Ulam-Hyers stability and well-posedness of fixed point problems for α-λ-contractions on quasi b-metric spaces

Kutbi, MA, Sintunavarat, W: Ulam-Hyers stability and well-posedness of fixed point problems for α-λ-contraction mapping in metric spaces. Abstr. Appl. Anal. 2014, Article ID 268230 (2014) Czerwik, S: Contraction mappings in b-metric spaces. Acta Math. Inform. Univ. Ostrav. 1, 5-11 (1993) Aydi, H, Bota, MF, Karapınar, E, Moradi, S: A common fixed point for weak ϕ-contractions on b-metric spaces. Fixed Point Theory 13(2), 337-346 (2012) Aydi, H, Karapınar, E, Bota, MF, Mitrović, S: A fixed point theorem for set-valued quasi-contractions in b-metric spaces. Fixed Point Theory Appl. 2012, Article ID 88 (2012) Aydi, H, Felhi, A, Sahmim, S: Common fixed points in rectangular b-metric spaces using \((E.A)\) property. J. Adv. Math. Stud. 8(2), 159-169 (2015) Czerwik, S: Nonlinear set-valued contraction mappings in b-metric spaces. Atti Semin. Mat. Fis. Univ. Modena 46(2), 263-276 (1998) Singh, SL, Czerwik, S, Krol, K, Singh, A: Coincidences and fixed points of hybrid contractions. Tamsui Oxf. J. Math. Sci. 24(4), 401-416 (2008) Al-Homidana, S, Ansari, QH, Yao, JC: Some generalizations of Ekeland-type variational principle with applications to equilibrium problems and fixed point theory. Nonlinear Anal. 69, 126-139 (2008) Aydi, H, Bilgili, N, Karapınar, E: Common fixed point results from quasi-metric spaces to G-metric spaces. J. Egypt. Math. Soc. 23, 356-361 (2015) Bilgili, N, Karapınar, E, Samet, B: Generalized α-ψ contractive mappings in quasi metric spaces and related fixed point theorems. J. Inequal. Appl. 2014, Article ID 36 (2014) Jleli, M, Samet, B: Remarks on G-metric spaces and fixed point theorems. Fixed Point Theory Appl. 2012, Article ID 210 (2012) Hussain Shah, M, Hussain, N: Nonlinear contractions in partially ordered quasi b-metric spaces. Commun. Korean Math. Soc. 27(1), 117-128 (2012) Samet, B, Vetro, C, Vetro, P: Fixed point theorems for α-ψ-contractive type mappings. Nonlinear Anal. 75, 2154-2165 (2012) Aydi, H, Jellali, M, Karapınar, E: Common fixed points for generalized α-implicit contractions in partial metric spaces: consequences and application. Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat. 109(2), 367-384 (2015) Aydi, H, Karapınar, E: Fixed point results for generalized α-ψ-contractions in metric-like spaces and applications. Electron. J. Differ. Equ. 2015, 133 (2015) Jleli, M, Karapınar, E, Samet, B: Best proximity points for generalized α-ψ-proximal contractive type mappings. J. Appl. Math. 2013, Article ID 534127 (2013) Jleli, M, Karapınar, E, Samet, B: Fixed point results for α-\(\psi_{\lambda}\) contractions on gauge spaces and applications. Abstr. Appl. Anal. 2013, Article ID 730825 (2013) Karapınar, E, Samet, B: Generalized α-ψ-contractive type mappings and related fixed point theorems with applications. Abstr. Appl. Anal. 2012, Article ID 793486 (2012) Ulam, SM: Problems in Modern Mathematics. Wiley, New York (1964) Hyers, DH: On the stability of the linear functional equation. Proc. Natl. Acad. Sci. USA 27(4), 222-224 (1941) Brzdek, J, Cieplinski, K: A fixed point theorem and the Hyers-Ulam stability in non-Archimedean spaces. J. Math. Anal. Appl. 400(1), 68-75 (2013) Cadariu, L, Gavruta, L, Gavruta, P: Fixed points and generalized Hyers-Ulam stability. Abstr. Appl. Anal. 2012, Article ID 712743 (2012) Lazar, VL: Ulam-Hyers stability for partial differential inclusions. Electron. J. Qual. Theory Differ. Equ. 2012, 21 (2012) Jachymski, J: The contraction principle for mappings on a metric space with a graph. Proc. Am. Math. Soc. 136(4), 1359-1373 (2008) Karapınar, E: Fixed point theory for cyclic weak ϕ-contraction. Appl. Math. Lett. 24, 822-825 (2011) Păcurar, M, Rus, IA: Fixed point theory for cyclic φ-contractions. Nonlinear Anal. 72, 1181-1187 (2010) Reich, S, Zaslawski, AJ: Well-posedness of fixed point problems. Far East J. Math. Sci. Special Volume, Part III, 393-401 (2001)