Integral of an extension of the sine addition formula

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dc.citation.epage840
dc.citation.issue3
dc.citation.journalTitleМатематичне моделювання та комп'ютинг
dc.citation.spage833
dc.contributor.affiliationУніверситет Мулая Ісмаїла Мекнеса
dc.contributor.affiliationMoulay Ismail University of Meknes
dc.contributor.authorТіал, М.
dc.contributor.authorTial, M.
dc.coverage.placenameЛьвів
dc.coverage.placenameLviv
dc.date.accessioned2025-03-04T12:17:28Z
dc.date.created2023-02-28
dc.date.issued2023-02-28
dc.description.abstractУ цій роботі визначено неперервні розв’язки інтегрального функціонального рівняння розширення Стеткара закону додавання синусів. R G f(xyt)dµ(t) = f(x)χ1(y) +χ2(x)f(y), x, y ∈ G, де f : G → C, G — локально компактна Хаусдорфова група, µ— регулярна комплекснозначна борелівська міра на G з компактним носієм та χ1, χ2 — фіксовані характери на G.
dc.description.abstractIn this paper, we determine the continuous solutions of the integral functional equation of Stetkær's extension of the sine addition law ∫Gf(xyt)dμ(t) = f(x)χ1(y)+χ2(x)f(y), x, y∈G, where f : G→ C, G is a locally compact Hausdorff group, μ is a regular, compactly supported, complex-valued Borel measure on G and χ1, χ2 are fixed characters on G.
dc.format.extent833-840
dc.format.pages8
dc.identifier.citationTial M. Integral of an extension of the sine addition formula / M. Tial // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2023. — Vol 10. — No 3. — P. 833–840.
dc.identifier.citationenTial M. Integral of an extension of the sine addition formula / M. Tial // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2023. — Vol 10. — No 3. — P. 833–840.
dc.identifier.doidoi.org/10.23939/mmc2023.03.833
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/63520
dc.language.isoen
dc.publisherВидавництво Львівської політехніки
dc.publisherLviv Politechnic Publishing House
dc.relation.ispartofМатематичне моделювання та комп'ютинг, 3 (10), 2023
dc.relation.ispartofMathematical Modeling and Computing, 3 (10), 2023
dc.relation.references[1] Stetkær H. Functional equations on groups. World Scientific Publishing Company, Singapore (2013).
dc.relation.references[2] Acz´el J. Lectures on Functional Equations and Their Applications. Mathematics in Science and Engineering, vol. 19. Academic Press, New York (1966).
dc.relation.references[3] Kannappan P. Functional Equations and Inequalities with Applications. Springer, New York (2009).
dc.relation.references[4] Sz´ekelyhidi L. Convolution Type Functional Equations on Topological Abelian Groups. Series on Soviet and East European Mathematics. World Scientific Publishing Company (1991).
dc.relation.references[5] Chung J. K., Kannappan Pl., Ng C. T. A generalization of the cosine-sine functional equation on groups. Linear Algebra and its Applications. 66, 259–277 (1985).
dc.relation.references[6] Poulsen Th. A., Stetkær H. On the trigonometric subtraction and addition formulas. Aequationes Mathematicae. 59, 84–92 (2000).
dc.relation.references[7] Kabbaj S., Tial M., Zeglami D. The integral cosine addition and sine subtraction laws. Results in Mathematics. 73, 97 (2018).
dc.relation.references[8] Zeglami D., Tial M., Kabbaj S. The integral sine addition law. Proyecciones. 38 (2), 203–219 (2019).
dc.relation.references[9] Stetkær H. Extensions of the sine addition law on groups. Aequationes Mathematicae. 93, 467–484 (2019).
dc.relation.references[10] Ebanks B. Around the Sine Addition Law and d’Alembert’s Equation on Semigroups. Results in Mathematics. 77, 11 (2022).
dc.relation.references[11] Stetkær H. The cosine addition law with an additional term. Aequationes Mathematicae. 90, 1147–1168 (2016).
dc.relation.references[12] Stetkær H. Trigonometric Functional equations of rectangular type. Aequationes Mathematicae. 56, 251–270 (1998).
dc.relation.referencesen[1] Stetkær H. Functional equations on groups. World Scientific Publishing Company, Singapore (2013).
dc.relation.referencesen[2] Acz´el J. Lectures on Functional Equations and Their Applications. Mathematics in Science and Engineering, vol. 19. Academic Press, New York (1966).
dc.relation.referencesen[3] Kannappan P. Functional Equations and Inequalities with Applications. Springer, New York (2009).
dc.relation.referencesen[4] Sz´ekelyhidi L. Convolution Type Functional Equations on Topological Abelian Groups. Series on Soviet and East European Mathematics. World Scientific Publishing Company (1991).
dc.relation.referencesen[5] Chung J. K., Kannappan Pl., Ng C. T. A generalization of the cosine-sine functional equation on groups. Linear Algebra and its Applications. 66, 259–277 (1985).
dc.relation.referencesen[6] Poulsen Th. A., Stetkær H. On the trigonometric subtraction and addition formulas. Aequationes Mathematicae. 59, 84–92 (2000).
dc.relation.referencesen[7] Kabbaj S., Tial M., Zeglami D. The integral cosine addition and sine subtraction laws. Results in Mathematics. 73, 97 (2018).
dc.relation.referencesen[8] Zeglami D., Tial M., Kabbaj S. The integral sine addition law. Proyecciones. 38 (2), 203–219 (2019).
dc.relation.referencesen[9] Stetkær H. Extensions of the sine addition law on groups. Aequationes Mathematicae. 93, 467–484 (2019).
dc.relation.referencesen[10] Ebanks B. Around the Sine Addition Law and d’Alembert’s Equation on Semigroups. Results in Mathematics. 77, 11 (2022).
dc.relation.referencesen[11] Stetkær H. The cosine addition law with an additional term. Aequationes Mathematicae. 90, 1147–1168 (2016).
dc.relation.referencesen[12] Stetkær H. Trigonometric Functional equations of rectangular type. Aequationes Mathematicae. 56, 251–270 (1998).
dc.rights.holder© Національний університет “Львівська політехніка”, 2023
dc.subjectфункціональне рівняння
dc.subjectзакон додавання синусів
dc.subjectхарактер
dc.subjectадитивна функція
dc.subjectміра Бореля
dc.subjectfunctional equation
dc.subjectsine addition law
dc.subjectcharacter
dc.subjectadditive function
dc.subjectBorel measure
dc.titleIntegral of an extension of the sine addition formula
dc.title.alternativeІнтеграл від розширення формули додавання синуса
dc.typeArticle

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Mathematical Modeling And Computing. – 2023. – Vol. 10, No. 3