A new type of α − F − contraction on common fixed point theorems in metric spaces and its application ∗

Garima Gadkari; M S Rathore; Naval Singh

doi:10.48165/

Authors

Garima Gadkari Department of Mathematics, Mahakal Institute of Technology, Ujjain-456010, Madhya Pradesh, India.
M S Rathore Department of Mathematics, C.S.A. Govt. P.G. College, Sehore, Madhya Pradesh, India.
Naval Singh Govt. Science and Commerce P.G. College, Benazeer, Bhopal, Madhya Pradesh, Indi

DOI:

https://doi.org/10.48165/

Keywords:

Common fixed poin, Metric space, α− admissible mappings, F− con traction

Abstract

In this paper we introduce the notion of F− contraction via α− admissible pair of mappings. We also provide many common fixed point results regarding rational expressions in the setting of metric spaces. Moreover, we also present some illustrated examples as an application of this concept and we also establish an existence theorem for integral equations.

References

Banach, B. (1922). Sur les operations dans les ensembles abstraits et leur application aux equations integrales, Fundam. Math., 3, 133–181. Section 1

Wardowski, D. (2012). Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl., 94 (2012) doi:10.1186/1687-1812-2012-94. Section 1, Definition 1.1, Section 1, Section 1, Remark 1.3, Corollary 2.10.

Secelean, N.A. (2013). Iterated function systems consisting of F− contractions, Fixed Point Theory Appl., 277 (2013) doi:10.1186/1687-1812-2013-277. Section 1

Sgroi, M. and Vetro, C. (2013). Multi-valued F− contractions and the solution of ceratin functional and integral equations, Filomat, 27(7), 1259–1268. doi:10.2298/FIL1307259S. Section 1 [5] Piri, H. and Kumam, P. (2014). Some fixed point theorems concerning F− contraction in complete metric spaces, Fixed Point Theory Appl., 210 (2014) doi:10.1186/1687-1812-2014-210. Section 1 [6] Cosention, M. and Vetro, P. (2014). Fixed point results for F−contractive mappings of Hardy Rogers- type, Filomat, 28(4), 715–722. Section 1

Minak, G., Helvaci, A. and Altun, I. (2014). Ciri´c type generalized ´ F− contractions on complete metric spaces and fixed point results, Filomat, 28(6), 1143–1151. Section 1

Ahmad, J., Al-Rawashdeh, A. and Azam, A. (2015). New fixed point theorems for generalized F− contractions in complete metric spaces, Fixed Point Theory Appl., 80 (2015) doi:10.1186/s13663- 015-0333-2. Section 1

Klim, D. and Wardowski, D. (2015). Fixed points of dynamic processes of set-valued F−contractions and application to functional equations, Fixed Point Theory Appl., 22 (2015) doi:10.1186/s13663-015-0272-y. Section 1

Khan, S.U., Arshad, M., Hussain, A. and Nazam, M. (2016). Two new type of fixed point for F− contraction , J. Adv. Studies in Topology, 251–260. Section 1

Paesano, D., and Vetro, C. (2014). Multi-valued F−contractions in 0− complete partial metric spaces with application to Volterra type integral equation, Rev. R. Acad. Cienc. Exactas Fs. Nat. Ser. A Math., 108, 1005–1020. Section 1

Garima Gadkari, M.S. Rathore and Naval Singh

Arshad, M., Khan, S.U. and Ahmad, J. (2016). Fixed point results for F− contractions involving some new rational expressions, J. Fixed Point Theory Appl., 11, 79–97. Section 1 [13] Ali, M.U. and Kamran, T. (2016). Multivalued F− contractions and related fixed point theorems with an application, Filomat, 30(14), 3779–3793. Section 1

Budhia, L.B., Kumam, P., Martinez-Moreno, J. and Gopal, D. (2016). Extensions of almost −F and F−Suzuki contractions with graph and some applications to fractional calculus, Fixed Point Theory Appl., 2 (2016) doi:10.1186/s13663-015-0480-5. Section 1

