# Fixed points of generalized $F-H-\phi-\psi-\varphi-$ weakly contractive mappings

Volume 7, Issue 1, pp 1--15
Publication Date: June 27, 2021 Submission Date: May 14, 2020 Revision Date: September 11, 2020 Accteptance Date: December 25, 2020
• 549 Views

### Authors

G. V. Ravindranadh Babu - Department of Mathematics, Andhra University, Visakhapatnam - 530 003, India. M. Vinod Kumar - Department of Mathematics, Anil Neerukonda Institute of Technology and Sciences, Sangivalasa, Visakhapatnam - 531 162, India.

### Abstract

We introduce the notion of generalized $F-H-\phi-\psi-\varphi-$ weakly contractive mappings and prove the existence of fixed points of such mappings in complete metric spaces. We draw some corollaries and provide examples in support of our main results. Our results extend the results of Cho [S. Cho, Fixed Point Theory Appl., ${\bf 2018} (2018)$, 18 pages] and Choudhury, Konar, Rhoades and Metiya [B. S. Choudhury, P. Konar, B. E. Rhoades, N. Metiya, Nonlinear Anal., ${\bf 74} (2011)$, 2116--2126] in the sense that the control function that we used in our results need not have monotonicity property.

### Share and Cite

##### ISRP Style

G. V. Ravindranadh Babu, M. Vinod Kumar, Fixed points of generalized $F-H-\phi-\psi-\varphi-$ weakly contractive mappings, Mathematics in Natural Science, 7 (2021), no. 1, 1--15

##### AMA Style

Ravindranadh Babu G. V., Vinod Kumar M., Fixed points of generalized $F-H-\phi-\psi-\varphi-$ weakly contractive mappings. Math. Nat. Sci. (2021); 7(1):1--15

##### Chicago/Turabian Style

Ravindranadh Babu, G. V., Vinod Kumar, M.. "Fixed points of generalized $F-H-\phi-\psi-\varphi-$ weakly contractive mappings." Mathematics in Natural Science, 7, no. 1 (2021): 1--15

### Keywords

• $\alpha-$admissible
• $\mu-$subadmissible
• $C-$class function, the pair $(F,H)$ is upclass of type I
• the pair $(F,H)$ is special upclass of type I

•  47H10
•  54H25

### References

• [1] Ya. I. Alber, S. Guerre-Delabriere, Principles of weakly contractive maps in Hilbert spaces New results in Operator theory, Adv. Appl., 98 (1997), 7--22

• [2] A. H. Ansari, Note on φ-ψ-contractive type mappings and related fixed point, The 2nd Regional Conference on Mathematics and Applications, Payame Noor University Tehran, 2014 (2014), 377--380

• [3] A. H. Ansari, D. Dolicanin-Djekic, T. Dosenovic, S. Radenovic, Coupled coincidence point theorems for (α − µ − ψ − H − F)−two sided contractive type mappings in partially ordered metric spaces using compatible mappings, Filomat, 31 (2017), 2657--2673

• [4] A. H. Ansari, H. Isik, S. Radenovic, Coupled fixed point theorems for contractive mappings involving new function classes and applications, Filomat, 31 (2017), 1893--1907

• [5] A. H. Ansari, J. Kaewcharoen, C−class functions and fixed point theorems for generalized α − η − ψ − φ − F−contraction type mappings in α − η complete metric spaces, J. Nonlinear Sci. Appl., 9 (2016), 4177--4190

• [6] G. V. R. Babu, P. D. Sailaja, A fixed point theorem of generalized weakly contractive maps in orbitally complete metric space, Thai J. Math., 9 (2011), 1--10

• [7] S. Cho, Fixed point theorems for generalized weakly contractive mappings in metric spaces with application, Fixed Point Theory Appl., 2018 (2018), 18 pages

• [8] B. S. Choudhury, Unique fixed point theorems for weakly C−Contractive mappings, Khatmandu University J. Sci. Tech., 5 (2009), 6--13

• [9] B. S. Choudhury, P. Konar, B. E. Rhoades , N. Metiya, Fixed point theorems for generalized weakly contractive mappings, Nonlinear Anal., 74 (2011), 2116--2126

• [10] D. Doric, Common fixed point for generalized (ψ, φ)− weak contractions, Appl. Math. Lett., 22 (2009), 1896--1900

• [11] P. N. Dutta, B. S. Choudhury, A generalization of contraction principle in metric spaces, Fixed Point Theory Appl., 2008 (2008), 8 pages

• [12] J. Hasanzade Asl, S. Rezapour, N. Shahzad, On fixed points of α − ψ−contractive multifunctions, Fixed Point Theory Appl., 2012 (2012), 6 pages

• [13] N. Hussain, M. A. Kutbi, P. Salimi, Fixed point theory in α−complete metric spaces with applications, Abstr. Appl. Anal., 2014 (2014), 11 pages

• [14] R. Kannan, Some results on fixed points, Bull. Calcutta Math. Soc., 10 (1968), 71--76

• [15] E. Karapinar, P. Kumam, P. Salimi, On α − ψ− Meir-Keeler contractive mappings, Fixed Point Theory Appl., 2013 (2013), 12 pages

• [16] H. Qawagneh, M. S. M. Noorani, W. Shatanawt, H. Alsamir, Common fixed points for pairs of triangular α−admissible mappings, J. Nonlinear Sci. Appl., 10 (2017), 6192--6204

• [17] B. E. Rhoades, A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc., 226 (1977), 257--290

• [18] B. E. Rhoades, Some theorems on weakly contractive mappings, Nonlinear Anal., 47 (2001), 2683--2693

• [19] P. Salimi, A. Latif, N. Hussain, Modified α − ψ− contractive mappings with applications, Fixed Point Theory Appl., 2013 (2013), 19 pages

• [20] B. Samet, C. Vetro, P. Vetro, Fixed point theorems for α − ψ−contractive type mappings, Nonlinear Anal., 75 (2012), 2154--2165

• [21] Q. Zhang,Y. Song, Fixed point theory for generalized ϕ−weak contractions, App. Math. Letters, 22 (2009), 75--78