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Year 2020, Volume: 10 Issue: 1, 220 - 231, 01.01.2020

Abstract

References

  • Ahmad, B., Nieto, J.J., (2013), Boundary value problems for a class of sequential integrodifferential equations of fractional order, J. Funct. Spaces Appl., Article ID, pp. 149-659.
  • Ansari, A.H., Kumam, P., Samet, B., (2017), A fixed point problem with constraint inequalities via an implicit contraction, J. Fixed Point Theory and Appl., pp. 1145-1163.
  • Ahmadi, Z., Lashkaripour, R., Baghani, H., A fixed point problem with constraint inequalities via a contraction in incomplete metric spaces, Filomat, to appear.
  • Babu, G.V.R., Sarma, K.K.M., Krishna, P.H., (2014), Fixed points of ψ-weak Geraghty contractions in partially ordered metric spaces, J. Adv. Res. Pure Math., 6, pp. 9-23.
  • Baghani, H., Eshaghi Gordji, M., Ramezani, M., (2016), Orthogonal sets: The axiom of choice and proof of a fixed point theorem, J. Fixed Point Theory and Appl., 18, pp. 465-477.
  • Baghani, H., Ramezani, M, (2017), A fixed point theorem for a new class of set-valued mappings in R-complete(not necessarily complete) metric spaces, Filomat, 31, pp. 3875-3884.
  • Baghani, H., Ramezani, M., (2017), Contractive gauge functions in strongly orthogonal metric spaces, Int. J. Nonlinear Anal., 2, 23-28.
  • Eshaghi Gordji, M., Ramezani, M., De La Sen, M., Cho, Y.J., (2017), On orthogonal sets and Banach fixed Point theorem, Fixed Point Theory, 18, 569-578.
  • Hussain, N., Kadelburg, Z., Radenovic, S., Al-Solamy, F.R., (2012), Comparison functions and fixed point results in partial metric spaces, Abstract and Applied Analysis Article ID., 15, 605-781.
  • Jleli, M., Samet, B., (2016), A fixed point problem under two constraint inequalities, Fixed Point Theory and Appl., doi:10.1186/s13663-016-0504-9.
  • Kawasaki, T., Toyoda, M., (2015), Fixed point theorem and fractional differential equations with multiple delays related with chaos neuron models, Appl. Math., 6, 2192-2198.
  • Khojasteh, F., Shukla, S., Radenovi, S., (2015), A new approach to the study of fixed point theorems via simulation functions, Filomat, 29, 1189-1194.
  • Ntouyas, S.K., Tariboon, J., (2017), Fractional boundary value problems with multiple orders of fractional with multiple orders of fractional derivatives and integrals, Electronic Journal of Diferential Equations, 100, 1-18.
  • Roldan-Lopez-de-Hierro, AF., Karapinar, E, Roldan-Lopez-de-Hierro, C., Martinez-Moreno, J., (2015), Coincidence point theorems on metric spaces via simulation functions, J. Comput. Appl. Math., 275, 345-355.
  • Wang, W.X., Zhang, L., Liang, Zh., (2006),Initial value problems for nonlinear impulsive integro- differential equations in Banach space, J. Math. Anal. Appl., 320, 510-527.
  • Yang, Sh., Zhang, Sh., (2016), Impulsive boundary value problem for a fractional differential equation, Boundary Value Problems, doi:10.1186/s13661-016-0711-7.

A FIXED POINT PROBLEM VIA SIMULATION FUNCTIONS IN INCOMPLETE METRIC SPACES WITH ITS APPLICATION

Year 2020, Volume: 10 Issue: 1, 220 - 231, 01.01.2020

Abstract

In this paper, rstly, we review the notion of the SO-complete metric spaces. This notion let us to consider some xed point theorems for single-valued mappings in incomplete metric spaces. Secondly, as motivated by the recent work of A.H. Ansari et al. [J. Fixed Point Theory Appl. 2017 , 1145{1163], we obtain that an existence and uniqueness result for the following problem: nding x 2 X such that x = Tx, Ax R1 Bx and Cx R2 Dx, where X; d is an incomplete metric space equipped with the two binary relations R1 and R2, A;B;C;D : X ! X are discontinuous mappings and T : X ! X satis es in a new contractive condition. This result is a real generalization of main theorem of A.H. Ansari's. Finally, we provide some examples for our results and as an application, we nd that the solutions of a di erential equation.

