Results 31 to 40 of about 4,563,831 (252)
On Approximate Solutions of Functional Equations in Vector Lattices
Abstract and Applied Analysis, 2014 We provide a method of approximation of approximate solutions of functional equations in the class of functions acting into a Riesz space (algebra). The main aim of the paper is to provide a general theorem that can act as a tool applicable to a possibly
Bogdan Batko
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A General Uniqueness Theorem concerning the Stability of Additive and Quadratic Functional Equations
Journal of Function Spaces, 2015 We prove a general uniqueness theorem that can be easily applied to the (generalized) Hyers-Ulam stability of the Cauchy additive functional equation, the quadratic functional equation, and the quadratic-additive type functional equations.
Yang-Hi Lee, Soon-Mo Jung
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Cauchy′s functional equation in restricted complex domains [PDF]
International Journal of Mathematics and Mathematical Sciences, 2006 Using a method modified from that used by Pisot and Schoenberg in 1964‐1965, a Cauchy′s functional equation with restricted domains in the complex field is solved for uniformly continuous solutions.
Watcharapon Pimsert +2 more
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On the stability of a Cauchy type functional equation
Demonstratio Mathematica, 2018 In this work, the Hyers-Ulam type stability and the hyperstability of the functional equationare proved.
Lee Jung Rye +3 more
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Stability of Cauchy\u27s equation on Δ+. [PDF]
, 2023 The most famous functional equation f(x+y)=f(x)+f(y) known as Cauchy\u27s equation due to its appearance in the seminal analysis text Cours d\u27Analyse (Cauchy 1821), was used to understand fundamental aspects of the real numbers and the importance of ...
Wells, Holden
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Advanced Materials Technologies, EarlyView.High‐aspect‐ratio low‐melting‐point alloy inclusions are embedded within multilayer silicone laminates to create thermally programmable stiffness. Sequential activation of alloy‐rich layers produces four distinct mechanical states and reconfigures tendon‐driven actuator trajectories under the same load.
Palpolage Don Shehan Hiroshan Gunawardane +4 more
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The Cauchy-Riemann Differential Equations of Complex Functions [PDF]
Formalized Mathematics, 2009 Summary. In this article we prove Cauchy-Riemann dierential equations of complex functions. These theorems give necessary and sucient condition for dierentiable function.
Hiroshi Yamazaki +3 more
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Sustainable Materials Design With Multi‐Modal Artificial Intelligence
Advanced Science, EarlyView.Critical mineral scarcity, high embodied carbon, and persistent pollution from materials processing intensify the need for sustainable materials design. This review frames the problem as multi‐objective optimization under heterogeneous, high‐dimensional evidence and highlights multi‐modal AI as an enabling pathway.
Tianyi Xu +8 more
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A Fixed Point Approach to the Stability of Quadratic Functional Equation with Involution
Fixed Point Theory and Applications, 2008 Cădariu and Radu applied the fixed point method to the investigation of Cauchy and Jensen functional equations. In this paper, we will adopt the idea of Cădariu and Radu to prove the Hyers-Ulam-Rassias stability of the quadratic functional equation
Zoon-Hee Lee, Soon-Mo Jung
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Discrete Dynamics in Nature and Society, 2011 We investigate the generalized Hyers-Ulam stability of the functional inequalities ∥f((x+y+z)/4)+f((3x−y−4z)/4)+f((4x+3z)/4)∥≤∥2f(x)∥ and ∥f((y−x)/3)+f((x−3z)/3)+f((3x+3z−y)/3)∥≤∥f(x)∥ in non-Archimedean normed spaces in the spirit of the Th. M.
A. Ebadian +3 more
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