Share:


Some generalizations of Kannan's theorems via σc-function and its application

    Suprokash Hazra Affiliation
    ; Satish Shukla Affiliation
DOI: https://doi.org/10.3846/mma.2019.032

Abstract

In this article, we go on to discuss various proper extensions of Kannan’s two different fixed point theorems, and introduce the new concept of , which is independent of the three notions of simulation function, manageable functions, and R-functions. These results are analogous to some well-known theorems, and extend several known results in this literature. An application of the new results to the integral equation is also provided.

Keyword : fixed point, coincidence point, Kannan’s mapping, simulation function, R-function, manageable function, σc-function

How to Cite
Hazra, S., & Shukla, S. (2019). Some generalizations of Kannan’s theorems via σc-function and its application. Mathematical Modelling and Analysis, 24(4), 530-549. https://doi.org/10.3846/mma.2019.032
Published in Issue
Oct 25, 2019
Abstract Views
1197
PDF Downloads
568
Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

References

S. Banach. Sur les opérations dans les ensembles abstraits et leur, application aux équations intégrales. Fundam. Math., 3:133–181, 1922.

A.F.R. López de Hierro and N. Shahzad. New fixed point theorem under r-contractions. Fixed Point Theory and Applications, 2015(98), 2015. https://doi.org/10.1186/s13663-015-0345-y

W.-S. Du and F. Khojasteh. New results and generalizations for approximate fixed point property and their applications. Abstr. Appl. Anal., 2014, 2014. https://doi.org/10.1155/2014/581267

B. Fisher. A fixed point theorem. Mathematics Magazine, 48(4):223–225, 1975. https://doi.org/10.1080/0025570X.1975.11976494

M. Geraghty. On contractive mappings. Proc. Am. Math. Soc., 40:604–608, 1973. https://doi.org/10.2307/2039421

M. Javahernia, A. Razani and F. Khojasteh. Common fixed point of the generalized Mizoguchi-Takahashi’s type contractions. Fixed Point Theory and Applications, 2014(195), 2014. https://doi.org/10.1186/1687-1812-2014-195

R. Kannan. Some results on fixed points. Bull. Calcutta Math. Soc., 60(4):71–76, 1968. https://doi.org/10.2307/2316437

R. Kannan. Some results on fixed points-II. Amer. Math. Monthly, 76(4):405– 408, 1969. https://doi.org/10.1080/00029890.1969.12000228

F. Khojasteh, S. Shukla and S. Radenovíc. A new approach to the study of fixed point theory for simulation functions. Filomat, 29(6):1189–1194, 2015.
https://doi.org/10.2298/FIL1506189K

P.V. Koparde and B.B. Waghmode. Kannan type mappings in Hilbert space. Scientist Phyl. Sciences, 3(1):45–50, 1991. https://doi.org/10.1016/S0362546X(99)00448-4

T-C. Lim. On characterizations of Meir-Keeler contractive maps. Nonlinear Anal., 46:113–120, 2001.

A. Malčeski, S. Malčeski, K. Nevska and R. Malčeski. New extension of Kannan and Chatterjea fixed point theorems on complete metric spaces. British Journal of Mathematics & Computer Science, 17(1):1–10, 2016. https://doi.org/10.9734/BJMCS/2016/25864

K. Patel and G.M. Deheri. Kannan type mappings in Hilbert space. Turkish Journal of Analysis and Number Theory, 3(2):70–74, 2015. https://doi.org/10.12691/tjant-3-2-7