Tomar, A. and Sharma, R. (2018). Some coincidence and common fixed point theorems concerning F−contraction and applications, J. Inter. Math. Virt. Institute, 8, 181–198. Section 1 [16] Samet, B., Vetro, C. and Vetro, P. (2012). Fixed point theorems for α − ψ− contractive type mappings, Nonlinear Anal., 75, 2154–2165. Section 1

Ali, M.U., Kamran, T. and Karapinar, E. (2014). A new approach to (α, ψ) − contractive nonself multivalued mappings, J. Inequal. Appl., 71 (2014) doi:10.1186/1029-242X-2014-71. Section 1 [18] Asl, J.H., Rezapour, S. and Shahzad, N. (2012). On fixed points of α − ψ− contractive multifunc tions, Fixed Point Theory Appl., 212 (2012) doi:10.1186/1687-1812-2012-212. Section 1 [19] Aydi, H. and Karapinar, E. (2015). Fixed point results for generalized α − ψ− contractions in metric-like spaces and applications, Electron J. Differential Equations, Vol. 2015(2015), No. 133, 1–15. Section 1

Aydi, H. (2016). α− implicit contractive pair of mappings on quasi b− metric spaces and ap plication to integral equations, J. Nonlinear Convex Anal., 17, 2417–2433. Section 1, Definition 1.5

Aydi, H., Jleli, M. and Karapinar, E. (2016). On fixed point results for α− implicit contractions in quasi-metric spaces and consequences, Nonlinear Anal. Model. Control, 21, 40–56. Section 1 [22] Cho, S.H. (2013). Fixed point theorems for α − ψ−contractive type mappings in metric spaces, Appl. Math. Sci., 7, 6765–6778. Section 1

Jleli, M., Karapinar, E. and Samet, B. (2013). Best proximity points for generalized α − ψ− proximal contractive type mappings, J. Appl. Math., Volume 2013, Article ID 534127, 10 pages http://dx.doi.org/10.1155/2013/534127. Section 1

Jleli, M., Karapinar, E. and Samet, B. (2013). Fixed point results for α − ψλ− contractions on gauge spaces and applications, Abstr. Appl. Anal., 7 pages. Section 1

Jleli, M., Samet, B., Vetro, C. and Vetro, F. (2015). Fixed points for multivalued mappings in b− metric spaces, Abstr. Appl. Anal., 7 pages. Section 1

Karapinar, E. and Samet, B. (2012). Generalized α − ψ− contractive type mappings and related fixed point theorems with applications, Abstr. Appl. Anal., 17 pages. Section 1 [27] Karapinar, E. and Agarwal, R.P. (2013). A note on coupled fixed point theorems for α − ψ−contractive type mappings in a partially ordered metric spaces, Fixed Point Theory Appl., 216 (2013) doi:10.1186/1687-1812-2013-216. Section 1

Karapinar, E. (2014). Discussion onα−ψ− contractions on generalized metric spaces, Abstr. Appl. Anal., Article ID 962784. Section 1

Mohammadi, B., Rezapour, S. and Shahzad, N. (2013). Some results on fixed points of α−ψ− Ciri´c ´ generalized multifunctions, Fixed Point Theory Appl., 24 (2013) doi:10.1186/1687-1812-2013-24. Section 1

Salimi, P., Latif, A. and Hussain, N. (2013). Modified α − ψ− contractive mappings with applica tions, Fixed Point Theory Appl., 151 (2013) doi:10.1186/1687-1812-2013-151. Section 1 [31] Shatanawi, W. and Al-Rawashdeh, A. (2012). Common fixed points of almost generalized (ψ, φ) − contractive mappings in ordered metric spaces, Fixed Point Theory Appl., 80 (2012) doi:10.1186/1687-1812-2012-80. Section 1

Sistani, T. and Kazemipour, M. (2014). Fixed point theorems for α − ψ−contractions on metric spaces with a graph, J. Adv. Math. Stud., 7, 65–79. Section 1

Al-Rawashdeh, A., Aydi, H., Felhi, A., Sahmim, S. and Shatanawi, W. (2016). On common fixed points for α − F− contractions and applications, J. Nonlinear Sci. & Appl., 9, 3445–3458. Section 1