Xuexiao You, Muhammad Adil Khan, Hidayat Ullah, Tareq Saeed

المصدر: Mathematics; Volume 10; Issue 8; Pages: 1274

مصطلحات موضوعية: convex function, Slater’s inequality, Jensen’s inequality, power mean, information theory, Zipf–Mandelbrot entropy

وصف الملف: application/pdf

Relation: Computational and Applied Mathematics; https://dx.doi.org/10.3390/math10081274

الاتاحة: https://doi.org/10.3390/math10081274

المؤلفون: Sadia Khalid, Ðilda Pečarić, Josip Pečarić

المصدر: Journal of Inequalities and Applications, Vol 2019, Iss 1, Pp 1-14 (2019)

مصطلحات موضوعية: Shannon entropy, Zipf–Mandelbrot entropy, Non-increasing sequence in weighted mean, Wright-convex function, Cauchy means, n-exponential convexity and logarithmic convexity, Mathematics, QA1-939

وصف الملف: electronic resource

Relation: http://link.springer.com/article/10.1186/s13660-019-2037-3; https://doaj.org/toc/1029-242X

URL الوصول: https://doaj.org/article/3f94ad7ffeee479393c598bbb1c54676

المؤلفون: Khurshid Ahmad, Muhammad Adil Khan, Shahid Khan, Amjad Ali, Yu-Ming Chu

المصدر: Results in Physics, Vol 18, Iss , Pp 103305- (2020)

مصطلحات موضوعية: Jensen inequality, Convex function, Shannon entropy, Zipf-Mandelbrot entropy, Physics, QC1-999

وصف الملف: electronic resource

Relation: http://www.sciencedirect.com/science/article/pii/S2211379720317721; https://doaj.org/toc/2211-3797

URL الوصول: https://doaj.org/article/c255f74ede604235bd84b42ac0082011

المؤلفون: Mehmood Nasir, Butt Saad Ihsan, Pečarić Ðilda, Pečarić Josip

المصدر: Demonstratio Mathematica, Vol 51, Iss 1, Pp 112-130 (2018)

مصطلحات موضوعية: n-convex function, Hermite interpolating polynomial, new Green functions, Shannon entropy, Relative entropy, Zipf-Mandelbrot entropy, 26A51, 26D15, 26E60, 94A17, 94A15, Mathematics, QA1-939

وصف الملف: electronic resource

Relation: http://www.degruyter.com/view/j/dema.2018.51.issue-1/dema-2018-0011/dema-2018-0011.xml?format=INT; https://doaj.org/toc/2391-4661

URL الوصول: https://doaj.org/article/6bede4e0de6b4a9982ba8618057cbd8a

المؤلفون: Khan M.A., Pecaric D., Pecaric J.

المصدر: Mathematical Methods in the Applied Sciences

مصطلحات موضوعية: convex function, Jensen inequality, Shannon entropy, Zipf-Mandelbrot entropy

Relation: https://doi.org/10.1002/mma.4531; https://openrepository.ru/article?id=260253

الاتاحة: https://openrepository.ru/article?id=260253

المؤلفون: Mehmood N., Butt S.I., Pecaric D., Pecaric J.

المصدر: DEMONSTRATIO MATHEMATICA

مصطلحات موضوعية: n-convex function, Hermite interpolating polynomial, new Green functions, Shannon entropy, Relative entropy, Zipf-Mandelbrot entropy

Relation: https://doi.org/10.1515/dema-2018-0011; https://openrepository.ru/article?id=260194

الاتاحة: https://openrepository.ru/article?id=260194

المؤلفون: Muhammad Adil Khan, Zaid Mohammad Al-sahwi, Yu-Ming Chu

المصدر: Entropy; Volume 20; Issue 8; Pages: 608

مصطلحات موضوعية: Jensen inequality, convex function, Shannon entropy, Zipf–Mandelbrot entropy

وصف الملف: application/pdf

Relation: https://dx.doi.org/10.3390/e20080608

الاتاحة: https://doi.org/10.3390/e20080608

المؤلفون: Ɖilda Pečarić, Muhammad Adil Khan, Josip Pečarić

المصدر: Bulletin of the Malaysian Mathematical Sciences Society. 44:267-278

مصطلحات موضوعية: Zipf's law, Inequality, General Mathematics, media_common.quotation_subject, 010102 general mathematics, Information theory, 01 natural sciences, 010101 applied mathematics, Entropy (information theory), 0101 mathematics, Jensen's inequality, Mathematical economics, Jensen’s inequality, Mean, Csiszár div, Shannon entropy, Zipf–Mandelbrot entropy, Mathematics, media_common

