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- W2041831710 abstract "Let<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M1><mml:mrow><mml:mi>S</mml:mi></mml:mrow></mml:math>be a commutative semigroup if not otherwise specified and<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M2><mml:mi>f</mml:mi><mml:mo>:</mml:mo><mml:mi>S</mml:mi><mml:mo>→</mml:mo><mml:mi>ℝ</mml:mi></mml:math>. In this paper we consider the stability of exponential functional equations<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M3><mml:mo stretchy=false>|</mml:mo><mml:mi>f</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mi>x</mml:mi><mml:mo>+</mml:mo><mml:mi>σ</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mi>y</mml:mi><mml:mo stretchy=false>)</mml:mo><mml:mo stretchy=false>)</mml:mo><mml:mo>-</mml:mo><mml:mi>g</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mi>x</mml:mi><mml:mo stretchy=false>)</mml:mo><mml:mi>f</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mi>y</mml:mi><mml:mo stretchy=false>)</mml:mo><mml:mo stretchy=false>|</mml:mo><mml:mo>≤</mml:mo><mml:mi>ϕ</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mi>x</mml:mi><mml:mo stretchy=false>)</mml:mo></mml:math>or<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M4><mml:mi mathvariant=normal> </mml:mi><mml:mi>ϕ</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mi>y</mml:mi><mml:mo stretchy=false>)</mml:mo></mml:math>,<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M5><mml:mo stretchy=false>|</mml:mo><mml:mi>f</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mi>x</mml:mi><mml:mo>+</mml:mo><mml:mi>σ</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mi>y</mml:mi><mml:mo stretchy=false>)</mml:mo><mml:mo stretchy=false>)</mml:mo><mml:mo>-</mml:mo><mml:mi>f</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mi>x</mml:mi><mml:mo stretchy=false>)</mml:mo><mml:mi>g</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mi>y</mml:mi><mml:mo stretchy=false>)</mml:mo><mml:mo stretchy=false>|</mml:mo><mml:mo>≤</mml:mo><mml:mi>ϕ</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mi>x</mml:mi><mml:mo stretchy=false>)</mml:mo></mml:math>or<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M6><mml:mi>ϕ</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mi>y</mml:mi><mml:mo stretchy=false>)</mml:mo></mml:math>for all<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M7><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:mi>y</mml:mi><mml:mo>∈</mml:mo><mml:mi>S</mml:mi></mml:math>and where<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M8><mml:mi>σ</mml:mi><mml:mo>:</mml:mo><mml:mi>S</mml:mi><mml:mo>→</mml:mo><mml:mi>S</mml:mi></mml:math>is an involution. As main results we investigate bounded and unbounded functions satisfying the above inequalities. As consequences of our results we obtain the Ulam-Hyers stability of functional equations (Chung and Chang (in press); Chávez and Sahoo (2011); Houston and Sahoo (2008); Jung and Bae (2003)) and a generalized result of Albert and Baker (1982)." @default.
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- W2041831710 date "2014-01-01" @default.
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- W2041831710 title "Stability of Exponential Functional Equations with Involutions" @default.
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- W2041831710 doi "https://doi.org/10.1155/2014/619710" @default.
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