On common fixed point theorems in partial metric spaces using $C$-class function

Gurucharan Singh Saluja

Abstract


The purpose of this paper is to prove some common fixed point theorems in the set up of partial metric spaces with the help of $C$-class function and auxiliary functions and give some consequences of the established results. Also we give some examples in support of the result. Our results extend and generalize several results in the existing literature regarding rational type contraction mappings and partial metric spaces.

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bibitem{ANR12} M. Abbas, T. Nazir and S. Ramaguera, Fixed point results for generalized cyclic contraction mappings in partial metric spaces, Rev. R. Acad. Cienc. Exactas. Fis. Nat. Ser. A Mat., RACSAM, {bf 106(1)} (2012), 287-297.

bibitem{AKT11} T. Abdeljawad, E. Karapinar and K. Tas, Existence and uniqueness of a common fixed point on partial metric spaces, Appl. Math. Lett. {bf 24} (2011), 1900-1904.

bibitem{ABA12} O. Acar, V. Berinde and I. Altun, Fixed point theorems for Ciric-type strong almost contractions on partial metric spaces, Fixed Point Theory Appl. {bf 12} (2012), 247-259.

bibitem{A14} A. H. Ansari, Note on $varphi-psi$-contractive type mappings and related fixed points, The 2nd Regional Conference on Math. and Appl. Payame Noor University, {bf (2014)}, 377-380.

bibitem{ACI14} A. H. Ansari, S. Chandok and C. Ionescu, Fixed point theorems on $b$-metric spaces for weak contractions with auxiliary functions, J. Inequl. Appl. {bf 2014}, 2014:429, 17 pages.

bibitem{AAV12} H. Aydi, M. Abbas and C. Vetro, Partial Hausdorff metric and Nadler's fixed point theorem on partial metric spaces, Topology and Its Appl. {bf 159} (2012), No. 14, 3234-3242.

bibitem{B22} S. Banach, Surles operation dans les ensembles

abstraits et leur application aux equation integrals, Fund. Math.

{bf 3}(1922), 133-181.

bibitem{CK12} S. Chandok and J. K. Kim, Fixed point theorem in ordered metric spaces for generalized contractions mappings satisfying rational type expressions, J. Nonlinear Funct. Anal. Appl. {bf 17} (2012), 301-306.

bibitem{C13} S. Chandok, Some common fixed point results for rational type contraction mappings in partially ordered metric spaces, Math. Bohem. {bf 138} (2013), 403-413.

bibitem{CK13} S. Chandok and D. Kumar, Some common fixed point results for rational type contraction mappings in complex valued metric spaces, J. Operator {bf 2013} (2013), 813707.

bibitem{CNT13} S. Chandok, T. D. Narang and M. A. Taoudi, Some common fixed point results in partially ordered metric spaces for generalized rational type contraction mappings, Vietnam J. Math. {bf 41} (2013), 323-331.

bibitem{CZ13} C. Chen and C. Zhu, Fixed point theorems for weakly $C$-contractive mappings in partial metric spaces, Fixed Point Theory Appl. {bf 2013}, 2013, 107.

bibitem{DG75} B. K. Dass and S. Gupta, An extension of Banach contraction principle through rational expressions, Indian J. Pure Appl. Math. {bf 6} (1975), 1455-1458.

bibitem{HAZ14} E. Hoxha, A. H. Ansari and K. Zoto, Some common fixed point results through generalized altering distances on dislocated metric spaces, Proceedings of EIIC, September 1-5, 2014, pages 403-409.

bibitem{K11} E. Karapinar, Generalization of Caristi-Kirk's theorem on partial metric spaces, Fixed Point Theorem Appl. {bf 2011(4)} (2011).

bibitem{KY11} E. Karapinar and U. Y$ddot{u}$ksel, Some common fixed point theorems in partial metric space, J. Appl. Math. {bf 2011}, Article ID: 263621, 2011.

bibitem{KEU12} E. Karapinar, I. M. Erhan and A. Y. Ulus, Fixed point theorem for cyclic maps on partial metric spaces, Appl. Math. Inf. Sci. {bf 6} (2012), 239-244.

