FIXED POINT RESULTS IN PARTIAL METRIC SPACES VIA INTEGRAL TYPE CONTRACTION WITH APPLICATION

Gurucharan Singh Saluja

DOI Number
https://doi.org/10.22190/FUMI240818048S
First page
697
Last page
715

Abstract


In this paper, we derive some fixed point results via integral type contractive condition having rational terms in the setting of complete partial metric spaces and provide some consequences of the established results. Also, we give some examples in support of the established results. An application to the Fredholm integral equation is also given. Our results generalize, extend and enrich several previously published well-known fixed point results from the existing literature (see, e.g. [10], [11], [26] and many others).


Keywords

fixed point, partial metric space, Fredholm integral equation

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References


M. Abbas, H. Aydi and S. Radenovi´c: Fixed point of T-Hardy-Rogers contractive mappings in ordered partial metric spaces. Int. J. Math. Math. Sci. 2012, Article ID 313675 (2012).

M. Abbas, T. Nazir and S. Romaguera: Fixed point results for generalized cyclic contraction mappings in partial metric spaces. Rev. R. Acad. Cienc. Exactas Fis. Nat., Ser. A Mat. RACSAM. 106(1) (2012), 287–297.

T. Abdeljawad, E. Karapınar and K. Tas: Existence and uniqueness of a common fixed point on partial metric spaces. Appl. Math. Lett. 24(11) (2011), 1894–1899.

I. Altun, D. Turkoglu and B. E. Rhoades: Fixed points of weakly compatible maps satisfying a general contractive condition of integral type. Fixed Point Theory Appl. (2007), Art. ID 17301, 1-–9.

I. Altun, F. Sola and H. Simsek: Generalized contractions on partial metric spaces. Topology and its Appl. 157 (2010), 2778–2785.

I. Altun and A. Erduran: Fixed point theorems for monotone mappings on partial metric spaces. Fixed Point Theory Appl. 2011, Article ID 508730 (2011). doi:10.1155/2011/508730

H. Aydi: Fixed point results for weakly contractive mappings in ordered partial metric spaces. J. Adv. Math. Stud. 4(2) (2011), 1–12.

H. Aydi, M. Abbas and C. Vetro: Partial Hausdorff metric and Nadler’s fixed point theorem on partial metric spaces. Topology and Its Appl. 159 (2012), No. 14, 3234–3242.

H. Aydi: A common fixed point result by altering distances involving a contractive condition of integral type in partial metric spaces. Demonstratio Math. 46(2) (2013), 383–394.

S. Banach: Sur les operation dans les ensembles abstraits et leur application aux equation integrals. Fund. Math. 3(1922), 133–181.

A. Branciari: A fixed point theorem for mappings satisfying a general contractive condition of integral type. Int. J. Math. Math. Sci. 29(9) (2002), 531–536.

S. Chandok, D. Kumar and M. S. Khan: Some results in partial metric space using auxiliary functions. Applied Math. E-Notes 15 (2015), 233–242.

C. -M. Chen, E. Karapinar and D. O’Regan: On (α−ϕ)-Meir-Keeler contractions on partial Hausdorff metric spaces. U.P.B. Sci. Bull., Series A, Vol. 80, No. 1, (2018), 101–110.

I. Erhan, E. Karapinar and D. Turkoglu: Different types Meir-Keeler contractions on partial metric spaces. J. Comput. Anal. Appl. 14(6) (2012), 1000–1005.

R. Heckmann: Approximation of metric spaces by partial metric spaces. Appl. Categ. Structures, 7, No. 1-2, (1999), 71–83.

E. Karapınar: A note on common fixed point theorems in partial metric spaces. Miskolc Math. Notes 12(2) (2011), 185–191.

E. Karapınar and I. M. Erhan: Fixed point theorems for operators on partial metric spaces. Appl. Math. Lett. 24(11) (2011), 1900–1904.

E. Karapınar and I. M. Erhan: Cyclic contractions and fixed point theorems. Filomat 26(4) (2012), 777–782.

E. Karapinar, W. Shatanawi and K. Tas: Fixed point theorems on partial metric spaces involving rational expressions. Miskolc Math. Notes 14 (2013), 135–142.

E. Karapınar and S. Romaguera: Nonunique fixed point theorems in partial metric spaces: Filomat 27(7) (2013), 1305–1314.

E. Karapınar: Rational forms that imply the uniqueness of fixed points in partial metric spaces. J. Nonlinear Convex Anal. 20(10) (2019), 2171–2186.

E. Karapınar, R. P. Agarwal, S. S. Yesilkaya and C. Wang: Fixed-point results for Meir-Keeler type contractions in partial metric spaces: A Survey. Mathematics 2022; 10(17), 3109. https://doi.org/10.3390/math10173109

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

H. P. A. K¨unzi, H. Pajoohesh and M. P. Schellekens: Partial quasi-metrics. Theoritical Comput. Sci. 365(3) (2006), 237–246.

Z. Liu, J. Li and S. M. Kang: Fixed point theorems of contractive mappings of integral type. Fixed Point Theory Appl. 2013, 2013:300, 17 pp.

S. G. Matthews: Partial metric topology. Research report 2012, Dept. Computer Science, University of Warwick, 1992.

S. G. Matthews: Partial metric topology. In: Proceedings of the 8th summer conference on topology and its applications, Annals of the New York Academy of Sciences, 728 (1994), 183–197.

S. Oltra and O. Valero: Banach’s fixed point theorem for partial metric spaces. Rend. Ist. Mat. Univ. Trieste 36(1-2) (2004), 17–26.

M. U. Rahman, M. Sarwar and M. U. Rahman: Fixed point results of Altman integral type mappings in S-metric spaces. Int. J. Anal. Appl. 10(1) (2016), 58–63.

R. A. Rashwan and H. A. Hammad: Common fixed point theorems for weakly compatible mappings satisfying a general contractive condition of integral type. Palestine J. Math. 8(2) (2019), 114–126.

B. E. Rhoades: Two fixed point theorems for mappings satisfying a general contractive condition of integral type. Int. J. Math. Sci. 3 (2003), 4007–4013.

S. Romaguera and M. P. Schellekens: Duality and quasi-normability for complexity spaces. Appl. General Topology 3 (2002), 91–112.

M. P. Schellekens: Characterization of partial metrizability: domains are quantifiable. Theoritical Comput. Sci. 305(1-3) (2003), 409–432.

M. P. Schellekens: The correspondence between partial metrics and semivaluations. Theoritical Comput. Sci. 315(1) (2004), 135–149.

O. Valero: On Banach fixed point theorems for partial metric spaces. Appl. Gen. Topl. 6(2) (2005), 229–240.




DOI: https://doi.org/10.22190/FUMI240818048S

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