### Some Fixed Point Theorems for Generalized \(\alpha\)-\(\eta\)-\(\psi\)-Geraghty Contractive Type Mappings in Partial \(b\)-Metric Spaces

#### Abstract

#### Keywords

#### Full Text:

PDF#### References

A. Amini-Harandi and H. Emami, A fixed point theorem for contraction type maps in partially ordered metric spaces and application to ordinary differential equations, Nonlinear Anal. 72(2010), 2238 – 2242.

I.A. Bakhtin, The contraction principle in quasimetric spaces, Funct. Anal. 30 (1989), 26 – 37.

S. Banach, Sur les operations dans les ensembles abstraits et leur applications aux equations integrales, Fundam. Math. 3 (1922), 133 – 181.

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

S.H. Cho, J.S. Bae and E. Karapınar, Fixed point theorems for (alpha)-Geraghty contraction type maps in metric spaces, J. Inequal. Appl. 2013, 329.

P. Chuadchawna, A. Kaewcharoen and S. Plubtieng, Fixed point theorems for generalized (alpha)-(eta)-(psi)-Geraghty contraction type mappings in (alpha)-(eta)-complete metric spaces, J. Nonlinear Sci. Appl. 9 (2016), 471 – 485.

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

E. Karapinar and B. Samet, Generalized (alpha)-(psi)-contractive type mappings and related fixed point theorems with applications, Abstr. Appl. Anal. 2012 (2012), 17 pages.

E. Karapinar, P. Kumam and P. Salimi, On (alpha)-(psi)-Meir-Keeler contractive mappings, J. Inequal. Appl. 94 (2013).

E. Karapinar, (alpha)-(psi)-Geraghty contraction type mappings and some related fixed point results, Filomat 28(1) (2014), 37 – 48.

M.S. Khan, M. Swaeh and S. Sessa, Fixed point theorems by altering distances between the points, Bull. Aust. Math. Soc. 30 (1984), 1 – 9.

P. Kumam, N.V. Dung and V.T.L. Hang, Some equivalences between cone b-metric spaces and b-metric spaces, Abstr. Appl. Anal. 2013 (2013), 8 pages.

S.G. Matthews, Partial metric topology, Proc. 8th Summer Conference on General Topology and Applications, Ann. N.Y. Acad. Sci. 728 (1994), 183 – 197.

A. Mukheimer, (alpha)-(psi)-(varphi)-contractive mappings in ordered partial b-metric spaces, J. Nonlinear Sci. Appl. 7 (2014), 168 – 179.

Z. Mustafa, J. Rezaei Roshan, V. Parvaneh and Z. Kadelburg, Some common fixed point results in ordered partial b-metric spaces, J. Inequal. Appl. 2013 (2013), 526.

O. Popescu, Some new fixed point theorems for (alpha)-Geraghty contraction type maps in metric spaces, J. Inequal. Appl. 2014 (2014), 190.

V.L. Rosa and P. Vetro, Fixed points for Geraghty-contractions in partial metric spaces, J. Nonlinear Sci. Appl. 7 (2014), 1 – 10.

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

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

K.P.R. Sastry, K.K.M. Sarma, Ch. Srinivasa Rao and V. Perraju, Fixed point theorems for Geraghty contractions in partially ordered partial b-metric spaces, Func. Anal. - TMA 1 (2015), 8 – 19.

S. Shukla, Partial b-metric spaces and fixed point theorems, Mediterr. J. Math. 11 (2014), 703 – 711.

DOI: http://dx.doi.org/10.26713%2Fjims.v10i3.583

eISSN 0975-5748; pISSN 0974-875X