### FIXED POINTS OF ALMOST CONTRACTIVE TYPE MAPPINGS IN PARTIALLY ORDERED B-METRIC SPACES AND APPLICATIONS TO QUADRATIC INTEGRAL EQUATIONS

**DOI Number**

**First page**

**Last page**

#### Abstract

#### Keywords

#### Keywords

#### Full Text:

PDF#### References

A. Aghajani, M. Abbas and J. R. Roshan: Common fixed point of generalized weak contractive mappings in partially ordered b-metric spaces. Math. Slovaca 64 (2014), no. 4, 941–960.

T. Alber and S. Guerre-Delabriere: Principles of weakly contractive maps in Hilbert spaces. Oper. Theory, Adv. Appl. 98 (1997), 7–22.

I. Altan, B. Damjanovi´c and D. Dori´c: Fixed point and common fixed point theorems on ordered cone metric spaces. Appl. Math. Lett. 23 (2010), 310–316.

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.

H. Aydi, M. Bota, E. Karapinar and S. Mitrovi´c: A fixed point theorem for set-valued quasi-contractions in b-metric spaces. Fixed Point Theory Appl. 2012:88 (2012) 1–8.

I. A. Bakhtin: The contraction principle in quasimetric spaces. Func. An., U´ lyanowsk, Gos. Fed. Ins. 30 (1989), 26–37 (in Russian).

S. Banach: Sur les op´erations dans les ensembles abstraits et leur application aux equations itegrales. Fund. Math. 3 (1922), 133–181.

I. Beg: Fixed point theorems in 2-metric spaces with an application to variational inequalities. Math. Sci. Res. Hot-Line 2 (1998), 1–7.

K. C. Border: Fixed Point Theorems with Applications to Economics and Game Theory. Cambridge University Press, Cambridge, 1990.

M. Boriceanu: Strict fixed point theorems for multivalued operators in b-metric spaces. Int. J. Mod. Math. 4 (2009), no. 3, 285–301.

M. Boriceanu, M. Bota and A. Petrusel: Multivalued fractals in b-metric spaces. Cent. Eur. J. Math. 8 (2010), no. 2, 367–377.

M. Bota, A. Molnar and C. Varga: On Ekeland’s variational principle in b-metric spaces. Fixed Point Theory 12 (2011), no. 2, 21–28.

L. ´Ciri´c, M. Abbas, R. Saadati and N. Hussain: Common fixed points of almost generalized contractive mappings in ordered metric spaces. Appl. Math. Comput. 217 (2011), 5784–5789.

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

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

M. S. El Naschie: Elementary number theory in superstrings, loop quantum mechanics, twistors and E-infinity high energy physics. Chaos Solitons Fractals 27 (2006), 297–330.

J. Harjani and K. Sadarangni: Fixed point theorems for weakly contraction mappings in partially ordered sets. Nonlinear Anal. 71 (2009), 3403–3410.

J. Harjani and K. Sadarangni: Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations. Nonlinear Anal. 72 (2010), 1188–1197.

N. Hussain, D. Dori´c, Z. Kadelburg and S. Radenovi´c: Suzuki-type fixed point results in metric type spaces. Fixed Point Theory Appl. 2012:126 (2012), 1–12.

N. Hussain, V. Parvaneh, J. R. Roshan and Z. Kadelburg. Fixed points of cyclic weakly ( , ',L,A,B)-contractive mappings in ordered b-metric spaces with applications. Fixed Point Theory Appl. 2013:256 (2013), 1–18.

N. Hussain and M. H. Shah: KKM mappings in cone b-metric spaces. Comput. Math. Appl. 62 (2011), 1677–1684.

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

M. A. Khamsi: Remarks on cone metric spaces and fixed point theorems of contractive mappings. Fixed Point Theory Appl. 2010 (2010), Article ID 315398, 1–7.

M. A. Khamsi and N. Hussain: KKM mappings in metric type spaces. Nonlinear Anal. 73 (2010), no. 9, 3123–3129.

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

M. Jovanovi´c, Z. Kadelburg and S. Radenovi´c: Common fixed point results in metric-type spaces. Fixed Point Theory Appl. 2010 (2010), Article ID 978121, 1–15.

H. K. Nashine and B. Samet: Fixed point results for mappings satisfying ( ,')- weakly contractive condition in partially ordered metric spaces. Nonlinear Anal. 74 (2011), 2201–2209.

J. J. Nieto and R. Rod´riguez-L´opez: Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations. Order 22 (2005), 223–239.

J. J. Nieto and R. Rod´riguez-L´opez: Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations. Acta Math. Sin. (Engl. Ser.) 23 (2007), 2205–2212.

M. Pacurar. Sequences of almost contractions and fixed points in b-metric spaces. An. Univ. Vest. Timi¸s. Ser. Mat.-Inform. 3 (2010), 125–137.

S. Radenovic´c and Z. Kadelburg: Generalized weak contractions in partially ordered metric spaces. Comput. Math. Appl. 60 (2010), 1776–1783.

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

B. E. Rhoades: Some theorems on weakly contractive maps. Nonlinear Anal. 47 (2001), 2683–2693.

J. R. Roshan, V. Parvaneh, S. Sedghi, N. Shobkolaei and W. Shatanawi: Common fixed points of almost generalized ( , ')s-contractive mappings in ordered b-metric spaces. Fixed Point Theory Appl. 2013:159 (2013), 1–23.

W. Shatanawi and A. Al-Rawashdeh: Common fixed points of almost generalized ( , ')-contractive mappings in ordered metric spaces. Fixed Point Theory Appl. 2012:80 (2012), 1–14.

S. L. Singh and B. Prasad: Some coincidence theorems and stability of iterative procedures. Comput. Math. Appl. 55 (2008), 2512–2520.

F. Yan, Y. Su and Q. Feng: A new contraction mapping principle in partially ordered metric spaces and applications to ordinary differential equations. Fixed Point Theory Appl. 2012:152 (2012), 1–13.

E. Zeidler: Nonlinear Functional Analysis and Its Applications. Springer, New

York, 1989.

### Refbacks

- There are currently no refbacks.

ISSN 0352-9665 (Print)