References

  • Ahmad, B., Nieto, J.J., (2013), Boundary value problems for a class of sequential integrodifferential equations of fractional order, J. Funct. Spaces Appl., Article ID, pp. 149-659.
  • Ansari, A.H., Kumam, P., Samet, B., (2017), A fixed point problem with constraint inequalities via an implicit contraction, J. Fixed Point Theory and Appl., pp. 1145-1163.
  • Ahmadi, Z., Lashkaripour, R., Baghani, H., A fixed point problem with constraint inequalities via a contraction in incomplete metric spaces, Filomat, to appear.
  • Babu, G.V.R., Sarma, K.K.M., Krishna, P.H., (2014), Fixed points of ψ-weak Geraghty contractions in partially ordered metric spaces, J. Adv. Res. Pure Math., 6, pp. 9-23.
  • Baghani, H., Eshaghi Gordji, M., Ramezani, M., (2016), Orthogonal sets: The axiom of choice and proof of a fixed point theorem, J. Fixed Point Theory and Appl., 18, pp. 465-477.
  • Baghani, H., Ramezani, M, (2017), A fixed point theorem for a new class of set-valued mappings in R-complete(not necessarily complete) metric spaces, Filomat, 31, pp. 3875-3884.
  • Baghani, H., Ramezani, M., (2017), Contractive gauge functions in strongly orthogonal metric spaces, Int. J. Nonlinear Anal., 2, 23-28.
  • Eshaghi Gordji, M., Ramezani, M., De La Sen, M., Cho, Y.J., (2017), On orthogonal sets and Banach fixed Point theorem, Fixed Point Theory, 18, 569-578.
  • Hussain, N., Kadelburg, Z., Radenovic, S., Al-Solamy, F.R., (2012), Comparison functions and fixed point results in partial metric spaces, Abstract and Applied Analysis Article ID., 15, 605-781.
  • Jleli, M., Samet, B., (2016), A fixed point problem under two constraint inequalities, Fixed Point Theory and Appl., doi:10.1186/s13663-016-0504-9.
  • Kawasaki, T., Toyoda, M., (2015), Fixed point theorem and fractional differential equations with multiple delays related with chaos neuron models, Appl. Math., 6, 2192-2198.
  • Khojasteh, F., Shukla, S., Radenovi, S., (2015), A new approach to the study of fixed point theorems via simulation functions, Filomat, 29, 1189-1194.
  • Ntouyas, S.K., Tariboon, J., (2017), Fractional boundary value problems with multiple orders of fractional with multiple orders of fractional derivatives and integrals, Electronic Journal of Diferential Equations, 100, 1-18.
  • Roldan-Lopez-de-Hierro, AF., Karapinar, E, Roldan-Lopez-de-Hierro, C., Martinez-Moreno, J., (2015), Coincidence point theorems on metric spaces via simulation functions, J. Comput. Appl. Math., 275, 345-355.
  • Wang, W.X., Zhang, L., Liang, Zh., (2006),Initial value problems for nonlinear impulsive integro- differential equations in Banach space, J. Math. Anal. Appl., 320, 510-527.
  • Yang, Sh., Zhang, Sh., (2016), Impulsive boundary value problem for a fractional differential equation, Boundary Value Problems, doi:10.1186/s13661-016-0711-7.
There are 16 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

R. Lashkaripour This is me

H. Baghani This is me

Z. Ahmadi This is me

Publication Date January 1, 2020
Published in Issue Year 2020 Volume: 10 Issue: 1

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