bibitem{KST13} E. Karapinar, W. Shatanawi and K. Tas, Fixed point theorems on partial metric spaces involving rational expressions, Miskolc Math. Notes {bf 14} (2013), 135-142.

bibitem{KSLP21} D. Kumar, S. Sadat, J. R. Lee and C. Park, Some theorems in partial metric space using auxiliary functions, AIMS Math. {bf 6(7)} (2021), 6734-6748.

bibitem{K01} H. P. A. K$ddot{u}$nzi, Nonsymmetric distances and their associated topologies about the origins of basic ideas in the area of asymptotic topology, Handbook of the History Gen. Topology (eds. C.E. Aull and R. Lowen), Kluwer Acad. Publ., {bf 3} (2001), 853-868.

bibitem{M92} S. G. Matthews, Partial metric topology, Research report 2012, Dept. Computer Science, University of Warwick, 1992.

bibitem{M94} S. G. Matthews, Partial metric topology, Proceedings of the 8th summer conference on topology and its applications, Annals of the New York Academy of Sciences, {bf 728} (1994), 183-197.

bibitem{NKRK12} H. K. Nashine, Z. Kadelburg, S. Radenovic and J. K. Kim, Fixed point theorems under Hardy-Rogers contractive conditions on $0$-complete ordered partial metric spaces, Fixed Point Theory Appl. {bf 2012} (2012), 1-15.

bibitem{OO04} S. Oltra and O. Oltra, Banach's fixed point theorem for partial metric spaces, Rend. Ist. Mat. Univ. Trieste {bf 36(1-2)} (2004), 17-26.

bibitem{R79} I. A. Rus, Principles and applications of the fixed point theory, (in Romanian), Editura Dacia, Ciuj-Napoca, 1979.

bibitem{R96} I. A. Rus, Picard operator and applications, Babes-Bolyal Univ., 1996.

bibitem{S16a} G. S. Saluja, Some fixed point theorems for generalized contractions involving rational expressions in b-metric spaces, Commun. Optim. Theory {bf 2016} (2016), Article ID 17.

bibitem{S16b} G. S. Saluja, Some common fixed point theorems for generalized contraction involving rational expressions in b-metric spaces, J. Contemp. Appl. Math. {bf 6(2)} (2016), 67-78.

bibitem{S17} G. S. Saluja, Fixed point results under generalized contraction involving rational expression in complex valued metric spaces, International J. Math. Combin. {bf 1} (2017), 55-62.

bibitem{S17a} G. S. Saluja, Fixed point theorems under rational contraction in complex valued metric spaces, Nonlinear Functional Analysis and Applications {bf 22(1)} (2017), 209-216.

bibitem{S18a} G. S. Saluja, On common fixed point theorems for rational contractions in $b$-metric spaces, The Aligarh Bull. Math. {bf 37(1-2)} (2018), 1-12.

bibitem{S18b} G. S. Saluja, Some common fixed point theorems using rational contraction in complex valued metric spaces, Palestine J. Math. {bf 7(1)} (2018), 92-99.

bibitem{S120} G. S. Saluja, Some fixed point results in partial metric spaces under contractive type mappings, J. Indian Math. Soc. {bf 87 (3-4)} (2020), 219-230.

bibitem{S220} G. S. Saluja, Some fixed point theorems in partial cone metric spaces under contractive type conditions, Annals Univ. Oradea Fasc. Matematica Tom {bf 27(2)} (2020), 17-29.

bibitem{S320} G. S. Saluja, Fixed point theorems using implicit relation in partial metric spaces, Facta Univ. (NIS), Ser. Math. Infor. {bf 35(3)} (2020), 857-872.

bibitem{S420} G. S. Saluja, Some fixed point theorems for $(psi-phi)$-weak contraction mappings in partial metric spaces, Math. Moravica {bf 24(2)} (2020), 99-115.

bibitem{S520} G. S. Saluja, Fixed point theorems on cone S-metric spaces using implicit relation, Cubo, A Math. Journal, {bf 22(2)} (2020), 273-288.

bibitem{V05} U. Valero, On Banach fixed point theorems for partial metric spaces, Appl. Gen. Topl. {bf 6(2)} (2005), 229-240.


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