URL الوصول: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6784fc1876b0c2186394bd4e86c1084a
https://doi.org/10.1007/s40840-020-00944-5

المؤلفون: Nasir Mehmood, Đilda Pečarić, Saad Ihsan Butt, Josip Pečarić

المصدر: Journal of Mathematical Inequalities. :249-271

مصطلحات موضوعية: Discrete mathematics, Polynomial, Information theory, Jensen's inequality, 2n-convex function, Lidstone's polynomial, new Green functions, divergence functional, Shannon entropy, relative entropy, Zipf-Mandelbrot entropy, Analysis, Mathematics

URL الوصول: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9ba4f43c8f9d473b46c9be86906020be
https://doi.org/10.7153/jmi-2020-14-17

المؤلفون: Ðilda Pečarić, Josip Pečarić, Muhammad Adil Khan

المصدر: Mathematical Methods in the Applied Sciences. 42:7411-7424

مصطلحات موضوعية: convex functions, Csiszár divergence, hybrid Zipf-Mandelbrot entropy, Jensen's inequality, Slater's inequali, Zipf's law, General Mathematics, General Engineering, Statistical physics, Mandelbrot set, Convex function, Jensen's inequality, Mathematics

URL الوصول: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::cbf689b1d422766f080ca49d6aca58e0
https://doi.org/10.1002/mma.5858

المؤلفون: Yu-Ming Chu, Shahid Ullah Khan, Khurshid Ahmad, Amjad Ali, Muhammad Adil Khan

المصدر: Results in Physics, Vol 18, Iss, Pp 103305-(2020)

مصطلحات موضوعية: 010302 applied physics, Zipf's law, Ecology (disciplines), Jensen inequality, Shannon entropy, General Physics and Astronomy, 02 engineering and technology, Mandelbrot set, 021001 nanoscience & nanotechnology, Information theory, 01 natural sciences, Convexity, lcsh:QC1-999, Convex function, 0103 physical sciences, Applied mathematics, Zipf-Mandelbrot entropy, 0210 nano-technology, Jensen's inequality, lcsh:Physics

URL الوصول: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a5178e7e29c0cff8eab6ffc40802cd79
http://www.sciencedirect.com/science/article/pii/S2211379720317721

المؤلفون: Đilda Pečarić, Josip Pečarić, Muhammad Adil Khan

المصدر: Journal of Computational and Applied Mathematics. 346:192-204

مصطلحات موضوعية: Computational Mathematics, Zipf–Mandelbrot entropy Csiszar divergence Convex functions Jensen’s inequality Slater’s inequality, Mathematics::Dynamical Systems, Zipf's law, Applied Mathematics, Applied mathematics, Applied science, Mandelbrot set, Information theory, Convex function, Mathematics

URL الوصول: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b81436080859a06bd160e01a4d456f0c
https://doi.org/10.1016/j.cam.2018.07.002

المؤلفون: Sadia Khalid, Đilda Pečarić, Josip Pečarić

المصدر: Adv. Oper. Theory 4, no. 4 (2019), 724-737

مصطلحات موضوعية: Pure mathematics, ‎26A51‎, Algebra and Number Theory, Zipf's law, Mean value, Mandelbrot set, Convexity, 26D15, ‎‎Zipf-Mandelbrot entropy‎, n-convex function‎ , n-exponential convexity , ‎divided difference , logarithmic convexity , Shannon entropy , ‎‎Zipf-Mandelbrot entropy‎, ‎$n$-convex function‎, $n$-exponential convexity, ‎divided difference, 26A48‎, Entropy (information theory), Convex function, logarithmic convexity‎, Shannon entropy‎, Analysis, 26A24, Mathematics

وصف الملف: application/pdf

URL الوصول: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::99e9952f79707c6498bdd16f16f788d3
https://doi.org/10.15352/aot.1810-1426

المؤلفون: Muhammad Adil Khan, Đilda Pečarić, Josip Pečarić

المصدر: Mathematical Methods in the Applied Sciences. 40:7316-7322

مصطلحات موضوعية: convex function, Jensen inequality, Shannon entropy, Zipf-Mandelbrot entropy, Discrete mathematics, Mathematics::Dynamical Systems, Shannon's source coding theorem, General Mathematics, 010102 general mathematics, General Engineering, Maximum entropy thermodynamics, Min entropy, Entropy in thermodynamics and information theory, 01 natural sciences, 010101 applied mathematics, Rényi entropy, Entropy power inequality, Combinatorics, 0101 mathematics, Entropic uncertainty, Limiting density of discrete points, Mathematics

