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Georgian Mathematical Journal

Editor-in-Chief: Kiguradze, Ivan / Buchukuri, T.

Editorial Board: Kvinikadze, M. / Bantsuri, R. / Baues, Hans-Joachim / Besov, O.V. / Bojarski, B. / Duduchava, R. / Engelbert, Hans-Jürgen / Gamkrelidze, R. / Gubeladze, J. / Hirzebruch, F. / Inassaridze, Hvedri / Jibladze, M. / Kadeishvili, T. / Kegel, Otto H. / Kharazishvili, Alexander / Kharibegashvili, S. / Khmaladze, E. / Kiguradze, Tariel / Kokilashvili, V. / Krushkal, S. I. / Kurzweil, J. / Kwapien, S. / Lerche, Hans Rudolf / Mawhin, Jean / Ricci, P.E. / Tarieladze, V. / Triebel, Hans / Vakhania, N. / Zanolin, Fabio


IMPACT FACTOR 2018: 0.551

CiteScore 2018: 0.52

SCImago Journal Rank (SJR) 2018: 0.320
Source Normalized Impact per Paper (SNIP) 2018: 0.711

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1572-9176
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On generalized α-ψ-Geraghty contractions on b-metric spaces

Hojjat Afshari / Hassen Aydi
  • Department of Mathematics, College of Education in Jubail, Imam Abdulrahman Bin Faisal University, P.O. 12020, Industrial Jubail 31961, Saudi Arabia; and Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
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/ Erdal KarapınarORCID iD: http://orcid.org/0000-0002-6798-3254
Published Online: 2018-01-10 | DOI: https://doi.org/10.1515/gmj-2017-0063

Abstract

In this paper, we consider generalized α-ψ-Geraghty contractive type mappings and investigate the existence and uniqueness of a fixed point for mappings involving such contractions. In particular, we extend, improve and generalize some earlier results in the literature on this topic. An application concerning the existence of an integral equation is also considered to illustrate the novelty of the main result.

Keywords: fixed point

MSC 2010: 74H10; 54H25; 46T99; 47H10

References

  • [1]

    M. U. Ali, T. Kamran and E. Karapınar, (α,ψ,ξ)-contractive multivalued mappings, Fixed Point Theory Appl. 2014 (2014), Paper No. 7. Web of ScienceGoogle Scholar

  • [2]

    H. Aydi, M.-F. Bota, E. Karapınar and S. Mitrović, A fixed point theorem for set-valued quasi-contractions in b-metric spaces, Fixed Point Theory Appl. 2012 (2012), Paper No. 8. Web of ScienceGoogle Scholar

  • [3]

    H. Aydi, M.-F. Bota, E. Karapinar and S. Moradi, A common fixed point for weak ϕ-contractions on b-metric spaces, Fixed Point Theory 13 (2012), no. 2, 337–346. Google Scholar

  • [4]

    H. Aydi, A. Felhi and S. Sahmim, Common fixed points in rectangular b-metric spaces using (E.A) property, J. Adv. Math. Stud. 8 (2015), no. 2, 159–169. Google Scholar

  • [5]

    H. Aydi, M. Jellali and E. Karapınar, Common fixed points for generalized α-implicit contractions in partial metric spaces: consequences and application, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Math. RACSAM 109 (2015), no. 2, 367–384. Google Scholar

  • [6]

    H. Aydi and E. Karapinar, Fixed point results for generalized α-ψ-contractions in metric-like spaces and applications, Electron. J. Differential Equations 2015 (2015), Paper No. 133. Google Scholar

  • [7]

    H. Aydi, E. Karapınar and B. Samet, Fixed points for generalized (α,ψ)-contractions on generalized metric spaces, J. Inequal. Appl. 2014 (2014), Paper No. 229. Web of ScienceGoogle Scholar

  • [8]

    A. Azam, N. Mehmood, J. Ahmad and S. Radenović, Multivalued fixed point theorems in cone b-metric spaces, J. Inequal. Appl. 2013 (2013), Paper No. 582. Web of ScienceGoogle Scholar

  • [9]

    M. Cosentino, M. Jleli, B. Samet and C. Vetro, Solvability of integrodifferential problems via fixed point theory in b-metric spaces, Fixed Point Theory Appl. 2015 (2015), Paper No. 70. Web of ScienceGoogle Scholar

  • [10]

    M. Cosentino, P. Salimi and P. Vetro, Fixed point results on metric-type spaces, Acta Math. Sci. Ser. B Engl. Ed. 34 (2014), no. 4, 1237–1253. Google Scholar

  • [11]

    S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostraviensis 1 (1993), 5–11. Google Scholar

  • [12]

    S. Czerwik, Nonlinear set-valued contraction mappings in b-metric spaces, Atti Semin. Mat. Fis. Univ. Modena 46 (1998), no. 2, 263–276. Google Scholar

