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Space of Functions with Growths Tempered by a Modulus of Continuity

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Advances in Nonlinear Analysis via the Concept of Measure of Noncompactness

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Abstract

The principal aim of this chapter is to consider the function space consisting of functions defined on a compact metric space with growths tempered by a given modulus of continuity and its connection with the measures of noncompactness. The chapter is inspired in the papers [1, 2].

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References

  1. Banaś, J., Nalepa, R.: On the space of functions with growths tempered by a modulus of continuity and its applications. J. Function Spaces 820437, 13 (2013)

    Google Scholar 

  2. Banaś, J., Nalepa, R.: On a measure of noncompactness in the space of functions with tempered increments. J. Math. Anal. Appl. 435, 1634–1651 (2016)

    Google Scholar 

  3. Banaś, J., Goebel, K.: Measures of Noncompactness in Banach Spaces. Lect. Notes Pure Appl. Math. Dekker, New York (1980)

    Google Scholar 

  4. Darbo, G.: Punti uniti in transformazioni a condominio non compatto. Rend. Semin. Mat. Univ. Padova. 24, 84–92 (1955)

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  5. Sadovskii, B.N.: On a fixed point principle. Funkt. Anal. 4, 74–76 (1967)

    MathSciNet  MATH  Google Scholar 

  6. Zhao, Y., Sun, S., Han, Z., Li, Q.: Positive solutions to boundary value problems of nonlinear fractional differential equations. Abstr. Appl. Anal. 390543, 16 (2011)

    Google Scholar 

  7. Caballero, J., Harjani, J., Sadarangani, K.: On existence and uniqueness of positive solutions to a class of fractional boundary problems. Bound. Value Probl. 2011(95), 9 (2011)

    Google Scholar 

  8. Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. North-Holland Mathematics Studies. Elsevier Science B.V, Amsterdam (2006)

    Google Scholar 

  9. Yu, Y., Jiang, D.: Multiple positive solutions for the boundary value problem of a nonlinear fractional differential equation. Northeast Normal University (2009)

    Google Scholar 

  10. Aghajani, A., Banaś, J., Sabzali, N.: Some generalizations of Darbo fixed point theorem and applications. Bull. Belg. Math. Soc. 20, 345–358 (2013)

    Google Scholar 

  11. Aghajani, A., Allahyari, R., Mursaleen, M.: A generalization of Darbo’s theorem with application to the solvability of systems of integral equations. J. Comp. Appl. Math. 260, 68–77 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  12. Dhage, B.C., Dhage, S.B., Pathak, H.K.: A generalization of Darbo’s fixed point theorem and local attractivity of generalized nonlinear functional integral equations. Differ. Equ. Appl. 1, 57–77 (2015)

    MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad de Las Palmas de Gran Canaria, Campus de Tafira Baja, 35017, Las Palmas de Gran Canaria, Spain

    I. J. Cabrera, J. Harjani, B. López & K. B. Sadarangani

Authors
  1. I. J. Cabrera
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  2. J. Harjani
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  3. B. López
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  4. K. B. Sadarangani
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Corresponding author

Correspondence to I. J. Cabrera .

Editor information

Editors and Affiliations

  1. Department of Nonlinear Analysis, Rzeszów University of Technology, Rzeszów, Poland

    Józef Banaś

  2. Department of Mathematics, King Saud University, Riyadh, Saudi Arabia

    Mohamed Jleli

  3. Department of Mathematics, Aligarh Muslim University, Aligarh, Uttar Pradesh, India

    Mohammad Mursaleen

  4. Department of Mathematics, King Saud University, Riyadh, Saudi Arabia

    Bessem Samet

  5. Dipartimento di Matematica e Informatica, University of Palermo, Palermo, Italy

    Calogero Vetro

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Cabrera, I.J., Harjani, J., López, B., Sadarangani, K.B. (2017). Space of Functions with Growths Tempered by a Modulus of Continuity. In: Banaś, J., Jleli, M., Mursaleen, M., Samet, B., Vetro, C. (eds) Advances in Nonlinear Analysis via the Concept of Measure of Noncompactness. Springer, Singapore. https://doi.org/10.1007/978-981-10-3722-1_4

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