URL الوصول: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4e056ae9cc394e288e6e6ff68374ed94
https://doi.org/10.1002/mma.4531

المؤلفون: Nasir Mehmood, Saad Ihsan Butt, Ðilda Pečarić, Josip Pečarić

المصدر: Journal of Inequalities and Applications, Vol 2019, Iss 1, Pp 1-18 (2019)

مصطلحات موضوعية: Pure mathematics, Inequality, media_common.quotation_subject, MathematicsofComputing_NUMERICALANALYSIS, Monotonic function, Kullback–Leibler divergence, Type (model theory), Information theory, 01 natural sciences, Jensen’s inequality, New Green functions, ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION, Discrete Mathematics and Combinatorics, Order (group theory), Point (geometry), Jensen’s inequality, Higher order convexity, Taylor’s formula, New Green functions, Shannon entropy, Kullback–Leibler divergence, Zipf–Mandelbrot entropy, 0101 mathematics, Mathematics, media_common, Higher order convexity, lcsh:Mathematics, Applied Mathematics, 010102 general mathematics, Shannon entropy, Regular polygon, lcsh:QA1-939, Taylor’s formula, 010101 applied mathematics, Convex function, Analysis

URL الوصول: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::da30def9f8a22d8f6c7839c085b8be4f
https://doi.org/10.1186/s13660-019-2191-7

المؤلفون: Josip Pečarić, Đilda Pečarić, Slavica Ivelić Bradanović, Ana Barbir

مصطلحات موضوعية: Inequality, Applied Mathematics, General Mathematics, media_common.quotation_subject, Converse, Sherman inequality, Majorization inequality, Jensen inequality, f-divergence, Zipf-Mandelbrot entropy, convex function, Mathematical economics, Mathematics, media_common

URL الوصول: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7c383a4baa8ac78d8c46c0663b7e07ff
https://www.bib.irb.hr/1042731

المؤلفون: Zaid Mohammad Al-Sahwi, Muhammad Adil Khan, Yu-Ming Chu

المصدر: Entropy, Vol 20, Iss 8, p 608 (2018)
Entropy
Volume 20
Issue 8

مصطلحات موضوعية: General Physics and Astronomy, lcsh:Astrophysics, Zipf–Mandelbrot entropy, Mandelbrot set, 01 natural sciences, Article, Domain (mathematical analysis), lcsh:QB460-466, Entropy (information theory), 0101 mathematics, lcsh:Science, Mathematics, convex function, Discrete mathematics, Zipf's law, 010102 general mathematics, Jensen inequality, Shannon entropy, Function (mathematics), lcsh:QC1-999, 010101 applied mathematics, 26D15, lcsh:Q, Convex function, Jensen's inequality, lcsh:Physics

وصف الملف: application/pdf

URL الوصول: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8a43c196553a7d59141cc6ab20db393a
https://pubmed.ncbi.nlm.nih.gov/33265697

المؤلفون: Mehmood, N., Butt, S. I., Pečarić, D., Pečarić, J.

المصدر: Demonstratio Mathematica. Warsaw Technical University Institute of Mathematics.

مصطلحات موضوعية: n-convex function, Hermite interpolating polynomial, new Green functions, Shannon entropy, relative entropy, Zipf-Mandelbrot entropy, funkcja n-wypukła, interpolacja Hermite'a, funkcja Greena, entropia Shannona, entropia względna, entropia Zipfa-Mandelbrota

URL الوصول: http://yadda.icm.edu.pl/baztech/element/bwmeta1.element.baztech-9fb67418-161f-48fd-bf66-7f848ff3d6db

المؤلفون: Khan M.A., Pečarić Ɖ., Pečarić J.

المصدر: Bulletin of the Malaysian Mathematical Sciences Society

مصطلحات موضوعية: Csiszár divergence, Jensen’s inequality, Means, Shannon entropy, Zipf–Mandelbrot entropy

Relation: https://doi.org/10.1007/s40840-020-00944-5; https://repository.rudn.ru/records/article/record/65399/

الاتاحة: https://repository.rudn.ru/records/article/record/65399/