  • [13]

    M. Demma and P. Vetro, Picard sequence and fixed point results on b-metric spaces, J. Funct. Spaces 2015 (2015), Article ID 189861. Web of ScienceGoogle Scholar

  • [14]

    H. Huang and S. Xu, Fixed point theorems of contractive mappings in cone b-metric spaces and applications, Fixed Point Theory Appl. 2013 (2013), Paper No. 112. Web of ScienceGoogle Scholar

  • [15]

    N. Hussain and M. H. Shah, KKM mappings in cone b-metric spaces, Comput. Math. Appl. 62 (2011), no. 4, 1677–1684. Web of ScienceCrossrefGoogle Scholar

  • [16]

    M. A. Geraghty, On contractive mappings, Proc. Amer. Math. Soc. 40 (1973), 604–608. CrossrefGoogle Scholar

  • [17]

    M. Jleli, B. Samet, C. Vetro and F. Vetro, Fixed points for multivalued mappings in b-metric spaces, Abstr. Appl. Anal. 2015 (2015), Article ID 718074. Google Scholar

  • [18]

    M. Jovanović, Z. Kadelburg and S. Radenović, Common fixed point results in metric-type spaces, Fixed Point Theory Appl. 2010 (2010), Article ID 978121. Web of ScienceGoogle Scholar

  • [19]

    E. Karapınar, A discussion on “α-ψ-Geraghty contraction type mappings”, Filomat 28 (2014), no. 4, 761–766. Web of ScienceCrossrefGoogle Scholar

  • [20]

    E. Karapınar, α-ψ-Geraghty contraction type mappings and some related fixed point results, Filomat 28 (2014), no. 1, 37–48. Web of ScienceCrossrefGoogle Scholar

  • [21]

    E. Karapınar, P. Kumam and P. Salimi, On α-ψ-Meir-Keeler contractive mappings, Fixed Point Theory Appl. 2013 (2013), Paper No. 94. Web of ScienceGoogle Scholar

  • [22]

    E. Karapınar and B. Samet, Generalized α-ψ contractive type mappings and related fixed point theorems with applications, Abstr. Appl. Anal. 2012 (2012), Article ID 793486. Web of ScienceGoogle Scholar

  • [23]

    J. J. Nieto and R. Rodríguez-López, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order 22 (2005), no. 3, 223–239. CrossrefGoogle Scholar

  • [24]

    D. Paesano and P. Vetro, Fixed point theorems for α-set-valued quasi-contractions in b-metric spaces, J. Nonlinear Convex Anal. 16 (2015), no. 4, 685–696. Google Scholar

  • [25]

    O. Popescu, Some new fixed point theorems for α-Geraghty contraction type maps in metric spaces, Fixed Point Theory Appl. 2014 (2014), Paper No. 190. Web of ScienceGoogle Scholar

  • [26]

    A. C. M. Ran and M. C. B. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc. 132 (2004), no. 5, 1435–1443. CrossrefGoogle Scholar

  • [27]

    J. R. Roshan, V. Parvaneh, S. Sedghi, N. Shobkolaei and W. Shatanawi, Common fixed points of almost generalized (ψ,ϕ)s-contractive mappings in ordered b-metric spaces, Fixed Point Theory Appl. 2013 (2013), Paper No. 159. Google Scholar

  • [28]

    B. Samet, C. Vetro and F. Vetro, Approximate fixed points of set-valued mapping in b-metric space, J. Nonlinear Sci. Appl. 9 (2016), no. 6, 3760–3772. Google Scholar

  • [29]

    B. Samet, C. Vetro and P. Vetro, Fixed point theorems for α-ψ-contractive type mappings, Nonlinear Anal. 75 (2012), no. 4, 2154–2165. CrossrefGoogle Scholar

  • [30]

    R. J. Shahkoohi and A. Razani, Some fixed point theorems for rational Geraghty contractive mappings in ordered b-metric spaces, J. Inequal. Appl. 2014 (2014), Paper No. 373. Web of ScienceGoogle Scholar

  • [31]

    L. Shi and S. Xu, Common fixed point theorems for two weakly compatible self-mappings in cone b-metric spaces, Fixed Point Theory Appl. 2013 (2013), Paper No. 120. Web of ScienceGoogle Scholar

  • [32]

    M. Turinici, Abstract comparison principles and multivariable Gronwall–Bellman inequalities, J. Math. Anal. Appl. 117 (1986), no. 1, 100–127. CrossrefGoogle Scholar

About the article

Received: 2015-10-05

Revised: 2016-10-06

Accepted: 2016-10-26

Published Online: 2018-01-10


Citation Information: Georgian Mathematical Journal, ISSN (Online) 1572-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/gmj-2017-0063.

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