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A Local Fractional Integral Inequality on Fractal Space Analogous to Anderson’s Inequality

Author

Listed:
  • Wei Wei
  • H. M. Srivastava
  • Yunyi Zhang
  • Lei Wang
  • Peiyi Shen
  • Jing Zhang

Abstract

Anderson′s inequality (Anderson, 1958) as well as its improved version given by Fink (2003) is known to provide interesting examples of integral inequalities. In this paper, we establish local fractional integral analogue of Anderson′s inequality on fractal space under some suitable conditions. Moreover, we also show that the local fractional integral inequality on fractal space, which we have proved in this paper, is a new generalization of the classical Anderson′s inequality.

Suggested Citation

  • Wei Wei & H. M. Srivastava & Yunyi Zhang & Lei Wang & Peiyi Shen & Jing Zhang, 2014. "A Local Fractional Integral Inequality on Fractal Space Analogous to Anderson’s Inequality," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:797561
    DOI: 10.1155/2014/797561
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    References listed on IDEAS

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    1. Ji-Huan He, 2012. "Asymptotic Methods for Solitary Solutions and Compactons," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    2. Yong-Ju Yang & Dumitru Baleanu & Xiao-Jun Yang, 2013. "A Local Fractional Variational Iteration Method for Laplace Equation within Local Fractional Operators," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    3. Dumitru Baleanu & J. A. Tenreiro Machado & Carlo Cattani & Mihaela Cristina Baleanu & Xiao-Jun Yang, 2014. "Local Fractional Variational Iteration and Decomposition Methods for Wave Equation on Cantor Sets within Local Fractional Operators," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-6, January.
    4. Xiao-Jun Yang & Dumitru Baleanu & H. M. Srivastava & J. A. Tenreiro Machado, 2013. "On Local Fractional Continuous Wavelet Transform," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-5, November.
    5. Xiao-Jun Yang & Dumitru Baleanu & H. M. Srivastava & J. A. Tenreiro Machado, 2013. "On Local Fractional Continuous Wavelet Transform," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    6. Jie Fan & Jihuan He, 2012. "Fractal Derivative Model for Air Permeability in Hierarchic Porous Media," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-7, November.
    7. Yong-Ju Yang & Dumitru Baleanu & Xiao-Jun Yang, 2013. "A Local Fractional Variational Iteration Method for Laplace Equation within Local Fractional Operators," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-6, April.
    8. Jie Fan & Jihuan He, 2012. "Fractal Derivative Model for Air Permeability in Hierarchic Porous Media," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    9. Dumitru Baleanu & J. A. Tenreiro Machado & Carlo Cattani & Mihaela Cristina Baleanu & Xiao-Jun Yang, 2014. "Local Fractional Variational Iteration and Decomposition Methods for Wave Equation on Cantor Sets within Local Fractional Operators," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    10. Ji-Huan He, 2012. "Asymptotic Methods for Solitary Solutions and Compactons," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-130, November.
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    Cited by:

    1. Xiao-Jun Yang & Jordan Hristov & H. M. Srivastava & Bashir Ahmad, 2014. "Modelling Fractal Waves on Shallow Water Surfaces via Local Fractional Korteweg‐de Vries Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    2. Guang-Sheng Chen & H. M. Srivastava & Pin Wang & Wei Wei, 2014. "Some Further Generalizations of Hölder′s Inequality and Related Results on Fractal Space," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    3. Huixia Mo & Xin Sui, 2014. "Generalized s‐Convex Functions on Fractal Sets," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

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