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a trigonometric functional equation with an automorphism
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نویسنده
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aserrar youssef ,elqorachi elhoucien ,rassias themistocles m.
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منبع
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international journal of nonlinear analysis and applications - 2024 - دوره : 15 - شماره : 11 - صفحه:403 -415
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چکیده
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Let s be a semigroup. in the present paper, we determine the complex-valued solutions (f, g) of the functional equation g(xσ(y)) = g(x)g(y) − f(x)f(y) + αf(xσ(y)), x, y ∈ s, where σ : s → s is an automorphism that need not be involutive, and α ∈ c is a fixed constant. our results generalize and extend the ones by stetkær in the cosine addition law with an additional term. aequat math., no. 6, 90, 1147-1168 (2016), and also the ones by aserrar and elqorachi in a generalization of the cosine addition law on semigroups. aequat math. 97, 787–804 (2023). some consequences of our results are presented.
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کلیدواژه
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functional equation ,semigroup ,addition law ,automorphism
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آدرس
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ibn zohr university, faculty of sciences, department of mathematics, morocco, ibn zohr university, faculty of sciences, department of mathematics, morocco, national technical university of athens, department of mathematics, greece
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پست الکترونیکی
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trassias@math.ntua.gr
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Authors
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