### Global Best Approximate Solutions for Set Valued Contraction in \(b\)-metric Spaces with Applications

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A. Abkar and M. Gabeleh, The existence of best proximity points for multivalued non-self-mappings, Acad. Cienc. Exactas Fs. Nat. Ser. A Math. RACSAM 107 (2013), 319 – 325.

M.U. Ali, T. Kamram and E. Karapinar, Further discussion on modified multivalued (alpha_*)-(psi)-contractive type mapping, Filomat 29 (8) (2015), 1893 – 1900.

M.U. Ali, T. Kamram and N. Shahzad, Best proximity point for (alpha)-(psi)-proximal contractive multimaps, Abstract and Applied Analysis 2014 (2014), 6 pages.

M.U. Ali, T. Kamran and E. Karapinar, A new approach to ((alpha-psi))-contractive nonself multivalued mappings, J. Inequal. Appl. 2014 (2014), Article ID 71.

A. Amini-Harandi, Best proximity points for proximal generalized contractions in metric spaces, Optim. Lett. 7 (2013), 913 – 921.

A. Amini-Harandi, Fixed point theory for quasi-contraction maps in b-metric spaces, Fixed Point Theory 15 (2) (2014), 351 – 358.

P. Amiri, S. Rezapour and N. Shahzad, Fixed points of generalized ((alpha-psi))-contractions, Rev. R. Acad. Cienc. Exactas Fis. Nat., Ser. A Mat. 108 (2) (2014), 519 – 526.

J.H. Asl, S. Rezapour and N. Shahzad, On fixed points of (alpha)-(psi)-contractive multifunctions, Fixed Point Theory Appl. 2012 (2012), Article ID 212.

H. Aydi, M.F. Bota, S. Mitrovic and E. Karapinar, A fixed point theorem for set-valued quasicontractions in b-metric spaces, Fixed Point Theory Appl. 2012 (2012), 88.

I.A. Bakhtin, The contraction mapping principle in quasi-metric spaces, J. Funct. Anal. 30 (1989), 26 – 37.

S.S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux equations intégrales, Fundamenta Mathematicae 3 (1922), 133 – 181.

S.S. Basha, Discrete optimization in partially ordered sets, J. Global Optim. 54 (2012), 511 – 517. [13] M. Boriceanu, Fixed point theory for multivalued generalized contraction on a set with two bmetrics, Stud. Univ. Babes-Bolyai Math. LIV (3) (2009), 1 – 14.

M. Boriceanu, A. Petrusel and A.I. Rus, Fixed point theorems for some multivalued generalized contraction in b-metric spaces, Internat. J. Math. Statistics 6 (1998), 263 – 276.

M.F. Bota, E. Karapnar and O. Mlesnite, Ulam-Hyers stability results for fixed point problems via (alpha)-(psi)-contractive mapping in b-metric space, Abstr. Appl. Anal. 2013 (2013), 6 pages.

B.S. Choudhury and K.P. Das, A new contraction principle in Menger spaces, Acta Math. Sin. 24 (8) (2008), 1379 – 1386.

B.S. Choudhurya, P. Maitya and N. Metiya, Best proximity point results in set-valued analysis, Nonlinear Analysis: Modelling and Control 21 (3) (2016), 293 – 305.

B.S. Choudhurya, P. Maitya and N. Metiya, Best proximity point results in set-valued analysis, Nonlinear Analysis: Modelling and Control 21 (3) (2016), 293 – 305.

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

S. Czerwik, Nonlinear set-valued contraction mappings in b-metric spaces, Atti Semin Math Fis Univ Modena 46 (2) (1998), 263 – 276.

K. Fan, Extensions of two fixed point theorems of F.E. Browder, Math. Z. 122 (1969), 234 – 240.

N. Hussain, A. Latif and P. Salimi, Best proximity point results for modified Suzuki (alpha)-(psi)-proximal contractions, Fixed Point Theory and Applications 2014 (2014), 10.

N. Hussain, M.A. Kutbi and P. Salimi, Best proximity point results for modified (alpha)-(psi)-proximal rational contractions, Abstr. Appl. Anal. 2013 (2013), Article ID 927457.

M. Jleli and B. Semet, Best proximity points for (alpha)-(psi)-proximal contractive type mappings and applications, Bulletin des Sciences Mathématiques 137 (8) (December 2013), 977 – 995.

E. Karapinar and B. Samet, Generalized (alpha)-(psi)-contractive type mappings and related fixed point theorems with applications, Abstr. Appl. Anal. 2012 (2012), Article ID 793486.

A. Latif, M. Abbas and A. Husain, Coincidence best proximity point of Fg-weak contractive mappings in partially ordered metric spaces, Journal of Nonlinear Science and Application 9 (2016), 2448 – 2457.

B. Mohammadi, S. Rezapour and N. Shahzad, Some results on fixed points of (alpha)-(psi)-Ciric generalized multifunctions, Fixed Point Theory Appl. 2013 (2013), Article ID 24.

S.B. Nadler Jr., Multivalued contraction mappings, Pacific J. Math. 30 (1969), 475 – 488. [29] V. Pragadeeswarar and M. Marudai, Best proximity points for generalized proximal weak contractions in partially ordered metric spaces, Optim. Lett. 9 (2015), 105 – 118.

V. Pragadeeswarar, M. Marudai and P. Kumam, Best proximity point theorems for multivalued mappings on partially ordered metric spaces, J. Nonlinear Sci. Appl. 9 (2016), 1911 – 1921.

P. Salimi, A. Latif and N. Hussain, Modified (alpha)-(psi)-contractive mappings with applications, Fixed Point Theory and Applications 2013 (2013), Article ID 151.

B. Samet, The class of (®-Ã)-type contractions in b-metric spaces and fixed point theorems, Fixed Point Theo. and Appl. 2015 (2015), 92.

B. Samet, C. Vetro and P. Vetro, Fixed point theorem for (alpha)-(psi)-contractive type mappings, Nonlinear Anal. 75 (2012), 2154 – 2165.

DOI: http://dx.doi.org/10.26713%2Fcma.v9i3.793

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