A General Fixed Point Method for the Stability of Cauchy Functional Equation

Cădariu, Liviu; Radu, Viorel

doi:10.1007/978-1-4614-0055-4_3

Cited by 22 publications

(27 citation statements)

References 17 publications

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“…In 2003, V. Radu [34] proposed a new method, successively developed in [7,8,9], to obtain the existence of the exact solutions and the error estimations, based on the fixed point alternative. Subsequently, these results were generalized by D. Miheţ [30], L. Gȃvruţa [22] and L. Cȃdariu and V. Radu [11].…”

Section: Introductionmentioning

confidence: 82%

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Weighted space method for the stability of some nonlinear equations

Cădariu

Gǎvruţa

Găvruţa

2012

Appl Anal Discrete Math

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Dedicated to Professor Th. M. Rassias, on the occasion of his 60th birthdayWe prove the stability of some equations of a single variable, including a nonlinear functional equation, a linear functional equation as well as a Volterra integral equation, by using the weighted space method. Our results generalize and extend some recent theorems given in this field, with simplified proofs. Several direct applications of these results are also obtained.

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Section: Introductionmentioning

confidence: 82%

“…The above equation is called linear functional equation and was intensively investigated by Kuczma, Choczewski and Ger [29]. They obtained some results concerning monotonic, regular and convex solutions of (11).…”

Section: The Generalized Hyers-ulam Stability Of a Linear Functional mentioning

confidence: 97%

Weighted space method for the stability of some nonlinear equations

Cădariu

Gǎvruţa

Găvruţa

2012

Appl Anal Discrete Math

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“…Theorem 1.5 ( [6,18]). Let (X, d) be a complete generalized metric space and let J : X → X be a strictly contractive mapping with Lipschitz constant α < 1.…”

Section: Jung Rye Lee and Dong-yun Shinmentioning

confidence: 99%

Fuzzy Stability of an Aqcq-Functional Equation in Matrix Fuzzy Normed Spaces

Lee¹,

Shin²

2016

The Pure and Applied Mathematics

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“…Theorem 1.1 ( [2,5]). Let (X, d) be a complete generalized metric space and let J : X → X be a strictly contractive mapping with Lipschitz constant α < 1.…”

Section: Yong Hoon Choi and Sungsik Yunmentioning

confidence: 99%